Mock Version: 2.9
ENTER ['do_with_status'](['bash', '--login', '-c', '/usr/bin/rpmbuild -bs --target x86_64 --nodeps /builddir/build/SPECS/gap-pkg-digraphs.spec'], chrootPath='/var/lib/mock/fedora-rawhide-x86_64-1611958039.900791/root'env={'TERM': 'vt100', 'SHELL': '/bin/bash', 'HOME': '/builddir', 'HOSTNAME': 'mock', 'PATH': '/usr/bin:/bin:/usr/sbin:/sbin', 'PROMPT_COMMAND': 'printf "\\033]0;<mock-chroot>\\007"', 'PS1': '<mock-chroot> \\s-\\v\\$ ', 'LANG': 'C.UTF-8'}shell=Falselogger=<mockbuild.trace_decorator.getLog object at 0x7f187b6b7070>timeout=0uid=1001gid=135user='mockbuild'nspawn_args=['--capability=cap_ipc_lock', '--rlimit=RLIMIT_NOFILE=10240', '--capability=cap_ipc_lock', '--bind=/tmp/mock-resolv.joqr9ujs:/etc/resolv.conf', '--bind=/dev/btrfs-control', '--bind=/dev/loop-control', '--bind=/dev/loop0', '--bind=/dev/loop1', '--bind=/dev/loop2', '--bind=/dev/loop3', '--bind=/dev/loop4', '--bind=/dev/loop5', '--bind=/dev/loop6', '--bind=/dev/loop7', '--bind=/dev/loop8', '--bind=/dev/loop9', '--bind=/dev/loop10', '--bind=/dev/loop11']unshare_net=TrueprintOutput=True)
Using nspawn with args ['--capability=cap_ipc_lock', '--rlimit=RLIMIT_NOFILE=10240', '--capability=cap_ipc_lock', '--bind=/tmp/mock-resolv.joqr9ujs:/etc/resolv.conf', '--bind=/dev/btrfs-control', '--bind=/dev/loop-control', '--bind=/dev/loop0', '--bind=/dev/loop1', '--bind=/dev/loop2', '--bind=/dev/loop3', '--bind=/dev/loop4', '--bind=/dev/loop5', '--bind=/dev/loop6', '--bind=/dev/loop7', '--bind=/dev/loop8', '--bind=/dev/loop9', '--bind=/dev/loop10', '--bind=/dev/loop11']
Executing command: ['/usr/bin/systemd-nspawn', '-q', '-M', '2e13deeb77d84d3ebea672b4457534bf', '-D', '/var/lib/mock/fedora-rawhide-x86_64-1611958039.900791/root', '-a', '-u', 'mockbuild', '--capability=cap_ipc_lock', '--rlimit=RLIMIT_NOFILE=10240', '--capability=cap_ipc_lock', '--bind=/tmp/mock-resolv.joqr9ujs:/etc/resolv.conf', '--bind=/dev/btrfs-control', '--bind=/dev/loop-control', '--bind=/dev/loop0', '--bind=/dev/loop1', '--bind=/dev/loop2', '--bind=/dev/loop3', '--bind=/dev/loop4', '--bind=/dev/loop5', '--bind=/dev/loop6', '--bind=/dev/loop7', '--bind=/dev/loop8', '--bind=/dev/loop9', '--bind=/dev/loop10', '--bind=/dev/loop11', '--console=pipe', '--setenv=TERM=vt100', '--setenv=SHELL=/bin/bash', '--setenv=HOME=/builddir', '--setenv=HOSTNAME=mock', '--setenv=PATH=/usr/bin:/bin:/usr/sbin:/sbin', '--setenv=PROMPT_COMMAND=printf "\\033]0;<mock-chroot>\\007"', '--setenv=PS1=<mock-chroot> \\s-\\v\\$ ', '--setenv=LANG=C.UTF-8', '--resolv-conf=off', 'bash', '--login', '-c', '/usr/bin/rpmbuild -bs --target x86_64 --nodeps /builddir/build/SPECS/gap-pkg-digraphs.spec'] with env {'TERM': 'vt100', 'SHELL': '/bin/bash', 'HOME': '/builddir', 'HOSTNAME': 'mock', 'PATH': '/usr/bin:/bin:/usr/sbin:/sbin', 'PROMPT_COMMAND': 'printf "\\033]0;<mock-chroot>\\007"', 'PS1': '<mock-chroot> \\s-\\v\\$ ', 'LANG': 'C.UTF-8', 'SYSTEMD_NSPAWN_TMPFS_TMP': '0'} and shell False
Building target platforms: x86_64
Building for target x86_64
setting SOURCE_DATE_EPOCH=1611792000
Wrote: /builddir/build/SRPMS/gap-pkg-digraphs-1.4.0-1.fc34.src.rpm
Child return code was: 0
ENTER ['do_with_status'](['bash', '--login', '-c', '/usr/bin/rpmbuild -bb --target x86_64 --nodeps /builddir/build/SPECS/gap-pkg-digraphs.spec'], chrootPath='/var/lib/mock/fedora-rawhide-x86_64-1611958039.900791/root'env={'TERM': 'vt100', 'SHELL': '/bin/bash', 'HOME': '/builddir', 'HOSTNAME': 'mock', 'PATH': '/usr/bin:/bin:/usr/sbin:/sbin', 'PROMPT_COMMAND': 'printf "\\033]0;<mock-chroot>\\007"', 'PS1': '<mock-chroot> \\s-\\v\\$ ', 'LANG': 'C.UTF-8'}shell=Falselogger=<mockbuild.trace_decorator.getLog object at 0x7f187b6b7070>timeout=0uid=1001gid=135user='mockbuild'nspawn_args=['--capability=cap_ipc_lock', '--rlimit=RLIMIT_NOFILE=10240', '--capability=cap_ipc_lock', '--bind=/tmp/mock-resolv.joqr9ujs:/etc/resolv.conf', '--bind=/dev/btrfs-control', '--bind=/dev/loop-control', '--bind=/dev/loop0', '--bind=/dev/loop1', '--bind=/dev/loop2', '--bind=/dev/loop3', '--bind=/dev/loop4', '--bind=/dev/loop5', '--bind=/dev/loop6', '--bind=/dev/loop7', '--bind=/dev/loop8', '--bind=/dev/loop9', '--bind=/dev/loop10', '--bind=/dev/loop11']unshare_net=TrueprintOutput=True)
Using nspawn with args ['--capability=cap_ipc_lock', '--rlimit=RLIMIT_NOFILE=10240', '--capability=cap_ipc_lock', '--bind=/tmp/mock-resolv.joqr9ujs:/etc/resolv.conf', '--bind=/dev/btrfs-control', '--bind=/dev/loop-control', '--bind=/dev/loop0', '--bind=/dev/loop1', '--bind=/dev/loop2', '--bind=/dev/loop3', '--bind=/dev/loop4', '--bind=/dev/loop5', '--bind=/dev/loop6', '--bind=/dev/loop7', '--bind=/dev/loop8', '--bind=/dev/loop9', '--bind=/dev/loop10', '--bind=/dev/loop11']
Executing command: ['/usr/bin/systemd-nspawn', '-q', '-M', 'c2bfa8b6a755417e8261566b3debd0f2', '-D', '/var/lib/mock/fedora-rawhide-x86_64-1611958039.900791/root', '-a', '-u', 'mockbuild', '--capability=cap_ipc_lock', '--rlimit=RLIMIT_NOFILE=10240', '--capability=cap_ipc_lock', '--bind=/tmp/mock-resolv.joqr9ujs:/etc/resolv.conf', '--bind=/dev/btrfs-control', '--bind=/dev/loop-control', '--bind=/dev/loop0', '--bind=/dev/loop1', '--bind=/dev/loop2', '--bind=/dev/loop3', '--bind=/dev/loop4', '--bind=/dev/loop5', '--bind=/dev/loop6', '--bind=/dev/loop7', '--bind=/dev/loop8', '--bind=/dev/loop9', '--bind=/dev/loop10', '--bind=/dev/loop11', '--console=pipe', '--setenv=TERM=vt100', '--setenv=SHELL=/bin/bash', '--setenv=HOME=/builddir', '--setenv=HOSTNAME=mock', '--setenv=PATH=/usr/bin:/bin:/usr/sbin:/sbin', '--setenv=PROMPT_COMMAND=printf "\\033]0;<mock-chroot>\\007"', '--setenv=PS1=<mock-chroot> \\s-\\v\\$ ', '--setenv=LANG=C.UTF-8', '--resolv-conf=off', 'bash', '--login', '-c', '/usr/bin/rpmbuild -bb --target x86_64 --nodeps /builddir/build/SPECS/gap-pkg-digraphs.spec'] with env {'TERM': 'vt100', 'SHELL': '/bin/bash', 'HOME': '/builddir', 'HOSTNAME': 'mock', 'PATH': '/usr/bin:/bin:/usr/sbin:/sbin', 'PROMPT_COMMAND': 'printf "\\033]0;<mock-chroot>\\007"', 'PS1': '<mock-chroot> \\s-\\v\\$ ', 'LANG': 'C.UTF-8', 'SYSTEMD_NSPAWN_TMPFS_TMP': '0'} and shell False
Building target platforms: x86_64
Building for target x86_64
setting SOURCE_DATE_EPOCH=1611792000
Executing(%prep): /bin/sh -e /var/tmp/rpm-tmp.eCircv
+ umask 022
+ cd /builddir/build/BUILD
+ cd /builddir/build/BUILD
+ rm -rf digraphs-1.4.0
+ /usr/bin/gzip -dc /builddir/build/SOURCES/digraphs-1.4.0.tar.gz
+ /usr/bin/tar -xof -
+ STATUS=0
+ '[' 0 -ne 0 ']'
+ cd digraphs-1.4.0
+ /usr/bin/chmod -Rf a+rX,u+w,g-w,o-w .
+ rm -fr extern/edge-addition-planarity-suite-Version_3.0.0.5
+ RPM_EC=0
++ jobs -p
+ exit 0
Executing(%build): /bin/sh -e /var/tmp/rpm-tmp.IKegcK
+ umask 022
+ cd /builddir/build/BUILD
+ cd digraphs-1.4.0
+ export LC_ALL=C.UTF-8
+ LC_ALL=C.UTF-8
+ CFLAGS='-O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection'
+ export CFLAGS
+ CXXFLAGS='-O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection'
+ export CXXFLAGS
+ FFLAGS='-O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I/usr/lib64/gfortran/modules'
+ export FFLAGS
+ FCFLAGS='-O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I/usr/lib64/gfortran/modules'
+ export FCFLAGS
+ LDFLAGS='-Wl,-z,relro -Wl,--as-needed  -Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld '
+ export LDFLAGS
+ LT_SYS_LIBRARY_PATH=/usr/lib64:
+ export LT_SYS_LIBRARY_PATH
+ CC=gcc
+ export CC
+ CXX=g++
+ export CXX
+ '[' '-flto=auto -ffat-lto-objectsx' '!=' x ']'
++ find . -type f -name configure -print
+ for file in $(find . -type f -name configure -print)
+ /usr/bin/sed -r --in-place=.backup 's/^char \(\*f\) \(\) = /__attribute__ ((used)) char (*f) () = /g' ./configure
+ diff -u ./configure.backup ./configure
+ mv ./configure.backup ./configure
+ /usr/bin/sed -r --in-place=.backup 's/^char \(\*f\) \(\);/__attribute__ ((used)) char (*f) ();/g' ./configure
+ diff -u ./configure.backup ./configure
+ mv ./configure.backup ./configure
+ /usr/bin/sed -r --in-place=.backup 's/^char \$2 \(\);/__attribute__ ((used)) char \$2 ();/g' ./configure
+ diff -u ./configure.backup ./configure
--- ./configure.backup	2021-01-27 21:28:39.000000000 +0000
+++ ./configure	2021-01-29 22:08:56.956227340 +0000
@@ -1842,7 +1842,7 @@
 #ifdef __cplusplus
 extern "C"
 #endif
-char $2 ();
+__attribute__ ((used)) char $2 ();
 /* The GNU C library defines this for functions which it implements
     to always fail with ENOSYS.  Some functions are actually named
     something starting with __ and the normal name is an alias.  */
+ /usr/bin/sed --in-place=.backup '1{$!N;$!N};$!N;s/int x = 1;\nint y = 0;\nint z;\nint nan;/volatile int x = 1; volatile int y = 0; volatile int z, nan;/;P;D' ./configure
+ diff -u ./configure.backup ./configure
+ mv ./configure.backup ./configure
+ /usr/bin/sed --in-place=.backup 's#^lt_cv_sys_global_symbol_to_cdecl=.*#lt_cv_sys_global_symbol_to_cdecl="sed -n -e '\''s/^T .* \\(.*\\)$/extern int \\1();/p'\'' -e '\''s/^$symcode* .* \\(.*\\)$/extern char \\1;/p'\''"#' ./configure
+ diff -u ./configure.backup ./configure
--- ./configure.backup	2021-01-29 22:08:56.956227340 +0000
+++ ./configure	2021-01-29 22:08:56.982226435 +0000
@@ -6914,7 +6914,7 @@
 # Transform an extracted symbol line into a proper C declaration.
 # Some systems (esp. on ia64) link data and code symbols differently,
 # so use this general approach.
-lt_cv_sys_global_symbol_to_cdecl="sed -n"\
+lt_cv_sys_global_symbol_to_cdecl="sed -n -e 's/^T .* \(.*\)$/extern int \1();/p' -e 's/^$symcode* .* \(.*\)$/extern char \1;/p'"
 $lt_cdecl_hook\
 " -e 's/^T .* \(.*\)$/extern int \1();/p'"\
 " -e 's/^$symcode$symcode* .* \(.*\)$/extern char \1;/p'"
@@ -19342,7 +19342,7 @@
 compiler='`$ECHO "$compiler" | $SED "$delay_single_quote_subst"`'
 GCC='`$ECHO "$GCC" | $SED "$delay_single_quote_subst"`'
 lt_cv_sys_global_symbol_pipe='`$ECHO "$lt_cv_sys_global_symbol_pipe" | $SED "$delay_single_quote_subst"`'
-lt_cv_sys_global_symbol_to_cdecl='`$ECHO "$lt_cv_sys_global_symbol_to_cdecl" | $SED "$delay_single_quote_subst"`'
+lt_cv_sys_global_symbol_to_cdecl="sed -n -e 's/^T .* \(.*\)$/extern int \1();/p' -e 's/^$symcode* .* \(.*\)$/extern char \1;/p'"
 lt_cv_sys_global_symbol_to_import='`$ECHO "$lt_cv_sys_global_symbol_to_import" | $SED "$delay_single_quote_subst"`'
 lt_cv_sys_global_symbol_to_c_name_address='`$ECHO "$lt_cv_sys_global_symbol_to_c_name_address" | $SED "$delay_single_quote_subst"`'
 lt_cv_sys_global_symbol_to_c_name_address_lib_prefix='`$ECHO "$lt_cv_sys_global_symbol_to_c_name_address_lib_prefix" | $SED "$delay_single_quote_subst"`'
+ '[' 1 = 1 ']'
+++ dirname ./configure
++ find . -name config.guess -o -name config.sub
+ for i in $(find $(dirname ./configure) -name config.guess -o -name config.sub)
++ basename ./cnf/config.sub
+ '[' -f /usr/lib/rpm/redhat/config.sub ']'
+ /usr/bin/rm -f ./cnf/config.sub
++ basename ./cnf/config.sub
+ /usr/bin/cp -fv /usr/lib/rpm/redhat/config.sub ./cnf/config.sub
'/usr/lib/rpm/redhat/config.sub' -> './cnf/config.sub'
+ for i in $(find $(dirname ./configure) -name config.guess -o -name config.sub)
++ basename ./cnf/config.guess
+ '[' -f /usr/lib/rpm/redhat/config.guess ']'
+ /usr/bin/rm -f ./cnf/config.guess
++ basename ./cnf/config.guess
+ /usr/bin/cp -fv /usr/lib/rpm/redhat/config.guess ./cnf/config.guess
'/usr/lib/rpm/redhat/config.guess' -> './cnf/config.guess'
+ '[' 1 = 1 ']'
+ '[' x '!=' 'x-Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld' ']'
++ find . -name ltmain.sh
+ for i in $(find . -name ltmain.sh)
+ /usr/bin/sed -i.backup -e 's~compiler_flags=$~compiler_flags="-Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld"~' ./cnf/ltmain.sh
+ ./configure --build=x86_64-redhat-linux-gnu --host=x86_64-redhat-linux-gnu --program-prefix= --disable-dependency-tracking --prefix=/usr --exec-prefix=/usr --bindir=/usr/bin --sbindir=/usr/sbin --sysconfdir=/etc --datadir=/usr/share --includedir=/usr/include --libdir=/usr/lib64 --libexecdir=/usr/libexec --localstatedir=/var --sharedstatedir=/var/lib --mandir=/usr/share/man --infodir=/usr/share/info --with-gaproot=/usr/lib/gap --disable-silent-rules --with-external-planarity --without-intrinsics
checking build system type... x86_64-redhat-linux-gnu
checking host system type... x86_64-redhat-linux-gnu
checking for a BSD-compatible install... /usr/bin/install -c
checking whether build environment is sane... yes
checking for a thread-safe mkdir -p... /usr/bin/mkdir -p
checking for gawk... gawk
checking whether make sets $(MAKE)... yes
checking whether make supports nested variables... yes
checking whether make supports nested variables... (cached) yes
checking whether make supports the include directive... yes (GNU style)
checking for x86_64-redhat-linux-gnu-gcc... gcc
checking whether the C compiler works... yes
checking for C compiler default output file name... a.out
checking for suffix of executables... 
checking whether we are cross compiling... no
checking for suffix of object files... o
checking whether we are using the GNU C compiler... yes
checking whether gcc accepts -g... yes
checking for gcc option to accept ISO C89... none needed
checking whether gcc understands -c and -o together... yes
checking dependency style of gcc... none
checking for x86_64-redhat-linux-gnu-ar... no
checking for x86_64-redhat-linux-gnu-lib... no
checking for x86_64-redhat-linux-gnu-link... no
checking for ar... ar
checking the archiver (ar) interface... ar
checking for gcc option to accept ISO C99... none needed
checking whether we are using the GNU C++ compiler... yes
checking whether g++ accepts -g... yes
checking dependency style of g++... none
checking how to print strings... printf
checking for a sed that does not truncate output... /usr/bin/sed
checking for grep that handles long lines and -e... /usr/bin/grep
checking for egrep... /usr/bin/grep -E
checking for fgrep... /usr/bin/grep -F
checking for ld used by gcc... /usr/bin/ld
checking if the linker (/usr/bin/ld) is GNU ld... yes
checking for BSD- or MS-compatible name lister (nm)... /usr/bin/nm -B
checking the name lister (/usr/bin/nm -B) interface... BSD nm
checking whether ln -s works... yes
checking the maximum length of command line arguments... 1572864
checking how to convert x86_64-redhat-linux-gnu file names to x86_64-redhat-linux-gnu format... func_convert_file_noop
checking how to convert x86_64-redhat-linux-gnu file names to toolchain format... func_convert_file_noop
checking for /usr/bin/ld option to reload object files... -r
checking for x86_64-redhat-linux-gnu-objdump... no
checking for objdump... objdump
checking how to recognize dependent libraries... pass_all
checking for x86_64-redhat-linux-gnu-dlltool... no
checking for dlltool... no
checking how to associate runtime and link libraries... printf %s\n
checking for x86_64-redhat-linux-gnu-ar... ar
checking for archiver @FILE support... @
checking for x86_64-redhat-linux-gnu-strip... no
checking for strip... strip
checking for x86_64-redhat-linux-gnu-ranlib... no
checking for ranlib... ranlib
checking command to parse /usr/bin/nm -B output from gcc object... ./configure: line 6920:  -e 's/^T .* \(.*\)$/extern int \1();/p' -e 's/^[ABCDGIRSTW][ABCDGIRSTW]* .* \(.*\)$/extern char \1;/p': No such file or directory
ok
checking for sysroot... no
checking for a working dd... /usr/bin/dd
checking how to truncate binary pipes... /usr/bin/dd bs=4096 count=1
checking for x86_64-redhat-linux-gnu-mt... no
checking for mt... no
checking if : is a manifest tool... no
checking how to run the C preprocessor... gcc -E
checking for ANSI C header files... yes
checking for sys/types.h... yes
checking for sys/stat.h... yes
checking for stdlib.h... yes
checking for string.h... yes
checking for memory.h... yes
checking for strings.h... yes
checking for inttypes.h... yes
checking for stdint.h... yes
checking for unistd.h... yes
checking for dlfcn.h... yes
checking for objdir... .libs
checking if gcc supports -fno-rtti -fno-exceptions... no
checking for gcc option to produce PIC... -fPIC -DPIC
checking if gcc PIC flag -fPIC -DPIC works... yes
checking if gcc static flag -static works... no
checking if gcc supports -c -o file.o... yes
checking if gcc supports -c -o file.o... (cached) yes
checking whether the gcc linker (/usr/bin/ld -m elf_x86_64) supports shared libraries... yes
checking whether -lc should be explicitly linked in... no
checking dynamic linker characteristics... GNU/Linux ld.so
checking how to hardcode library paths into programs... immediate
checking for shl_load... no
checking for shl_load in -ldld... no
checking for dlopen... no
checking for dlopen in -ldl... yes
checking whether a program can dlopen itself... yes
checking whether a statically linked program can dlopen itself... yes
checking whether stripping libraries is possible... yes
checking if libtool supports shared libraries... yes
checking whether to build shared libraries... yes
checking whether to build static libraries... no
checking how to run the C++ preprocessor... g++ -E
checking for ld used by g++... /usr/bin/ld -m elf_x86_64
checking if the linker (/usr/bin/ld -m elf_x86_64) is GNU ld... yes
checking whether the g++ linker (/usr/bin/ld -m elf_x86_64) supports shared libraries... yes
checking for g++ option to produce PIC... -fPIC -DPIC
checking if g++ PIC flag -fPIC -DPIC works... yes
checking if g++ static flag -static works... no
checking if g++ supports -c -o file.o... yes
checking if g++ supports -c -o file.o... (cached) yes
checking whether the g++ linker (/usr/bin/ld -m elf_x86_64) supports shared libraries... yes
checking dynamic linker characteristics... (cached) GNU/Linux ld.so
checking how to hardcode library paths into programs... immediate
checking for GAP root directory... /usr/lib/gap
checking for GAP architecture... checking whether to enable debug mode... no
checking whether to enable stats mode... no
checking whether to build with code coverage support... no
checking whether enable compiler warnings... no
checking whether to use external planarity... yes
checking for gp_InitGraph in -lplanarity... yes
checking planarity/graph.h usability... yes
checking planarity/graph.h presence... yes
checking for planarity/graph.h... yes
checking whether to use external bliss... no
configure: compiler intrinsics will not be used even if available
checking that generated files are newer than configure... done
configure: creating ./config.status
config.status: creating Makefile
config.status: creating src/_pkgconfig.h
config.status: executing depfiles commands
config.status: executing src/digraphs-config.h commands
config.status: creating src/digraphs-config.h - prefix DIGRAPHS for src/_pkgconfig.h defines
config.status: executing libtool commands
+ /usr/bin/make -O -j2 V=1 VERBOSE=1
make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.4.0'
/bin/sh ./libtool  --tag=CXX   --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src    -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o extern/bliss-0.73/digraphs_la-defs.lo `test -f 'extern/bliss-0.73/defs.cc' || echo './'`extern/bliss-0.73/defs.cc
libtool: compile:  g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c extern/bliss-0.73/defs.cc  -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-defs.o
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/bin/sh ./libtool  --tag=CXX   --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src    -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o extern/bliss-0.73/digraphs_la-partition.lo `test -f 'extern/bliss-0.73/partition.cc' || echo './'`extern/bliss-0.73/partition.cc
libtool: compile:  g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c extern/bliss-0.73/partition.cc  -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-partition.o
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/bin/sh ./libtool  --tag=CXX   --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src    -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o extern/bliss-0.73/digraphs_la-orbit.lo `test -f 'extern/bliss-0.73/orbit.cc' || echo './'`extern/bliss-0.73/orbit.cc
libtool: compile:  g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c extern/bliss-0.73/orbit.cc  -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-orbit.o
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/bin/sh ./libtool  --tag=CXX   --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src    -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o extern/bliss-0.73/digraphs_la-uintseqhash.lo `test -f 'extern/bliss-0.73/uintseqhash.cc' || echo './'`extern/bliss-0.73/uintseqhash.cc
libtool: compile:  g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c extern/bliss-0.73/uintseqhash.cc  -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-uintseqhash.o
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/bin/sh ./libtool  --tag=CXX   --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src    -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o extern/bliss-0.73/digraphs_la-heap.lo `test -f 'extern/bliss-0.73/heap.cc' || echo './'`extern/bliss-0.73/heap.cc
libtool: compile:  g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c extern/bliss-0.73/heap.cc  -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-heap.o
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/bin/sh ./libtool  --tag=CXX   --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src    -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o extern/bliss-0.73/digraphs_la-timer.lo `test -f 'extern/bliss-0.73/timer.cc' || echo './'`extern/bliss-0.73/timer.cc
libtool: compile:  g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c extern/bliss-0.73/timer.cc  -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-timer.o
extern/bliss-0.73/timer.cc: In member function ‘bliss_digraphs::Timer::reset()’:
extern/bliss-0.73/timer.cc:39:24: warning: ‘clkticks.tms_utime’ is used uninitialized [-Wuninitialized]
   39 |     ((double) clkticks.tms_utime + (double) clkticks.tms_stime) /
      |               ~~~~~~~~~^~~~~~~~~
extern/bliss-0.73/timer.cc:35:14: note: ‘clkticks’ declared here
   35 |   struct tms clkticks;
      |              ^~~~~~~~
extern/bliss-0.73/timer.cc:39:54: warning: ‘clkticks.tms_stime’ is used uninitialized [-Wuninitialized]
   39 |     ((double) clkticks.tms_utime + (double) clkticks.tms_stime) /
      |                                             ~~~~~~~~~^~~~~~~~~
extern/bliss-0.73/timer.cc:35:14: note: ‘clkticks’ declared here
   35 |   struct tms clkticks;
      |              ^~~~~~~~
extern/bliss-0.73/timer.cc: In member function ‘bliss_digraphs::Timer::get_duration()’:
extern/bliss-0.73/timer.cc:50:24: warning: ‘clkticks.tms_utime’ is used uninitialized [-Wuninitialized]
   50 |     ((double) clkticks.tms_utime + (double) clkticks.tms_stime) /
      |               ~~~~~~~~~^~~~~~~~~
extern/bliss-0.73/timer.cc:46:14: note: ‘clkticks’ declared here
   46 |   struct tms clkticks;
      |              ^~~~~~~~
extern/bliss-0.73/timer.cc:50:54: warning: ‘clkticks.tms_stime’ is used uninitialized [-Wuninitialized]
   50 |     ((double) clkticks.tms_utime + (double) clkticks.tms_stime) /
      |                                             ~~~~~~~~~^~~~~~~~~
extern/bliss-0.73/timer.cc:46:14: note: ‘clkticks’ declared here
   46 |   struct tms clkticks;
      |              ^~~~~~~~
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/bin/sh ./libtool  --tag=CXX   --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src    -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o extern/bliss-0.73/digraphs_la-utils.lo `test -f 'extern/bliss-0.73/utils.cc' || echo './'`extern/bliss-0.73/utils.cc
libtool: compile:  g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c extern/bliss-0.73/utils.cc  -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-utils.o
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/bin/sh ./libtool  --tag=CXX   --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src    -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o extern/bliss-0.73/digraphs_la-bliss_C.lo `test -f 'extern/bliss-0.73/bliss_C.cc' || echo './'`extern/bliss-0.73/bliss_C.cc
libtool: compile:  g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c extern/bliss-0.73/bliss_C.cc  -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-bliss_C.o
extern/bliss-0.73/bliss_C.cc: In function ‘void fill_size(BlissStats*, const bliss_digraphs::Stats&)’:
extern/bliss-0.73/bliss_C.cc:156:21: warning: comparison of integer expressions of different signedness: ‘int’ and ‘std::vector<int>::size_type’ {aka ‘long unsigned int’} [-Wsign-compare]
  156 |    for(int i = 0; i < sizes.size(); ++i) {
      |                   ~~^~~~~~~~~~~~~~
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libtool: compile:  gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c src/digraphs.c  -fPIC -DPIC -o src/.libs/digraphs_la-digraphs.o
src/digraphs.c: In function ‘FLOYD_WARSHALL.constprop.0’:
src/digraphs.c:1214:13: warning: ‘adj’ may be used uninitialized in this function [-Wmaybe-uninitialized]
 1214 |             free(adj);
      |             ^~~~~~~~~
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/bin/sh ./libtool  --tag=CC   --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS  -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection  -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o src/digraphs_la-bitarray.lo `test -f 'src/bitarray.c' || echo './'`src/bitarray.c
libtool: compile:  gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c src/bitarray.c  -fPIC -DPIC -o src/.libs/digraphs_la-bitarray.o
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/bin/sh ./libtool  --tag=CC   --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS  -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection  -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o src/digraphs_la-conditions.lo `test -f 'src/conditions.c' || echo './'`src/conditions.c
libtool: compile:  gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c src/conditions.c  -fPIC -DPIC -o src/.libs/digraphs_la-conditions.o
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/bin/sh ./libtool  --tag=CXX   --mode=compile g++ -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src    -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o extern/bliss-0.73/digraphs_la-graph.lo `test -f 'extern/bliss-0.73/graph.cc' || echo './'`extern/bliss-0.73/graph.cc
libtool: compile:  g++ -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c extern/bliss-0.73/graph.cc  -fPIC -DPIC -o extern/bliss-0.73/.libs/digraphs_la-graph.o
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/bin/sh ./libtool  --tag=CC   --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS  -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection  -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o src/digraphs_la-cliques.lo `test -f 'src/cliques.c' || echo './'`src/cliques.c
libtool: compile:  gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c src/cliques.c  -fPIC -DPIC -o src/.libs/digraphs_la-cliques.o
src/cliques.c: In function ‘init_graph_from_digraph_obj’:
src/cliques.c:175:14: warning: unused variable ‘out’ [-Wunused-variable]
  175 |   Obj        out     = FuncOutNeighbours(0L, digraph_obj);
      |              ^~~
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/bin/sh ./libtool  --tag=CC   --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS  -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection  -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o src/digraphs_la-homos-graphs.lo `test -f 'src/homos-graphs.c' || echo './'`src/homos-graphs.c
libtool: compile:  gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c src/homos-graphs.c  -fPIC -DPIC -o src/.libs/digraphs_la-homos-graphs.o
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/bin/sh ./libtool  --tag=CC   --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS  -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection  -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o src/digraphs_la-perms.lo `test -f 'src/perms.c' || echo './'`src/perms.c
libtool: compile:  gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c src/perms.c  -fPIC -DPIC -o src/.libs/digraphs_la-perms.o
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/bin/sh ./libtool  --tag=CC   --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS  -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection  -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o src/digraphs_la-homos.lo `test -f 'src/homos.c' || echo './'`src/homos.c
libtool: compile:  gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c src/homos.c  -fPIC -DPIC -o src/.libs/digraphs_la-homos.o
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/bin/sh ./libtool  --tag=CC   --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS  -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection  -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o src/digraphs_la-planar.lo `test -f 'src/planar.c' || echo './'`src/planar.c
libtool: compile:  gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c src/planar.c  -fPIC -DPIC -o src/.libs/digraphs_la-planar.o
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/bin/sh ./libtool  --tag=CC   --mode=compile gcc -DHAVE_CONFIG_H -I. -I./src  -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H       -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS  -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection  -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c -o src/digraphs_la-schreier-sims.lo `test -f 'src/schreier-sims.c' || echo './'`src/schreier-sims.c
libtool: compile:  gcc -DHAVE_CONFIG_H -I. -I./src -I/usr/lib/gap/gen -I/usr/lib/gap/src -I/usr/lib/gap -DHAVE_CONFIG_H -DSYS_DEFAULT_PATHS=/usr/lib/gap -I/usr/lib/gap/src -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -I./extern/ -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1 -m64 -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -c src/schreier-sims.c  -fPIC -DPIC -o src/.libs/digraphs_la-schreier-sims.o
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/bin/sh ./libtool  --tag=CXX   --mode=link g++  -I./extern/   -O2 -flto=auto -ffat-lto-objects -fexceptions -g -grecord-gcc-switches -pipe -Wall -Werror=format-security -Wp,-D_FORTIFY_SOURCE=2 -Wp,-D_GLIBCXX_ASSERTIONS -specs=/usr/lib/rpm/redhat/redhat-hardened-cc1 -fstack-protector-strong -specs=/usr/lib/rpm/redhat/redhat-annobin-cc1  -m64  -mtune=generic -fasynchronous-unwind-tables -fstack-clash-protection -fcf-protection -lpthread -Wl,-z,relro -Wl,--as-needed -module -avoid-version  -Wl,-z,relro -Wl,--as-needed  -Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld  -o digraphs.la -rpath /usr/lib64 src/digraphs_la-digraphs.lo src/digraphs_la-bitarray.lo src/digraphs_la-conditions.lo src/digraphs_la-homos.lo src/digraphs_la-cliques.lo src/digraphs_la-homos-graphs.lo src/digraphs_la-perms.lo src/digraphs_la-planar.lo src/digraphs_la-schreier-sims.lo extern/bliss-0.73/digraphs_la-defs.lo extern/bliss-0.73/digraphs_la-graph.lo extern/bliss-0.73/digraphs_la-partition.lo extern/bliss-0.73/digraphs_la-orbit.lo extern/bliss-0.73/digraphs_la-uintseqhash.lo extern/bliss-0.73/digraphs_la-heap.lo extern/bliss-0.73/digraphs_la-timer.lo extern/bliss-0.73/digraphs_la-utils.lo extern/bliss-0.73/digraphs_la-bliss_C.lo  -lplanarity 
libtool: link: g++  -fPIC -DPIC -shared -nostdlib /usr/lib/gcc/x86_64-redhat-linux/11/../../../../lib64/crti.o /usr/lib/gcc/x86_64-redhat-linux/11/crtbeginS.o  src/.libs/digraphs_la-digraphs.o src/.libs/digraphs_la-bitarray.o src/.libs/digraphs_la-conditions.o src/.libs/digraphs_la-homos.o src/.libs/digraphs_la-cliques.o src/.libs/digraphs_la-homos-graphs.o src/.libs/digraphs_la-perms.o src/.libs/digraphs_la-planar.o src/.libs/digraphs_la-schreier-sims.o extern/bliss-0.73/.libs/digraphs_la-defs.o extern/bliss-0.73/.libs/digraphs_la-graph.o extern/bliss-0.73/.libs/digraphs_la-partition.o extern/bliss-0.73/.libs/digraphs_la-orbit.o extern/bliss-0.73/.libs/digraphs_la-uintseqhash.o extern/bliss-0.73/.libs/digraphs_la-heap.o extern/bliss-0.73/.libs/digraphs_la-timer.o extern/bliss-0.73/.libs/digraphs_la-utils.o extern/bliss-0.73/.libs/digraphs_la-bliss_C.o   -lpthread -lplanarity -L/usr/lib/gcc/x86_64-redhat-linux/11 -L/usr/lib/gcc/x86_64-redhat-linux/11/../../../../lib64 -L/lib/../lib64 -L/usr/lib/../lib64 -L/usr/lib/gcc/x86_64-redhat-linux/11/../../.. -lstdc++ -lm -lc -lgcc_s /usr/lib/gcc/x86_64-redhat-linux/11/crtendS.o /usr/lib/gcc/x86_64-redhat-linux/11/../../../../lib64/crtn.o -Wl,-z,now -specs=/usr/lib/rpm/redhat/redhat-hardened-ld -O2 -flto=auto -g -grecord-gcc-switches -fstack-protector-strong -m64 -mtune=generic -Wl,-z -Wl,relro -Wl,--as-needed -Wl,-z -Wl,relro -Wl,--as-needed -Wl,-z -Wl,now   -Wl,-soname -Wl,digraphs.so -o .libs/digraphs.so
libtool: link: ( cd ".libs" && rm -f "digraphs.la" && ln -s "../digraphs.la" "digraphs.la" )
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make[1]: Entering directory '/builddir/build/BUILD/digraphs-1.4.0'
/usr/bin/mkdir -p ./bin/x86_64-redhat-linux-gnu-default64-kv7 ./bin/lib
cp .libs/digraphs.so /builddir/build/BUILD/digraphs-1.4.0/bin/x86_64-redhat-linux-gnu-default64-kv7/
SUCCESS!
make[1]: Leaving directory '/builddir/build/BUILD/digraphs-1.4.0'
+ mkdir ../pkg
+ ln -s ../digraphs-1.4.0 ../pkg
+ gap -l '/builddir/build/BUILD/digraphs-1.4.0/..;/usr/lib/gap'
 ┌───────┐   GAP 4.11.0 of 29-Feb-2020
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: x86_64-redhat-linux-gnu-default64-kv7
 Configuration:  gmp 6.2.0, GASMAN, readline
 Loading the library and packages ...
#I  autpgrp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  alnuth package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  crisp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  ctbllib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  factint package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  fga package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  irredsol package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  laguna package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polenta package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polycyclic package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  resclasses package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  sophus package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  tomlib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
 Packages:   GAPDoc 1.6.4, IO 4.7.0, PrimGrp 3.4.1, SmallGrp 1.4.2, 
             TransGrp 3.0
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> gap> gap> gap> gap> gap> gap> gap> gap> "Digraphs"
gap> gap> true
gap> gap> > > > > > > > > > > > > > > > > [ "attr.xml", "cliques.xml", "constructors.xml", "digraph.xml", 
  "display.xml", "examples.xml", "grahom.xml", "grape.xml", "io.xml", 
  "isomorph.xml", "labels.xml", "oper.xml", "orbits.xml", "planar.xml", 
  "prop.xml", "utils.xml", "../PackageInfo.g" ]
gap> gap> > > > #I Composing XML document . . .
#I Parsing XML document . . .
#I Checking XML structure . . .
#I Text version (also produces labels for hyperlinks):
#I First run, collecting cross references, index, toc, bib and so on . . .
#I Table of contents complete.
#I Producing the index . . .
#I Reading bibliography data files . . . 
#I   BibTeX format: digraphs
#I   checking and translating to BibXMLext . . .
#I Writing bibliography . . .
#I Second run through document . . .
#I Producing simplified search strings and labels for hyperlinks . . .
#I Constructing LaTeX version and calling pdflatex:
#I Writing LaTeX file, 4 x pdflatex with bibtex and makeindex, 
#I Writing manual.six file ... 
#I Finally the HTML version . . .
#I First run, collecting cross references, index, toc, bib and so on . . .
#I Table of contents complete.
#I Producing the index . . .
#I Writing bibliography . . .
#I Second run through document . . .
#I - also HTML version for MathJax . . .
#I First run, collecting cross references, index, toc, bib and so on . . .
#I Table of contents complete.
#I Producing the index . . .
#I Writing bibliography . . .
#I Second run through document . . .
rec( Name := "digraphs", attributes := rec(  ), bibdata := "digraphs", 
  bibentries := [ <BibXMLext entry: BM06>, <BibXMLext entry: CK86>, 
      <BibXMLext entry: Gab00>, <BibXMLext entry: JK07>, 
      <BibXMLext entry: MP14>, <BibXMLext entry: vLS81> ], 
  bibkeys := [ "BM06", "CK86", "Gab00", "JK07", "MP14", "vLS81" ], 
  biblabels := [ "BM06", "CK86", "Gab00", "JK07", "MP14", "vLS81" ], 
  bibpath := dir("/builddir/build/BUILD/digraphs-1.4.0/../pkg/digraphs-1.4.0/d\
oc/"), bibstrings := [ [ 0, 0 ] ], 
  bibtext := "\n<p><a id=\"biBBM06\" name=\"biBBM06\"></a></p>\n<p class='BibE\
ntry'>\n[<span class='BibKey'>BM06</span>]   <b class='BibAuthor'>Boyer, J. M.\
 and Myrvold, W. J.</b>,\n <i class='BibTitle'>On the Cutting Edge: Simplified\
 O(n) Planarity by Edge\n      Addition</i>,\n  in  <i class='BibBooktitle'>Gr\
aph Algorithms and Applications 5</i>,\n <span class='BibPublisher'>{WORLD} {S\
CIENTIFIC}</span>\n (<span class='BibYear'>2006</span>),\n <span class='BibPag\
es'>241--273</span>.\n</p>\n\n\n<p><a id=\"biBCK86\" name=\"biBCK86\"></a></p>\
\n<p class='BibEntry'>\n[<span class='BibKeyLink'><a href=\"http://www.ams.org\
/mathscinet-getitem?mr=818812\">CK86</a></span>]   <b class='BibAuthor'>Calder\
bank, R. and Kantor, W. M.</b>,\n <i class='BibTitle'>The geometry of two-weig\
ht codes</i>,\n <span class='BibJournal'>Bull. London Math. Soc.</span>,\n <em\
 class='BibVolume'>18</em> (<span class='BibNumber'>2</span>)\n (<span class='\
BibYear'>1986</span>),\n <span class='BibPages'>97--122</span>.\n</p>\n\n\n<p>\
<a id=\"biBGab00\" name=\"biBGab00\"></a></p>\n<p class='BibEntry'>\n[<span cl\
ass='BibKey'>Gab00</span>]   <b class='BibAuthor'>Gabow, H. N.</b>,\n <i class\
='BibTitle'>Path-based depth-first search for strong and biconnected\n        \
   components</i>,\n <span class='BibJournal'>Information Processing Letters</\
span>,\n <em class='BibVolume'>74</em> (<span class='BibNumber'>34</span>)\n (\
<span class='BibYear'>2000</span>),\n <span class='BibPages'>107 - 114</span>.\
\n</p>\n\n\n<p><a id=\"biBJK07\" name=\"biBJK07\"></a></p>\n<p class='BibEntry\
'>\n[<span class='BibKey'>JK07</span>]   <b class='BibAuthor'>Junttila, T. and\
 Kaski, P.</b> (<span class='BibEditor'>Applegate, D., Brodal, G. S., Panario,\
 D. and Sedgewick, R.</span>, Eds.),\n <i class='BibTitle'>Engineering an effi\
cient canonical labeling tool for large and\n           sparse graphs</i>,\n  \
in  <i class='BibBooktitle'>Proceedings of the Ninth Workshop on Algorithm Eng\
ineering and\n  Experiments and the Fourth Workshop on Analytic Algorithms and\
\n               Combinatorics</i>,\n <span class='BibPublisher'>SIAM</span>\n\
 (<span class='BibYear'>2007</span>),\n <span class='BibPages'>135--149</span>\
.\n</p>\n\n\n<p><a id=\"biBMP14\" name=\"biBMP14\"></a></p>\n<p class='BibEntr\
y'>\n[<span class='BibKey'>MP14</span>]   <b class='BibAuthor'>McKay, B. D. an\
d Piperno, A.</b>,\n <i class='BibTitle'>Practical graph isomorphism, II</i>,\
\n <span class='BibJournal'>Journal of Symbolic Computation</span>,\n <em clas\
s='BibVolume'>60</em> (<span class='BibNumber'>0</span>)\n (<span class='BibYe\
ar'>2014</span>),\n <span class='BibPages'>94 - 112</span>.\n</p>\n\n\n<p><a i\
d=\"biBvLS81\" name=\"biBvLS81\"></a></p>\n<p class='BibEntry'>\n[<span class=\
'BibKeyLink'><a href=\"http://www.ams.org/mathscinet-getitem?mr=602417\">vLS81\
</a></span>]   <b class='BibAuthor'>van Lint, J. H. and Schrijver, A.</b>,\n <\
i class='BibTitle'>Construction of strongly regular graphs, two-weight codes a\
nd\n           partial geometries by finite fields</i>,\n <span class='BibJour\
nal'>Combinatorica</span>,\n <em class='BibVolume'>1</em> (<span class='BibNum\
ber'>1</span>)\n (<span class='BibYear'>1981</span>),\n <span class='BibPages'\
>63--73</span>.\n</p>\n\n", bookname := "digraphs", 
  chapsectlinks := 
    rec( 
      1 := "<div class=\"ChapSects\"><a href=\"chap1_mj.html#X7F202ABA780E595D\
\">1 <span class=\"Heading\">\n    The <strong class=\"pkg\">Digraphs</strong>\
 package\n  </span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span\
 class=\"nocss\">&nbsp;</span><a href=\"chap1_mj.html#X7DFB63A97E67C0A1\">1.1 \
<span class=\"Heading\">Introduction</span></a>\n</span>\n<div class=\"ContSSB\
lock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap1_mj.html#X84541F61810C741D\">1.1-1 <span class=\"Heading\">Def\
initions</span></a>\n</span>\n</div></div>\n</div>\n", 
      2 := "<div class=\"ChapSects\"><a href=\"chap2_mj.html#X817088B27F90D596\
\">2 <span class=\"Heading\">Installing <strong class=\"pkg\">Digraphs</strong\
></span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"no\
css\">&nbsp;</span><a href=\"chap2_mj.html#X7DA3059C79842BF3\">2.1 <span class\
=\"Heading\">For those in a hurry</span></a>\n</span>\n</div>\n<div class=\"Co\
ntSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"\
chap2_mj.html#X780AA9D97EBCA95D\">2.2 <span class=\"Heading\">Optional package\
 dependencies</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.htm\
l#X8493C7587FCF6D8B\">2.2-1 <span class=\"Heading\">The Grape package</span></\
a>\n</span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><sp\
an class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X849F6196875A6DF5\">2.\
3 <span class=\"Heading\">Compiling the kernel module</span></a>\n</span>\n</d\
iv>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nb\
sp;</span><a href=\"chap2_mj.html#X857CBE5484CF703A\">2.4 <span class=\"Headin\
g\">Rebuilding the documentation</span></a>\n</span>\n<div class=\"ContSSBlock\
\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap2_mj.html#X870631C38610AC25\">2.4-1 DigraphsMakeDoc</a></span>\n</d\
iv></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap2_mj.html#X7862D3F37C5BBDEF\">2.5 <span class=\"\
Heading\">Testing your installation</span></a>\n</span>\n<div class=\"ContSSBl\
ock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap2_mj.html#X86AF4DAE80B978DA\">2.5-1 DigraphsTestInstall</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap2_mj.html#X7A20088B7C406C4A\">2.5-2 DigraphsTestStandard</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap2_mj.html#X7885EF3E785D4298\">2.5-3 DigraphsTestExtreme</a></span>\n</\
div></div>\n</div>\n", 
      3 := "<div class=\"ChapSects\"><a href=\"chap3_mj.html#X7D34861E863A5D93\
\">3 <span class=\"Heading\">Creating digraphs</span></a>\n<div class=\"ContSe\
ct\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap\
3_mj.html#X7D34861E863A5D93\">3.1 <span class=\"Heading\">Creating digraphs</s\
pan></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7877ADC77F85E\
630\">3.1-1 IsDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7D7EDF83820ED6F5\">3.1-2 Is\
MutableDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7CAFAA89804F80BD\">3.1-3 IsImmutab\
leDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap3_mj.html#X7E749324800B38A5\">3.1-4 IsCayleyDigrap\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap3_mj.html#X80F1B6D28478D8B9\">3.1-5 IsDigraphWithAdjacency\
Function</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap3_mj.html#X86E798B779515678\">3.1-6 DigraphByOutNei\
ghboursType</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap3_mj.html#X834843057CE86655\">3.1-7 Digraph</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap3_mj.html#X8023FE387A3AB609\">3.1-8 DigraphByAdjacencyMatrix</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap3_mj.html#X7F37B6768349E269\">3.1-9 DigraphByEdges</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap3_mj.html#X7B75C1D680757D6F\">3.1-10 EdgeOrbitsDigraph</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p3_mj.html#X81BC49B57EAADEFB\">3.1-11 DigraphByInNeighbours</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
3_mj.html#X7FCADADC7EC28478\">3.1-12 CayleyDigraph</a></span>\n</div></div>\n<\
div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</s\
pan><a href=\"chap3_mj.html#X83608C407CC8836D\">3.2 <span class=\"Heading\">Ch\
anging representations</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p3_mj.html#X7FBC4BDB82FBEDD2\">3.2-1 AsBinaryRelation</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X83CA27E67F685EB3\">3.2-2 AsDigraph</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7B3353428\
39E5146\">3.2-3 Graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7C4F13E080EC16B0\">3.2-4 As\
Graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X7C5360B2799943F3\">3.2-5 AsTransformation</\
a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span\
 class=\"nocss\">&nbsp;</span><a href=\"chap3_mj.html#X85126078848B420A\">3.3 \
<span class=\"Heading\">New digraphs from old</span></a>\n</span>\n<div class=\
\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X83D93A8A8251E6F9\">3.3-1 DigraphImmutableCo\
py</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap3_mj.html#X8399F7427B227228\">3.3-2 DigraphImmutableCopyI\
fImmutable</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap3_mj.html#X83C51DA182CCEA2F\">3.3-3 InducedSubdig\
raph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap3_mj.html#X7CAF093B85A93D2F\">3.3-4 ReducedDigraph</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap3_mj.html#X829E3EAC7C4B3B1E\">3.3-5 MaximalSymmetricSubdigraph</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap3_mj.html#X79BA6A66846D5A95\">3.3-6 MaximalAntiSymmetricSubdi\
graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X7DD9766C86D3ED20\">3.3-7 UndirectedSpanning\
Forest</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap3_mj.html#X7D1D26D27F5B56C2\">3.3-8 QuotientDigraph</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap3_mj.html#X78DECD26811EFD7C\">3.3-9 DigraphReverse</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap3_mj.html#X7F71D99D852B130F\">3.3-10 DigraphDual</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_m\
j.html#X874883DD7DD450C4\">3.3-11 DigraphSymmetricClosure</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_\
mj.html#X7A6C419080AD41DE\">3.3-12 DigraphTransitiveClosure</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
3_mj.html#X82AD17517E273600\">3.3-13 DigraphTransitiveReduction</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap3_mj.html#X83B2506D79453208\">3.3-14 DigraphAddVertex</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_\
mj.html#X8134BEE7786BD3A7\">3.3-15 DigraphAddVertices</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X7E58CC4880627658\">3.3-16 DigraphAddEdge</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7BE\
5C7028760B053\">3.3-17 DigraphAddEdgeOrbit</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8693A6\
1B7F752C76\">3.3-18 DigraphAddEdges</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7B634A2B83C08\
B16\">3.3-19 DigraphRemoveVertex</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7E290E847A5A299A\
\">3.3-20 DigraphRemoveVertices</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8433E3BC7E5EA6BF\
\">3.3-21 DigraphRemoveEdge</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X85981D9187F49018\">3.\
3-22 DigraphRemoveEdgeOrbit</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X87093FDA7F88E732\">3.\
3-23 DigraphRemoveEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X79324AF7818C0C02\">3.3-2\
4 DigraphRemoveLoops</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DCCD0247897A3DE\">3.3-25 Di\
graphRemoveAllMultipleEdges</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7821753D85402A8C\">3.\
3-26 DigraphReverseEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X814F1DFC83DB273F\">3.3-2\
7 DigraphDisjointUnion</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DA997697D310E44\">3.3-28 \
DigraphEdgeUnion</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DDFC759860E3390\">3.3-29 Digra\
phJoin</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap3_mj.html#X7D625CC87DBFFDED\">3.3-30 DigraphCartesian\
Product</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap3_mj.html#X84D24DC9833B54A5\">3.3-31 DigraphDirectPr\
oduct</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X8795087A78FE7D54\">3.3-32 DigraphCartesianP\
roductProjections</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X84FB64F185B804C2\">3.3-33 Digra\
phDirectProductProjections</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8595BF937B749F22\">3.3\
-34 LineDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8364C6F17A1680CB\">3.3-35 LineUnd\
irectedDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7FB8B48C87C0ED16\">3.3-36 DoubleDi\
graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X7C6E6CB284982C7A\">3.3-37 BipartiteDoubleDi\
graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X8167A50A83256ED1\">3.3-38 DigraphAddAllLoop\
s</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap3_mj.html#X865436437DF95FEF\">3.3-39 DistanceDigraph</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap3_mj.html#X86F9CCEA839ABC48\">3.3-40 DigraphClosure</a></span>\n<\
span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap3_mj.html#X7B5AC5FE859F4D80\">3.3-41 DigraphMycielskian</a></span>\n</di\
v></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap3_mj.html#X85B5D9B97F5187B7\">3.4 <span class=\"\
Heading\">Random digraphs</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap3_mj.html#X86CF9F66788B2A24\">3.4-1 RandomDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X78FE275E7E77D56F\">3.4-2 RandomMultiDigraph</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X\
7D36B5E57F055051\">3.4-3 RandomTournament</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7A023E4\
787682475\">3.4-4 RandomLattice</a></span>\n</div></div>\n<div class=\"ContSec\
t\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap3\
_mj.html#X7C76D1DC7DAF03D3\">3.5 <span class=\"Heading\">Standard examples</sp\
an></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X870594FC866AC8\
8E\">3.5-1 ChainDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X812417E278198D9C\">3.5-2\
 CompleteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8795B0AD856014FA\">3.5-3 Comple\
teBipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X873F29CC863241F8\">3.5-4 Compl\
eteMultipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X80C29DDE876FFBEB\">3.5-5 C\
ycleDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap3_mj.html#X80DAE31A79FEFD40\">3.5-6 EmptyDigraph\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chap3_mj.html#X80ED9CE785819607\">3.5-7 JohnsonDigraph</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap3_mj.html#X823F43217A6C375D\">3.5-8 PetersenGraph</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
3_mj.html#X7B5441F386BD105E\">3.5-9 GeneralisedPetersenGraph</a></span>\n</div\
></div>\n</div>\n", 
      4 := "<div class=\"ChapSects\"><a href=\"chap4_mj.html#X7AD6F77E7D95C996\
\">4 <span class=\"Heading\">Operators</span></a>\n<div class=\"ContSect\"><sp\
an class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap4_mj.htm\
l#X84E0B5B88358C96B\">4.1 <span class=\"Heading\">Operators for digraphs</span\
></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X829B911D7EFD2D85\
\">4.1-1 IsSubdigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X833C3299787E2309\">4.1-2 Is\
UndirectedSpanningTree</a></span>\n</div></div>\n</div>\n", 
      5 := "<div class=\"ChapSects\"><a href=\"chap5_mj.html#X8739F6CD78C90B14\
\">5 <span class=\"Heading\">Attributes and operations</span></a>\n<div class=\
\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hre\
f=\"chap5_mj.html#X7E814B6478F7D015\">5.1 <span class=\"Heading\">Vertices and\
 edges</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C4\
5F7D878D896AC\">5.1-1 DigraphVertices</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C6F19B57CB\
2E882\">5.1-2 DigraphNrVertices</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7D1C6A4D7ECEC317\
\">5.1-3 DigraphEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X85E1CFDD7E164AD0\">5.1-4 Di\
graphNrEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap5_mj.html#X7BDABAF07917462B\">5.1-5 DigraphNrLo\
ops</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap5_mj.html#X85D5E08280914EE4\">5.1-6 DigraphSinks</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap5_mj.html#X7F5C6268839BE98C\">5.1-7 DigraphSources</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap5_mj.html#X785C30378064CF47\">5.1-8 DigraphTopologicalSort</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p5_mj.html#X7CA91E4B7904F793\">5.1-9 DigraphVertexLabel</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj\
.html#X7E51F2FE87140B32\">5.1-10 DigraphVertexLabels</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.h\
tml#X79FAEACC7F438C2F\">5.1-11 DigraphEdgeLabel</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7\
C24851087D4A8FB\">5.1-12 DigraphEdgeLabels</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7EFAF0\
1B7A155157\">5.1-13 DigraphInEdges</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BECFE6687ECD0\
28\">5.1-14 DigraphOutEdges</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BB8ED88835F07B4\">5.\
1-15 IsDigraphEdge</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X848FED0B7B4ACD1F\">5.1-16 IsMa\
tching</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X7B7A67277B1C9A02\">5.1-17 DigraphMaximalMa\
tching</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X78E9847A858788D1\">5.1-18 DigraphMaximumMa\
tching</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X7D7CE8328187D0D\
F\">5.2 <span class=\"Heading\">Neighbours and degree</span></a>\n</span>\n<di\
v class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7DC2CD70830BEE60\">5.2-1 AdjacencyM\
atrix</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap5_mj.html#X87FA0A727CDB060B\">5.2-2 CharacteristicPoly\
nomial</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X8507DC4F794780C1\">5.2-3 BooleanAdjacencyM\
atrix</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap5_mj.html#X7AFCE34A7A04D5C1\">5.2-4 DigraphAdjacencyFu\
nction</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X7FDEBF3279759961\">5.2-5 DigraphRange</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap5_mj.html#X7E9880767AE68E00\">5.2-6 OutNeighbours</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap5_mj.html#X85C7AA5A81DA6E11\">5.2-7 InNeighbours</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.h\
tml#X7F5ACE807D1BC2E2\">5.2-8 OutDegrees</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7ADDFBFD\
7A365775\">5.2-9 InDegrees</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7A09EB648070276D\">5.2\
-10 OutDegreeOfVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X83315B0186850806\">5.2-11 O\
utNeighboursOfVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C9CD0527CB9E6EF\">5.2-12 In\
DegreeOfVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C0DA18B8291F302\">5.2-13 InNeighb\
oursOfVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap5_mj.html#X83271F607BD809CF\">5.2-14 DigraphLoo\
ps</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap5_mj.html#X7DDB33B686B3A2C6\">5.2-15 PartialOrderDigraphM\
eetOfVertices</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BEAE1C78267F54D\">5.2-16 DegreeMat\
rix</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap5_mj.html#X865390B08331936B\">5.2-17 LaplacianMatrix</a>\
</span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span c\
lass=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X8537F4088400DC48\">5.3 <s\
pan class=\"Heading\">Reachability and connectivity</span></a>\n</span>\n<div \
class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap5_mj.html#X7F16B9EB8398459C\">5.3-1 DigraphDiame\
ter</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap5_mj.html#X8104A9D37BCD8A05\">5.3-2 DigraphShortestDista\
nce</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap5_mj.html#X81F99BC67E9D050F\">5.3-3 DigraphShortestDista\
nces</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap5_mj.html#X8223718079D98A82\">5.3-4 DigraphLongestDista\
nceFromVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7CB7DDCD84621D38\">5.3-5 DigraphDis\
tanceSet</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap5_mj.html#X79A3DA4078CF3C90\">5.3-6 DigraphGirth</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap5_mj.html#X8374B7357EC189C1\">5.3-7 DigraphOddGirth</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X84688B337BDDBB09\">5.3-8 DigraphUndirectedGirth</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X842FAD6A7B835977\">5.3-9 DigraphConnectedComponents</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap5_mj.html#X8484EC557810CD31\">5.3-10 DigraphConnectedComponent</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap5_mj.html#X833ECD6B7A84944C\">5.3-11 DigraphStronglyConnectedCom\
ponents</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap5_mj.html#X7EFCB5017D662254\">5.3-12 DigraphStrongly\
ConnectedComponent</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7F1B5A2782F598B1\">5.3-13 Digr\
aphBicomponents</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7DDE06E47E605DD7\">5.3-14 Articul\
ationPoints</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap5_mj.html#X84D5A125848BD800\">5.3-15 Bridges</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap5_mj.html#X865590147BD1C507\">5.3-16 StrongOrientation</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap5_mj.html#X853D0B0981A33433\">5.3-17 DigraphPeriod</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p5_mj.html#X864A31A8809F61C2\">5.3-18 DigraphFloydWarshall</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5\
_mj.html#X7FBAB09E7C0BE5CF\">5.3-19 IsReachable</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7\
CAE81D97B43DDF3\">5.3-20 VerticesReachableFrom</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X80\
39170B82A32257\">5.3-21 DigraphPath</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X80E9D64584397\
3A6\">5.3-22 DigraphShortestPath</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C0416FE7A69CA2C\
\">5.3-23 IteratorOfPaths</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7ECD16838704FAAA\">5.3-\
24 DigraphAllSimpleCircuits</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C735C4E86BDD5F6\">5.\
3-25 DigraphLongestSimpleCircuit</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X870E04307C5F213F\
\">5.3-26 DigraphLayers</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7B2E42327DA118E0\">5.3-2\
7 DigraphDegeneracy</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X827C2BD17A4547E3\">5.3-28 Dig\
raphDegeneracyOrdering</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X863FDFC4839A3B82\">5.3-29 \
HamiltonianPath</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X82F30D5681466BC6\">5.3-30 NrSpann\
ingTrees</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap5_mj.html#X79352A8286D1D8F6\">5.3-31 DigraphDijkstr\
a</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><s\
pan class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X82F900777D677F55\">5\
.4 <span class=\"Heading\">Cayley graphs of groups</span></a>\n</span>\n<div c\
lass=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap5_mj.html#X7A000B1D7CCF7093\">5.4-1 GroupOfCayley\
Digraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap5_mj.html#X8528455987D7D2BF\">5.4-2 GeneratorsOfCayl\
eyDigraph</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocl\
ine\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X790FD6647ECC\
AE3C\">5.5 <span class=\"Heading\">Associated semigroups</span></a>\n</span>\n\
<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X87D5C60D7B0C1309\">5.5-1 AsSemi\
group</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap5_mj.html#X7C6D5EC27C51066B\">5.5-2 AsSemigroup</a></s\
pan>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span clas\
s=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X7E2305528492DDC0\">5.6 <span\
 class=\"Heading\">Planarity</span></a>\n</span>\n<div class=\"ContSSBlock\">\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X7DC478637E8C190D\">5.6-1 KuratowskiPlanarSubdigraph</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap5_mj.html#X78E8F09A8286501B\">5.6-2 KuratowskiOuterPlanarSubdigraph\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chap5_mj.html#X84E3947E7D39BA64\">5.6-3 PlanarEmbedding</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap5_mj.html#X85DFB8C18088711F\">5.6-4 OuterPlanarEmbedding</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X806D2D6B85E0B269\">5.6-5 SubdigraphHomeomorphicToK23</a></s\
pan>\n</div></div>\n</div>\n", 
      6 := "<div class=\"ChapSects\"><a href=\"chap6_mj.html#X7ADDEFD478D470D5\
\">6 <span class=\"Heading\">Properties of digraphs</span></a>\n<div class=\"C\
ontSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\
\"chap6_mj.html#X7F49388F8245F0E9\">6.1 <span class=\"Heading\">Edge propertie\
s</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7D92935C7\
D535187\">6.1-1 DigraphHasLoops</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7DB1BC2286FC08E2\
\">6.1-2 IsAntiSymmetricDigraph</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X860CFB0C8665F356\
\">6.1-3 IsBipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X790A4DBF8533516E\">6.\
1-4 IsCompleteBipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X81F28D4D879FE3B2\"\
>6.1-5 IsCompleteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7FD1A15779FEC341\">6.1-6\
 IsCompleteMultipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E894CCF7B1C27AE\"\
>6.1-7 IsEmptyDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X83762C257DED2751\">6.1-8 Is\
EquivalenceDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E8F37E585DAED52\">6.1-9 IsFun\
ctionalDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7BB84CFC7E8B2B26\">6.1-10 IsMultiD\
igraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap6_mj.html#X8462D8E2792B23F6\">6.1-11 IsReflexiveDigra\
ph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap6_mj.html#X81B3EA7887219860\">6.1-12 IsSymmetricDigraph</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap6_mj.html#X7DD8D1A185EBE865\">6.1-13 IsTournament</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap6_mj.html#X7F0835667F29F0C0\">6.1-14 IsTransitiveDigraph</a></span>\n<\
span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap6_mj.html#X8617726C7829F796\">6.1-15 IsPreorderDigraph</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p6_mj.html#X82BAE6D37D49A145\">6.1-16 IsPartialOrderDigraph</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
6_mj.html#X78D3E17B7F737516\">6.1-17 IsMeetSemilatticeDigraph</a></span>\n</di\
v></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap6_mj.html#X7AAF896982EC22FA\">6.2 <span class=\"\
Heading\">Regularity</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6\
_mj.html#X7A3F78B37E31D9E1\">6.2-1 IsInRegularDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.h\
tml#X7F0A806E7BCB413C\">6.2-2 IsOutRegularDigraph</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#\
X7AF9DB1E7DB12306\">6.2-3 IsRegularDigraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E2082\
AC7CAE59CD\">6.2-4 IsDistanceRegularDigraph</a></span>\n</div></div>\n<div cla\
ss=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a \
href=\"chap6_mj.html#X780DAEB37C5E07FD\">6.3 <span class=\"Heading\">Connectiv\
ity and cycles</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.h\
tml#X7BD08D4478218F77\">6.3-1 IsAcyclicDigraph</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X79\
563B297C220FB5\">6.3-2 IsChainDigraph</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X83C08C0B7EC\
1A91F\">6.3-3 IsConnectedDigraph</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X838FAF2D825977BE\
\">6.3-4 IsBiconnectedDigraph</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7D2A6572820B7F24\">\
6.3-5 IsBridgelessDigraph</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7B37B9467C68C208\">6.3-\
6 IsStronglyConnectedDigraph</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X80E883967EBE839E\">6\
.3-7 IsAperiodicDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7B46EA6C7B2DF2FB\">6.3-8\
 IsDirectedTree</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X80FC20FA7AC4BC2A\">6.3-9 IsUndire\
ctedTree</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap6_mj.html#X79DFBB198525544E\">6.3-10 IsEulerianDigr\
aph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap6_mj.html#X79EFEBC37C2D262D\">6.3-11 IsHamiltonianDigrap\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap6_mj.html#X7E91320B8028F5D8\">6.3-12 IsCycleDigraph</a></s\
pan>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span clas\
s=\"nocss\">&nbsp;</span><a href=\"chap6_mj.html#X7E2305528492DDC0\">6.4 <span\
 class=\"Heading\">Planarity</span></a>\n</span>\n<div class=\"ContSSBlock\">\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap6_mj.html#X8606D415858C40AA\">6.4-1 IsPlanarDigraph</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
6_mj.html#X8251E8B187E7F059\">6.4-2 IsOuterPlanarDigraph</a></span>\n</div></d\
iv>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nb\
sp;</span><a href=\"chap6_mj.html#X83DC8AD283C41326\">6.5 <span class=\"Headin\
g\">Homomorphisms and transformations</span></a>\n</span>\n<div class=\"ContSS\
Block\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap6_mj.html#X78C0B2637985648B\">6.5-1 IsDigraphCore</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap6_mj.html#X8361CA6E8401FF26\">6.5-2 IsEdgeTransitive</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6\
_mj.html#X7B26E4447A1611E9\">6.5-3 IsVertexTransitive</a></span>\n</div></div>\
\n</div>\n", 
      7 := "<div class=\"ChapSects\"><a href=\"chap7_mj.html#X84975388859F203D\
\">7 <span class=\"Heading\">Homomorphisms</span></a>\n<div class=\"ContSect\"\
><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap7_mj\
.html#X8200192B80AD2071\">7.1 <span class=\"Heading\">Acting on digraphs</span\
></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X808972017C486F1F\
\">7.1-1 OnDigraphs</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7AFBA7608498F9CE\">7.1-2 OnMu\
ltiDigraphs</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"to\
cline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap7_mj.html#X7E48B9F87A\
0F22D4\">7.2 <span class=\"Heading\">Isomorphisms and canonical labellings</sp\
an></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X83E593F3855B12\
2E\">7.2-1 DigraphsUseNauty</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X858C32127A190175\">7.\
2-2 AutomorphismGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7E7B0D88865A89F6\">7.2-3 Bl\
issAutomorphismGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X857758B18144C0CD\">7.2-4 Nau\
tyAutomorphismGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X877732B1783C391B\">7.2-5 Auto\
morphismGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7DA2C4FE837FFE01\">7.2-6 Automorphi\
smGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap7_mj.html#X7D676FE67A6684FF\">7.2-7 BlissCanonicalLa\
belling</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap7_mj.html#X87DA265D803DB337\">7.2-8 BlissCanonicalLa\
belling</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap7_mj.html#X877B1D377EC197D7\">7.2-9 BlissCanonicalDi\
graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap7_mj.html#X803ACEDA7BBAC5B3\">7.2-10 DigraphGroup</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap7_mj.html#X8096C5287E459279\">7.2-11 DigraphOrbits</a></span>\n<\
span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap7_mj.html#X8386028782F2D3FF\">7.2-12 DigraphOrbitReps</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
7_mj.html#X8657604E87A25E5F\">7.2-13 DigraphSchreierVector</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7\
_mj.html#X78913684795FB256\">7.2-14 DigraphStabilizer</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.h\
tml#X7B4F24B283C9EE28\">7.2-15 IsIsomorphicDigraph</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html\
#X7D4A1FA8868DA930\">7.2-16 IsIsomorphicDigraph</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8\
219FE6C839D9457\">7.2-17 IsomorphismDigraphs</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7ED\
93C0F86D9D34F\">7.2-18 IsomorphismDigraphs</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7E1C80\
6D81DFE15E\">7.2-19 RepresentativeOutNeighbours</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8\
0183D4A7C51365A\">7.2-20 IsDigraphIsomorphism</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7F1\
6B8B3825A627A\">7.2-21 IsDigraphColouring</a></span>\n</div></div>\n<div class\
=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hr\
ef=\"chap7_mj.html#X7E1A02FE8384C03C\">7.3 <span class=\"Heading\">Homomorphis\
ms of digraphs</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.h\
tml#X79ABF0E783FD67C7\">7.3-1 HomomorphismDigraphsFinder</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_m\
j.html#X85E9B019877AD7FE\">7.3-2 DigraphHomomorphism</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.h\
tml#X8653EDA183E06D05\">7.3-3 HomomorphismsDigraphs</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.htm\
l#X82D0FCD87D47ACA8\">7.3-4 DigraphMonomorphism</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8\
4B4BDB984C2A9A8\">7.3-5 MonomorphismsDigraphs</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7CB\
5AD9F861684FD\">7.3-6 DigraphEpimorphism</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7DFB1F5D\
873937B3\">7.3-7 EpimorphismsDigraphs</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7AD04CC186E\
86CCA\">7.3-8 DigraphEmbedding</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X82EBDF137EEDC5FD\"\
>7.3-9 EmbeddingsDigraphs</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X80FE9FCB79718A61\">7.3-\
10 IsDigraphHomomorphism</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7D6B5A0887903810\">7.3-1\
1 IsDigraphEmbedding</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7F80709A80CBFA98\">7.3-12 Di\
graphsRespectsColouring</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7E93B268823F6478\">7.3-1\
3 GeneratorsOfEndomorphismMonoid</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X86D0A74B83D6B9A7\
\">7.3-14 DigraphColouring</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7AB7200D831013C1\">7.3\
-15 DigraphGreedyColouring</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7F9CB3B27B9590DB\">7.3\
-16 DigraphWelshPowellOrder</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X807D49358529A37C\">7.\
3-17 ChromaticNumber</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X863487EF7D64EF56\">7.3-18 Di\
graphCore</a></span>\n</div></div>\n</div>\n", 
      8 := "<div class=\"ChapSects\"><a href=\"chap8_mj.html#X7A7E0B957932DF44\
\">8 <span class=\"Heading\">Finding cliques and independent sets</span></a>\n\
<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</\
span><a href=\"chap8_mj.html#X788474E38446039B\">8.1 <span class=\"Heading\">F\
inding cliques</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.h\
tml#X80670E3E7C36183F\">8.1-1 IsClique</a></span>\n<span class=\"ContSS\"><br \
/><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X7A3BC9FF81\
69ABCD\">8.1-2 CliquesFinder</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X789854AC7B466402\">8\
.1-3 DigraphClique</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X84EA2F9482B8D4AF\">8.1-4 Digra\
phMaximalCliques</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X78427A8B81FEB457\">8.1-5 Clique\
Number</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chap8_mj.html#X7E3125328770834\
8\">8.2 <span class=\"Heading\">Finding independent sets</span></a>\n</span>\n\
<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X790733B67B0BC894\">8.2-1 IsInde\
pendentSet</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap8_mj.html#X84350678782BFAB7\">8.2-2 DigraphIndepe\
ndentSet</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap8_mj.html#X7D2C78EB81A798A9\">8.2-3 DigraphMaximalI\
ndependentSets</a></span>\n</div></div>\n</div>\n", 
      9 := "<div class=\"ChapSects\"><a href=\"chap9_mj.html#X81714DBC80CC4BCB\
\">9 <span class=\"Heading\">Visualising and IO</span></a>\n<div class=\"ContS\
ect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"cha\
p9_mj.html#X7CF67F8278D9469C\">9.1 <span class=\"Heading\">Visualising a digra\
ph</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X83B33187\
84E78415\">9.1-1 Splash</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7F9B99C478EE093A\">9.1-2\
 DotDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap9_mj.html#X78DA31D1869D2F94\">9.1-3 DotSymmetric\
Digraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap9_mj.html#X84120D447E2CAC23\">9.1-4 DotPartialOrderD\
igraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap9_mj.html#X7F5653C8854FAEA6\">9.1-5 DotPreorderDigrap\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap9_mj.html#X808D12CF81E2C19F\">9.1-6 DotHighlightedDigraph<\
/a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><spa\
n class=\"nocss\">&nbsp;</span><a href=\"chap9_mj.html#X81C9B1DC791C0BBD\">9.2\
 <span class=\"Heading\">Reading and writing digraphs to a file</span></a>\n</\
span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X81FB5BE27903EC32\">9.2-1\
 String</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap9_mj.html#X873D6EB8836A3C61\">9.2-2 DigraphFromGraph\
6String</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap9_mj.html#X782A052979EA2376\">9.2-3 Graph6String</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap9_mj.html#X7845ACDA7D4D333D\">9.2-4 DigraphFile</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap9_mj.html#X7E8142007ED0CB9F\">9.2-5 ReadDigraphs</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.htm\
l#X82A4F0767C9EFC87\">9.2-6 WriteDigraphs</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X86D531B\
287733561\">9.2-7 IteratorFromDigraphFile</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7AAA358\
67B5D8BF4\">9.2-8 DigraphPlainTextLineEncoder</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X780\
8D99079295C22\">9.2-9 TournamentLineDecoder</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7DF22\
D1687D096D6\">9.2-10 AdjacencyMatrixUpperTriangleLineDecoder</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p9_mj.html#X875393338486D77D\">9.2-11 TCodeDecoder</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html\
#X8540FC21796A793F\">9.2-12 PlainTextString</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X81BD2\
3697857B244\">9.2-13 WritePlainTextDigraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X804FDF\
6A7ED64049\">9.2-14 WriteDIMACSDigraph</a></span>\n</div></div>\n</div>\n", 
      A := "<div class=\"ChapSects\"><a href=\"chapA_mj.html#X800DAF137BA8E25B\
\">A <span class=\"Heading\">\n    Grape to Digraphs Command Map\n  </span></a\
>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp\
;</span><a href=\"chapA_mj.html#X7CC8A9DB86F9F0F4\">A.1 <span class=\"Heading\
\">\n      Functions to construct and modify graphs\n    </span></a>\n</span>\
\n</div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chapA_mj.html#X7C38A6397D2770FB\">A.2 <span class=\"\
Heading\">\n      Functions to inspect graphs, vertices and edges\n    </span>\
</a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"tocline\"><span c\
lass=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X78A5A34783C70CD7\">A.3 <s\
pan class=\"Heading\">\n      Functions to determine regularity properties of \
graphs\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\
\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7C7497\
8D85F7AF5C\">A.4 <span class=\"Heading\">\n      Some special vertex subsets o\
f a graph\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span cla\
ss=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7E5\
1B92F7E89E266\">A.5 <span class=\"Heading\">\n      Functions to construct new\
 graphs from old\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><s\
pan class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.ht\
ml#X7A61E3FC7A2BB50E\">A.6 <span class=\"Heading\">\n      Vertex-Colouring an\
d Complete Subgraphs\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_\
mj.html#X7DFC61EC7CBDBC7E\">A.7 <span class=\"Heading\">\n      Automorphism g\
roups and isomorphism testing for graphs\n    </span></a>\n</span>\n</div>\n</\
div>\n" ), 
  chapsectlinkstext := 
    rec( 
      1 := "<div class=\"ChapSects\"><a href=\"chap1_mj.html#X7F202ABA780E595D\
\">1 <span class=\"Heading\">\n    The <strong class=\"pkg\">Digraphs</strong>\
 package\n  </span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span\
 class=\"nocss\">&nbsp;</span><a href=\"chap1_mj.html#X7DFB63A97E67C0A1\">1.1 \
<span class=\"Heading\">Introduction</span></a>\n</span>\n<div class=\"ContSSB\
lock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap1_mj.html#X84541F61810C741D\">1.1-1 <span class=\"Heading\">Def\
initions</span></a>\n</span>\n</div></div>\n</div>\n", 
      2 := "<div class=\"ChapSects\"><a href=\"chap2_mj.html#X817088B27F90D596\
\">2 <span class=\"Heading\">Installing <strong class=\"pkg\">Digraphs</strong\
></span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"no\
css\">&nbsp;</span><a href=\"chap2_mj.html#X7DA3059C79842BF3\">2.1 <span class\
=\"Heading\">For those in a hurry</span></a>\n</span>\n</div>\n<div class=\"Co\
ntSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"\
chap2_mj.html#X780AA9D97EBCA95D\">2.2 <span class=\"Heading\">Optional package\
 dependencies</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.htm\
l#X8493C7587FCF6D8B\">2.2-1 <span class=\"Heading\">The Grape package</span></\
a>\n</span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><sp\
an class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X849F6196875A6DF5\">2.\
3 <span class=\"Heading\">Compiling the kernel module</span></a>\n</span>\n</d\
iv>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nb\
sp;</span><a href=\"chap2_mj.html#X857CBE5484CF703A\">2.4 <span class=\"Headin\
g\">Rebuilding the documentation</span></a>\n</span>\n<div class=\"ContSSBlock\
\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap2_mj.html#X870631C38610AC25\">2.4-1 DigraphsMakeDoc</a></span>\n</d\
iv></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap2_mj.html#X7862D3F37C5BBDEF\">2.5 <span class=\"\
Heading\">Testing your installation</span></a>\n</span>\n<div class=\"ContSSBl\
ock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap2_mj.html#X86AF4DAE80B978DA\">2.5-1 DigraphsTestInstall</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap2_mj.html#X7A20088B7C406C4A\">2.5-2 DigraphsTestStandard</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap2_mj.html#X7885EF3E785D4298\">2.5-3 DigraphsTestExtreme</a></span>\n</\
div></div>\n</div>\n", 
      3 := "<div class=\"ChapSects\"><a href=\"chap3_mj.html#X7D34861E863A5D93\
\">3 <span class=\"Heading\">Creating digraphs</span></a>\n<div class=\"ContSe\
ct\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap\
3_mj.html#X7D34861E863A5D93\">3.1 <span class=\"Heading\">Creating digraphs</s\
pan></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7877ADC77F85E\
630\">3.1-1 IsDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7D7EDF83820ED6F5\">3.1-2 Is\
MutableDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7CAFAA89804F80BD\">3.1-3 IsImmutab\
leDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap3_mj.html#X7E749324800B38A5\">3.1-4 IsCayleyDigrap\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap3_mj.html#X80F1B6D28478D8B9\">3.1-5 IsDigraphWithAdjacency\
Function</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap3_mj.html#X86E798B779515678\">3.1-6 DigraphByOutNei\
ghboursType</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap3_mj.html#X834843057CE86655\">3.1-7 Digraph</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap3_mj.html#X8023FE387A3AB609\">3.1-8 DigraphByAdjacencyMatrix</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap3_mj.html#X7F37B6768349E269\">3.1-9 DigraphByEdges</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap3_mj.html#X7B75C1D680757D6F\">3.1-10 EdgeOrbitsDigraph</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p3_mj.html#X81BC49B57EAADEFB\">3.1-11 DigraphByInNeighbours</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
3_mj.html#X7FCADADC7EC28478\">3.1-12 CayleyDigraph</a></span>\n</div></div>\n<\
div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</s\
pan><a href=\"chap3_mj.html#X83608C407CC8836D\">3.2 <span class=\"Heading\">Ch\
anging representations</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p3_mj.html#X7FBC4BDB82FBEDD2\">3.2-1 AsBinaryRelation</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X83CA27E67F685EB3\">3.2-2 AsDigraph</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7B3353428\
39E5146\">3.2-3 Graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7C4F13E080EC16B0\">3.2-4 As\
Graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X7C5360B2799943F3\">3.2-5 AsTransformation</\
a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span\
 class=\"nocss\">&nbsp;</span><a href=\"chap3_mj.html#X85126078848B420A\">3.3 \
<span class=\"Heading\">New digraphs from old</span></a>\n</span>\n<div class=\
\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X83D93A8A8251E6F9\">3.3-1 DigraphImmutableCo\
py</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap3_mj.html#X8399F7427B227228\">3.3-2 DigraphImmutableCopyI\
fImmutable</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap3_mj.html#X83C51DA182CCEA2F\">3.3-3 InducedSubdig\
raph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap3_mj.html#X7CAF093B85A93D2F\">3.3-4 ReducedDigraph</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap3_mj.html#X829E3EAC7C4B3B1E\">3.3-5 MaximalSymmetricSubdigraph</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap3_mj.html#X79BA6A66846D5A95\">3.3-6 MaximalAntiSymmetricSubdi\
graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X7DD9766C86D3ED20\">3.3-7 UndirectedSpanning\
Forest</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap3_mj.html#X7D1D26D27F5B56C2\">3.3-8 QuotientDigraph</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap3_mj.html#X78DECD26811EFD7C\">3.3-9 DigraphReverse</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap3_mj.html#X7F71D99D852B130F\">3.3-10 DigraphDual</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_m\
j.html#X874883DD7DD450C4\">3.3-11 DigraphSymmetricClosure</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_\
mj.html#X7A6C419080AD41DE\">3.3-12 DigraphTransitiveClosure</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
3_mj.html#X82AD17517E273600\">3.3-13 DigraphTransitiveReduction</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap3_mj.html#X83B2506D79453208\">3.3-14 DigraphAddVertex</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_\
mj.html#X8134BEE7786BD3A7\">3.3-15 DigraphAddVertices</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X7E58CC4880627658\">3.3-16 DigraphAddEdge</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7BE\
5C7028760B053\">3.3-17 DigraphAddEdgeOrbit</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8693A6\
1B7F752C76\">3.3-18 DigraphAddEdges</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7B634A2B83C08\
B16\">3.3-19 DigraphRemoveVertex</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7E290E847A5A299A\
\">3.3-20 DigraphRemoveVertices</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8433E3BC7E5EA6BF\
\">3.3-21 DigraphRemoveEdge</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X85981D9187F49018\">3.\
3-22 DigraphRemoveEdgeOrbit</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X87093FDA7F88E732\">3.\
3-23 DigraphRemoveEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X79324AF7818C0C02\">3.3-2\
4 DigraphRemoveLoops</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DCCD0247897A3DE\">3.3-25 Di\
graphRemoveAllMultipleEdges</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7821753D85402A8C\">3.\
3-26 DigraphReverseEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X814F1DFC83DB273F\">3.3-2\
7 DigraphDisjointUnion</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DA997697D310E44\">3.3-28 \
DigraphEdgeUnion</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DDFC759860E3390\">3.3-29 Digra\
phJoin</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap3_mj.html#X7D625CC87DBFFDED\">3.3-30 DigraphCartesian\
Product</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap3_mj.html#X84D24DC9833B54A5\">3.3-31 DigraphDirectPr\
oduct</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X8795087A78FE7D54\">3.3-32 DigraphCartesianP\
roductProjections</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X84FB64F185B804C2\">3.3-33 Digra\
phDirectProductProjections</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8595BF937B749F22\">3.3\
-34 LineDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8364C6F17A1680CB\">3.3-35 LineUnd\
irectedDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7FB8B48C87C0ED16\">3.3-36 DoubleDi\
graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X7C6E6CB284982C7A\">3.3-37 BipartiteDoubleDi\
graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X8167A50A83256ED1\">3.3-38 DigraphAddAllLoop\
s</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap3_mj.html#X865436437DF95FEF\">3.3-39 DistanceDigraph</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap3_mj.html#X86F9CCEA839ABC48\">3.3-40 DigraphClosure</a></span>\n<\
span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap3_mj.html#X7B5AC5FE859F4D80\">3.3-41 DigraphMycielskian</a></span>\n</di\
v></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap3_mj.html#X85B5D9B97F5187B7\">3.4 <span class=\"\
Heading\">Random digraphs</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap3_mj.html#X86CF9F66788B2A24\">3.4-1 RandomDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X78FE275E7E77D56F\">3.4-2 RandomMultiDigraph</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X\
7D36B5E57F055051\">3.4-3 RandomTournament</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7A023E4\
787682475\">3.4-4 RandomLattice</a></span>\n</div></div>\n<div class=\"ContSec\
t\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap3\
_mj.html#X7C76D1DC7DAF03D3\">3.5 <span class=\"Heading\">Standard examples</sp\
an></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X870594FC866AC8\
8E\">3.5-1 ChainDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X812417E278198D9C\">3.5-2\
 CompleteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8795B0AD856014FA\">3.5-3 Comple\
teBipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X873F29CC863241F8\">3.5-4 Compl\
eteMultipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X80C29DDE876FFBEB\">3.5-5 C\
ycleDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap3_mj.html#X80DAE31A79FEFD40\">3.5-6 EmptyDigraph\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chap3_mj.html#X80ED9CE785819607\">3.5-7 JohnsonDigraph</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap3_mj.html#X823F43217A6C375D\">3.5-8 PetersenGraph</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
3_mj.html#X7B5441F386BD105E\">3.5-9 GeneralisedPetersenGraph</a></span>\n</div\
></div>\n</div>\n", 
      4 := "<div class=\"ChapSects\"><a href=\"chap4_mj.html#X7AD6F77E7D95C996\
\">4 <span class=\"Heading\">Operators</span></a>\n<div class=\"ContSect\"><sp\
an class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap4_mj.htm\
l#X84E0B5B88358C96B\">4.1 <span class=\"Heading\">Operators for digraphs</span\
></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X829B911D7EFD2D85\
\">4.1-1 IsSubdigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X833C3299787E2309\">4.1-2 Is\
UndirectedSpanningTree</a></span>\n</div></div>\n</div>\n", 
      5 := "<div class=\"ChapSects\"><a href=\"chap5_mj.html#X8739F6CD78C90B14\
\">5 <span class=\"Heading\">Attributes and operations</span></a>\n<div class=\
\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hre\
f=\"chap5_mj.html#X7E814B6478F7D015\">5.1 <span class=\"Heading\">Vertices and\
 edges</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C4\
5F7D878D896AC\">5.1-1 DigraphVertices</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C6F19B57CB\
2E882\">5.1-2 DigraphNrVertices</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7D1C6A4D7ECEC317\
\">5.1-3 DigraphEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X85E1CFDD7E164AD0\">5.1-4 Di\
graphNrEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap5_mj.html#X7BDABAF07917462B\">5.1-5 DigraphNrLo\
ops</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap5_mj.html#X85D5E08280914EE4\">5.1-6 DigraphSinks</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap5_mj.html#X7F5C6268839BE98C\">5.1-7 DigraphSources</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap5_mj.html#X785C30378064CF47\">5.1-8 DigraphTopologicalSort</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p5_mj.html#X7CA91E4B7904F793\">5.1-9 DigraphVertexLabel</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj\
.html#X7E51F2FE87140B32\">5.1-10 DigraphVertexLabels</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.h\
tml#X79FAEACC7F438C2F\">5.1-11 DigraphEdgeLabel</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7\
C24851087D4A8FB\">5.1-12 DigraphEdgeLabels</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7EFAF0\
1B7A155157\">5.1-13 DigraphInEdges</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BECFE6687ECD0\
28\">5.1-14 DigraphOutEdges</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BB8ED88835F07B4\">5.\
1-15 IsDigraphEdge</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X848FED0B7B4ACD1F\">5.1-16 IsMa\
tching</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X7B7A67277B1C9A02\">5.1-17 DigraphMaximalMa\
tching</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X78E9847A858788D1\">5.1-18 DigraphMaximumMa\
tching</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X7D7CE8328187D0D\
F\">5.2 <span class=\"Heading\">Neighbours and degree</span></a>\n</span>\n<di\
v class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7DC2CD70830BEE60\">5.2-1 AdjacencyM\
atrix</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap5_mj.html#X87FA0A727CDB060B\">5.2-2 CharacteristicPoly\
nomial</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X8507DC4F794780C1\">5.2-3 BooleanAdjacencyM\
atrix</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap5_mj.html#X7AFCE34A7A04D5C1\">5.2-4 DigraphAdjacencyFu\
nction</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X7FDEBF3279759961\">5.2-5 DigraphRange</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap5_mj.html#X7E9880767AE68E00\">5.2-6 OutNeighbours</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap5_mj.html#X85C7AA5A81DA6E11\">5.2-7 InNeighbours</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.h\
tml#X7F5ACE807D1BC2E2\">5.2-8 OutDegrees</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7ADDFBFD\
7A365775\">5.2-9 InDegrees</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7A09EB648070276D\">5.2\
-10 OutDegreeOfVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X83315B0186850806\">5.2-11 O\
utNeighboursOfVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C9CD0527CB9E6EF\">5.2-12 In\
DegreeOfVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C0DA18B8291F302\">5.2-13 InNeighb\
oursOfVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap5_mj.html#X83271F607BD809CF\">5.2-14 DigraphLoo\
ps</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap5_mj.html#X7DDB33B686B3A2C6\">5.2-15 PartialOrderDigraphM\
eetOfVertices</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BEAE1C78267F54D\">5.2-16 DegreeMat\
rix</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap5_mj.html#X865390B08331936B\">5.2-17 LaplacianMatrix</a>\
</span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span c\
lass=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X8537F4088400DC48\">5.3 <s\
pan class=\"Heading\">Reachability and connectivity</span></a>\n</span>\n<div \
class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap5_mj.html#X7F16B9EB8398459C\">5.3-1 DigraphDiame\
ter</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap5_mj.html#X8104A9D37BCD8A05\">5.3-2 DigraphShortestDista\
nce</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap5_mj.html#X81F99BC67E9D050F\">5.3-3 DigraphShortestDista\
nces</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap5_mj.html#X8223718079D98A82\">5.3-4 DigraphLongestDista\
nceFromVertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7CB7DDCD84621D38\">5.3-5 DigraphDis\
tanceSet</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap5_mj.html#X79A3DA4078CF3C90\">5.3-6 DigraphGirth</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap5_mj.html#X8374B7357EC189C1\">5.3-7 DigraphOddGirth</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X84688B337BDDBB09\">5.3-8 DigraphUndirectedGirth</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X842FAD6A7B835977\">5.3-9 DigraphConnectedComponents</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap5_mj.html#X8484EC557810CD31\">5.3-10 DigraphConnectedComponent</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap5_mj.html#X833ECD6B7A84944C\">5.3-11 DigraphStronglyConnectedCom\
ponents</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap5_mj.html#X7EFCB5017D662254\">5.3-12 DigraphStrongly\
ConnectedComponent</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7F1B5A2782F598B1\">5.3-13 Digr\
aphBicomponents</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7DDE06E47E605DD7\">5.3-14 Articul\
ationPoints</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap5_mj.html#X84D5A125848BD800\">5.3-15 Bridges</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap5_mj.html#X865590147BD1C507\">5.3-16 StrongOrientation</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap5_mj.html#X853D0B0981A33433\">5.3-17 DigraphPeriod</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p5_mj.html#X864A31A8809F61C2\">5.3-18 DigraphFloydWarshall</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5\
_mj.html#X7FBAB09E7C0BE5CF\">5.3-19 IsReachable</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7\
CAE81D97B43DDF3\">5.3-20 VerticesReachableFrom</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X80\
39170B82A32257\">5.3-21 DigraphPath</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X80E9D64584397\
3A6\">5.3-22 DigraphShortestPath</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C0416FE7A69CA2C\
\">5.3-23 IteratorOfPaths</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7ECD16838704FAAA\">5.3-\
24 DigraphAllSimpleCircuits</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C735C4E86BDD5F6\">5.\
3-25 DigraphLongestSimpleCircuit</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X870E04307C5F213F\
\">5.3-26 DigraphLayers</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7B2E42327DA118E0\">5.3-2\
7 DigraphDegeneracy</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X827C2BD17A4547E3\">5.3-28 Dig\
raphDegeneracyOrdering</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X863FDFC4839A3B82\">5.3-29 \
HamiltonianPath</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X82F30D5681466BC6\">5.3-30 NrSpann\
ingTrees</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap5_mj.html#X79352A8286D1D8F6\">5.3-31 DigraphDijkstr\
a</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><s\
pan class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X82F900777D677F55\">5\
.4 <span class=\"Heading\">Cayley graphs of groups</span></a>\n</span>\n<div c\
lass=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap5_mj.html#X7A000B1D7CCF7093\">5.4-1 GroupOfCayley\
Digraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap5_mj.html#X8528455987D7D2BF\">5.4-2 GeneratorsOfCayl\
eyDigraph</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocl\
ine\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X790FD6647ECC\
AE3C\">5.5 <span class=\"Heading\">Associated semigroups</span></a>\n</span>\n\
<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X87D5C60D7B0C1309\">5.5-1 AsSemi\
group</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap5_mj.html#X7C6D5EC27C51066B\">5.5-2 AsSemigroup</a></s\
pan>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span clas\
s=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X7E2305528492DDC0\">5.6 <span\
 class=\"Heading\">Planarity</span></a>\n</span>\n<div class=\"ContSSBlock\">\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X7DC478637E8C190D\">5.6-1 KuratowskiPlanarSubdigraph</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap5_mj.html#X78E8F09A8286501B\">5.6-2 KuratowskiOuterPlanarSubdigraph\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chap5_mj.html#X84E3947E7D39BA64\">5.6-3 PlanarEmbedding</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap5_mj.html#X85DFB8C18088711F\">5.6-4 OuterPlanarEmbedding</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X806D2D6B85E0B269\">5.6-5 SubdigraphHomeomorphicToK23</a></s\
pan>\n</div></div>\n</div>\n", 
      6 := "<div class=\"ChapSects\"><a href=\"chap6_mj.html#X7ADDEFD478D470D5\
\">6 <span class=\"Heading\">Properties of digraphs</span></a>\n<div class=\"C\
ontSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\
\"chap6_mj.html#X7F49388F8245F0E9\">6.1 <span class=\"Heading\">Edge propertie\
s</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7D92935C7\
D535187\">6.1-1 DigraphHasLoops</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7DB1BC2286FC08E2\
\">6.1-2 IsAntiSymmetricDigraph</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X860CFB0C8665F356\
\">6.1-3 IsBipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X790A4DBF8533516E\">6.\
1-4 IsCompleteBipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X81F28D4D879FE3B2\"\
>6.1-5 IsCompleteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7FD1A15779FEC341\">6.1-6\
 IsCompleteMultipartiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E894CCF7B1C27AE\"\
>6.1-7 IsEmptyDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X83762C257DED2751\">6.1-8 Is\
EquivalenceDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E8F37E585DAED52\">6.1-9 IsFun\
ctionalDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7BB84CFC7E8B2B26\">6.1-10 IsMultiD\
igraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap6_mj.html#X8462D8E2792B23F6\">6.1-11 IsReflexiveDigra\
ph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap6_mj.html#X81B3EA7887219860\">6.1-12 IsSymmetricDigraph</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap6_mj.html#X7DD8D1A185EBE865\">6.1-13 IsTournament</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap6_mj.html#X7F0835667F29F0C0\">6.1-14 IsTransitiveDigraph</a></span>\n<\
span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap6_mj.html#X8617726C7829F796\">6.1-15 IsPreorderDigraph</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p6_mj.html#X82BAE6D37D49A145\">6.1-16 IsPartialOrderDigraph</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
6_mj.html#X78D3E17B7F737516\">6.1-17 IsMeetSemilatticeDigraph</a></span>\n</di\
v></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap6_mj.html#X7AAF896982EC22FA\">6.2 <span class=\"\
Heading\">Regularity</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6\
_mj.html#X7A3F78B37E31D9E1\">6.2-1 IsInRegularDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.h\
tml#X7F0A806E7BCB413C\">6.2-2 IsOutRegularDigraph</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#\
X7AF9DB1E7DB12306\">6.2-3 IsRegularDigraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E2082\
AC7CAE59CD\">6.2-4 IsDistanceRegularDigraph</a></span>\n</div></div>\n<div cla\
ss=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a \
href=\"chap6_mj.html#X780DAEB37C5E07FD\">6.3 <span class=\"Heading\">Connectiv\
ity and cycles</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.h\
tml#X7BD08D4478218F77\">6.3-1 IsAcyclicDigraph</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X79\
563B297C220FB5\">6.3-2 IsChainDigraph</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X83C08C0B7EC\
1A91F\">6.3-3 IsConnectedDigraph</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X838FAF2D825977BE\
\">6.3-4 IsBiconnectedDigraph</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7D2A6572820B7F24\">\
6.3-5 IsBridgelessDigraph</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7B37B9467C68C208\">6.3-\
6 IsStronglyConnectedDigraph</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X80E883967EBE839E\">6\
.3-7 IsAperiodicDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7B46EA6C7B2DF2FB\">6.3-8\
 IsDirectedTree</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X80FC20FA7AC4BC2A\">6.3-9 IsUndire\
ctedTree</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap6_mj.html#X79DFBB198525544E\">6.3-10 IsEulerianDigr\
aph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap6_mj.html#X79EFEBC37C2D262D\">6.3-11 IsHamiltonianDigrap\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap6_mj.html#X7E91320B8028F5D8\">6.3-12 IsCycleDigraph</a></s\
pan>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span clas\
s=\"nocss\">&nbsp;</span><a href=\"chap6_mj.html#X7E2305528492DDC0\">6.4 <span\
 class=\"Heading\">Planarity</span></a>\n</span>\n<div class=\"ContSSBlock\">\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap6_mj.html#X8606D415858C40AA\">6.4-1 IsPlanarDigraph</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
6_mj.html#X8251E8B187E7F059\">6.4-2 IsOuterPlanarDigraph</a></span>\n</div></d\
iv>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nb\
sp;</span><a href=\"chap6_mj.html#X83DC8AD283C41326\">6.5 <span class=\"Headin\
g\">Homomorphisms and transformations</span></a>\n</span>\n<div class=\"ContSS\
Block\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap6_mj.html#X78C0B2637985648B\">6.5-1 IsDigraphCore</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap6_mj.html#X8361CA6E8401FF26\">6.5-2 IsEdgeTransitive</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6\
_mj.html#X7B26E4447A1611E9\">6.5-3 IsVertexTransitive</a></span>\n</div></div>\
\n</div>\n", 
      7 := "<div class=\"ChapSects\"><a href=\"chap7_mj.html#X84975388859F203D\
\">7 <span class=\"Heading\">Homomorphisms</span></a>\n<div class=\"ContSect\"\
><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap7_mj\
.html#X8200192B80AD2071\">7.1 <span class=\"Heading\">Acting on digraphs</span\
></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X808972017C486F1F\
\">7.1-1 OnDigraphs</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7AFBA7608498F9CE\">7.1-2 OnMu\
ltiDigraphs</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"to\
cline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap7_mj.html#X7E48B9F87A\
0F22D4\">7.2 <span class=\"Heading\">Isomorphisms and canonical labellings</sp\
an></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X83E593F3855B12\
2E\">7.2-1 DigraphsUseNauty</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X858C32127A190175\">7.\
2-2 AutomorphismGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7E7B0D88865A89F6\">7.2-3 Bl\
issAutomorphismGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X857758B18144C0CD\">7.2-4 Nau\
tyAutomorphismGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X877732B1783C391B\">7.2-5 Auto\
morphismGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7DA2C4FE837FFE01\">7.2-6 Automorphi\
smGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap7_mj.html#X7D676FE67A6684FF\">7.2-7 BlissCanonicalLa\
belling</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap7_mj.html#X87DA265D803DB337\">7.2-8 BlissCanonicalLa\
belling</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap7_mj.html#X877B1D377EC197D7\">7.2-9 BlissCanonicalDi\
graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap7_mj.html#X803ACEDA7BBAC5B3\">7.2-10 DigraphGroup</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap7_mj.html#X8096C5287E459279\">7.2-11 DigraphOrbits</a></span>\n<\
span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap7_mj.html#X8386028782F2D3FF\">7.2-12 DigraphOrbitReps</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
7_mj.html#X8657604E87A25E5F\">7.2-13 DigraphSchreierVector</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7\
_mj.html#X78913684795FB256\">7.2-14 DigraphStabilizer</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.h\
tml#X7B4F24B283C9EE28\">7.2-15 IsIsomorphicDigraph</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html\
#X7D4A1FA8868DA930\">7.2-16 IsIsomorphicDigraph</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8\
219FE6C839D9457\">7.2-17 IsomorphismDigraphs</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7ED\
93C0F86D9D34F\">7.2-18 IsomorphismDigraphs</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7E1C80\
6D81DFE15E\">7.2-19 RepresentativeOutNeighbours</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8\
0183D4A7C51365A\">7.2-20 IsDigraphIsomorphism</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7F1\
6B8B3825A627A\">7.2-21 IsDigraphColouring</a></span>\n</div></div>\n<div class\
=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hr\
ef=\"chap7_mj.html#X7E1A02FE8384C03C\">7.3 <span class=\"Heading\">Homomorphis\
ms of digraphs</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.h\
tml#X79ABF0E783FD67C7\">7.3-1 HomomorphismDigraphsFinder</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_m\
j.html#X85E9B019877AD7FE\">7.3-2 DigraphHomomorphism</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.h\
tml#X8653EDA183E06D05\">7.3-3 HomomorphismsDigraphs</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.htm\
l#X82D0FCD87D47ACA8\">7.3-4 DigraphMonomorphism</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8\
4B4BDB984C2A9A8\">7.3-5 MonomorphismsDigraphs</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7CB\
5AD9F861684FD\">7.3-6 DigraphEpimorphism</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7DFB1F5D\
873937B3\">7.3-7 EpimorphismsDigraphs</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7AD04CC186E\
86CCA\">7.3-8 DigraphEmbedding</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X82EBDF137EEDC5FD\"\
>7.3-9 EmbeddingsDigraphs</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X80FE9FCB79718A61\">7.3-\
10 IsDigraphHomomorphism</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7D6B5A0887903810\">7.3-1\
1 IsDigraphEmbedding</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7F80709A80CBFA98\">7.3-12 Di\
graphsRespectsColouring</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7E93B268823F6478\">7.3-1\
3 GeneratorsOfEndomorphismMonoid</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X86D0A74B83D6B9A7\
\">7.3-14 DigraphColouring</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7AB7200D831013C1\">7.3\
-15 DigraphGreedyColouring</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7F9CB3B27B9590DB\">7.3\
-16 DigraphWelshPowellOrder</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X807D49358529A37C\">7.\
3-17 ChromaticNumber</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X863487EF7D64EF56\">7.3-18 Di\
graphCore</a></span>\n</div></div>\n</div>\n", 
      8 := "<div class=\"ChapSects\"><a href=\"chap8_mj.html#X7A7E0B957932DF44\
\">8 <span class=\"Heading\">Finding cliques and independent sets</span></a>\n\
<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</\
span><a href=\"chap8_mj.html#X788474E38446039B\">8.1 <span class=\"Heading\">F\
inding cliques</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.h\
tml#X80670E3E7C36183F\">8.1-1 IsClique</a></span>\n<span class=\"ContSS\"><br \
/><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X7A3BC9FF81\
69ABCD\">8.1-2 CliquesFinder</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X789854AC7B466402\">8\
.1-3 DigraphClique</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X84EA2F9482B8D4AF\">8.1-4 Digra\
phMaximalCliques</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X78427A8B81FEB457\">8.1-5 Clique\
Number</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chap8_mj.html#X7E3125328770834\
8\">8.2 <span class=\"Heading\">Finding independent sets</span></a>\n</span>\n\
<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X790733B67B0BC894\">8.2-1 IsInde\
pendentSet</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap8_mj.html#X84350678782BFAB7\">8.2-2 DigraphIndepe\
ndentSet</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap8_mj.html#X7D2C78EB81A798A9\">8.2-3 DigraphMaximalI\
ndependentSets</a></span>\n</div></div>\n</div>\n", 
      9 := "<div class=\"ChapSects\"><a href=\"chap9_mj.html#X81714DBC80CC4BCB\
\">9 <span class=\"Heading\">Visualising and IO</span></a>\n<div class=\"ContS\
ect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"cha\
p9_mj.html#X7CF67F8278D9469C\">9.1 <span class=\"Heading\">Visualising a digra\
ph</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X83B33187\
84E78415\">9.1-1 Splash</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7F9B99C478EE093A\">9.1-2\
 DotDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap9_mj.html#X78DA31D1869D2F94\">9.1-3 DotSymmetric\
Digraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap9_mj.html#X84120D447E2CAC23\">9.1-4 DotPartialOrderD\
igraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap9_mj.html#X7F5653C8854FAEA6\">9.1-5 DotPreorderDigrap\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap9_mj.html#X808D12CF81E2C19F\">9.1-6 DotHighlightedDigraph<\
/a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><spa\
n class=\"nocss\">&nbsp;</span><a href=\"chap9_mj.html#X81C9B1DC791C0BBD\">9.2\
 <span class=\"Heading\">Reading and writing digraphs to a file</span></a>\n</\
span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X81FB5BE27903EC32\">9.2-1\
 String</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap9_mj.html#X873D6EB8836A3C61\">9.2-2 DigraphFromGraph\
6String</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap9_mj.html#X782A052979EA2376\">9.2-3 Graph6String</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap9_mj.html#X7845ACDA7D4D333D\">9.2-4 DigraphFile</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap9_mj.html#X7E8142007ED0CB9F\">9.2-5 ReadDigraphs</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.htm\
l#X82A4F0767C9EFC87\">9.2-6 WriteDigraphs</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X86D531B\
287733561\">9.2-7 IteratorFromDigraphFile</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7AAA358\
67B5D8BF4\">9.2-8 DigraphPlainTextLineEncoder</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X780\
8D99079295C22\">9.2-9 TournamentLineDecoder</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7DF22\
D1687D096D6\">9.2-10 AdjacencyMatrixUpperTriangleLineDecoder</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p9_mj.html#X875393338486D77D\">9.2-11 TCodeDecoder</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html\
#X8540FC21796A793F\">9.2-12 PlainTextString</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X81BD2\
3697857B244\">9.2-13 WritePlainTextDigraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X804FDF\
6A7ED64049\">9.2-14 WriteDIMACSDigraph</a></span>\n</div></div>\n</div>\n", 
      A := "<div class=\"ChapSects\"><a href=\"chapA_mj.html#X800DAF137BA8E25B\
\">A <span class=\"Heading\">\n    Grape to Digraphs Command Map\n  </span></a\
>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp\
;</span><a href=\"chapA_mj.html#X7CC8A9DB86F9F0F4\">A.1 <span class=\"Heading\
\">\n      Functions to construct and modify graphs\n    </span></a>\n</span>\
\n</div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chapA_mj.html#X7C38A6397D2770FB\">A.2 <span class=\"\
Heading\">\n      Functions to inspect graphs, vertices and edges\n    </span>\
</a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"tocline\"><span c\
lass=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X78A5A34783C70CD7\">A.3 <s\
pan class=\"Heading\">\n      Functions to determine regularity properties of \
graphs\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\
\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7C7497\
8D85F7AF5C\">A.4 <span class=\"Heading\">\n      Some special vertex subsets o\
f a graph\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span cla\
ss=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7E5\
1B92F7E89E266\">A.5 <span class=\"Heading\">\n      Functions to construct new\
 graphs from old\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><s\
pan class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.ht\
ml#X7A61E3FC7A2BB50E\">A.6 <span class=\"Heading\">\n      Vertex-Colouring an\
d Complete Subgraphs\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_\
mj.html#X7DFC61EC7CBDBC7E\">A.7 <span class=\"Heading\">\n      Automorphism g\
roups and isomorphism testing for graphs\n    </span></a>\n</span>\n</div>\n</\
div>\n" ), 
  chaptitle := 
    rec( 
      1 := "<span class=\"Heading\">\n    The <strong class=\"pkg\">Digraphs</\
strong> package\n  </span>", 
      2 := "<span class=\"Heading\">Installing <strong class=\"pkg\">Digraphs<\
/strong></span>", 3 := "<span class=\"Heading\">Creating digraphs</span>", 
      4 := "<span class=\"Heading\">Operators</span>", 
      5 := "<span class=\"Heading\">Attributes and operations</span>", 
      6 := "<span class=\"Heading\">Properties of digraphs</span>", 
      7 := "<span class=\"Heading\">Homomorphisms</span>", 
      8 := "<span class=\"Heading\">Finding cliques and independent sets</span\
>", 9 := "<span class=\"Heading\">Visualising and IO</span>", 
      A := "<span class=\"Heading\">\n    Grape to Digraphs Command Map\n  </s\
pan>" ), 
  content := 
    [ 
      rec( 
          content := "Book SYSTEM \"gapdoc.dtd\"\n   [ <!ENTITY Digraphs \"<Pac\
kage>Digraphs</Package>\">\n     <!ENTITY Grape \"<Alt Not='Text'><URL\n   Tex\
t='Grape'>http://www.maths.qmul.ac.uk/~leonard/grape/</URL></Alt><Alt\n   Only\
='Text'><Package>Grape</Package></Alt>\">\n     <!ENTITY bliss \"<Alt Not='Tex\
t'><URL\n   Text='bliss'>http://www.tcs.tkk.fi/Software/bliss/</URL></Alt><Alt\
\n   Only='Text'><Package>bliss</Package></Alt>\">\n     <!ENTITY edge-additio\
n-planarity-suite \"<Alt Not='Text'><URL \n         Text='edge-addition-planar\
ity-suite'>https://github.com/graph-algorithms/edge-addition-planarity-suite</\
URL></Alt><Alt\n       Only='Text'><Package>edge-addition-planarity-suite</Pac\
kage></Alt>\">\n     <!ENTITY nauty \"<Alt Not='Text'><URL\n   Text='nauty'>ht\
tp://pallini.di.uniroma1.it/</URL></Alt><Alt\n   Only='Text'><Package>nauty</P\
ackage></Alt>\">\n     <!ENTITY NautyTracesInterface \"<Alt Not='Text'><URL\n \
  Text='NautyTracesInterface'>https://github.com/gap-packages/NautyTracesInter\
face</URL></Alt><Alt\n   Only='Text'><Package>NautyTracesInterface</Package></\
Alt>\">\n     <!ENTITY IO \"<Alt Not='Text'><URL Text='IO'>\n     http://gap-p\
ackages.github.io/io/\n</URL></Alt><Alt Only='Text'><Package>IO</Package></Alt\
>\">\n     <!ENTITY Orb \"<Alt Not='Text'><URL Text='Orb'>\n     http://http:/\
/gap-packages.github.io/orb/</URL>\n     </Alt><Alt Only='Text'><Package>Orb</\
Package></Alt>\">\n     <!ENTITY datastructures \"<Alt Not='Text'><URL\n      \
 Text='datastructures'>https://github.com/gap-packages/datastructures</URL></A\
lt><Alt\n   Only='Text'><Package>datastructures</Package></Alt>\">\n     <!ENT\
ITY VERSION                  \"1.4.0\">\n<!ENTITY GAPVERS                  \"4\
.10.0\">\n<!ENTITY GRAPEVERS                \"4.8.1\">\n<!ENTITY IOVERS       \
            \"4.5.1\">\n<!ENTITY ORBVERS                  \"4.8.2\">\n<!ENTITY\
 DATASTRUCTURESVERS       \"0.2.5\">\n<!ENTITY NAUTYTRACESINTERFACEVERS \"0.2\
\">\n<!ENTITY ARCHIVENAME    \"digraphs-1.4.0\">\n<!ENTITY COPYRIGHTYEARS \"20\
14-20\">\n\n   ]", count := [ 0, 0, 0, 1 ], name := "XMLDOCTYPE", root := ~ ),
      rec( attributes := rec( Name := "digraphs" ), 
          content := 
            [ 
              rec( attributes := rec(  ), 
                  content := 
                    [ 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 0, 0, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Package", next := 28, root := ~, 
                                  start := 1, stop := 27 ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Title", 
                          next := 2024, root := ~, start := 1999, 
                          stop := 2023 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Version 1.4.0", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Version", 
                          next := 2063, root := ~, start := 2027, 
                          stop := 2062 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Jan De Beule\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "jdebeule@cage.ugent.be",
                                          count := [ 0, 0, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Email", next := 2129, root := ~, 
                                  start := 2092, stop := 2128 ), 
                              rec( content := "\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://homepages.vub.ac.b\
e/~jdbeule", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Homepage", next := 2190, 
                                  root := ~, start := 2134, stop := 2189 ), 
                              rec( content := "\n  ", count := [ 0, 0, 0, 1 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 0, 1 ], 
                          name := "Author", next := 2202, root := ~, 
                          start := 2067, stop := 2201 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Julius Jonušas\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "julius.jonusas@tuwien.ac.\
at", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                         ) ], count := [ 0, 0, 0, 1 ], 
                                  mathmode := "Text", name := "Email", 
                                  next := 2280, root := ~, start := 2238, 
                                  stop := 2279 ), 
                              rec( content := "\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://julius.jonusas.wor\
k", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                         ) ], count := [ 0, 0, 0, 1 ], 
                                  mathmode := "Text", name := "Homepage", 
                                  next := 2332, root := ~, start := 2285, 
                                  stop := 2331 ), 
                              rec( content := "\n  ", count := [ 0, 0, 0, 1 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 0, 1 ], 
                          name := "Author", next := 2344, root := ~, 
                          start := 2206, stop := 2343 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "James D. Mitchell\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "jdm3@st-and.ac.uk", 
                                          count := [ 0, 0, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Email", next := 2410, root := ~, 
                                  start := 2378, stop := 2409 ), 
                              rec( content := "\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "https://jdbm.me", 
                                          count := [ 0, 0, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Homepage", next := 2451, 
                                  root := ~, start := 2415, stop := 2450 ), 
                              rec( content := "\n  ", count := [ 0, 0, 0, 1 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 0, 1 ], 
                          name := "Author", next := 2463, root := ~, 
                          start := 2348, stop := 2462 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Michael Torpey\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "mct25@st-andrews.ac.uk",
                                          count := [ 0, 0, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Email", next := 2531, root := ~, 
                                  start := 2494, stop := 2530 ), 
                              rec( content := "\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "https://mtorpey.github.io\
", count := [ 0, 0, 0, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                     ], count := [ 0, 0, 0, 1 ], 
                                  mathmode := "Text", name := "Homepage", 
                                  next := 2582, root := ~, start := 2536, 
                                  stop := 2581 ), 
                              rec( content := "\n  ", count := [ 0, 0, 0, 1 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 0, 1 ], 
                          name := "Author", next := 2594, root := ~, 
                          start := 2467, stop := 2593 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Wilf A. Wilson\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "gap@wilf-wilson.net", 
                                          count := [ 0, 0, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Email", next := 2659, root := ~, 
                                  start := 2625, stop := 2658 ), 
                              rec( content := "\n    ", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "http://wilf.me", 
                                          count := [ 0, 0, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "Homepage", next := 2699, 
                                  root := ~, start := 2664, stop := 2698 ), 
                              rec( content := "\n  ", count := [ 0, 0, 0, 1 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 0, 1 ], 
                          name := "Author", next := 2711, root := ~, 
                          start := 2598, stop := 2710 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Stuart Burrell", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Author", 
                          next := 2746, root := ~, start := 2715, 
                          stop := 2745 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Reinis Cirpons", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Author", 
                          next := 2781, root := ~, start := 2750, 
                          stop := 2780 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Luke Elliott", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Author", 
                          next := 2814, root := ~, start := 2785, 
                          stop := 2813 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Max Horn", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Author", 
                          next := 2843, root := ~, start := 2818, 
                          stop := 2842 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Christopher Jefferson", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Author", 
                          next := 2885, root := ~, start := 2847, 
                          stop := 2884 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Markus Pfeiffer", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Author", 
                          next := 2921, root := ~, start := 2889, 
                          stop := 2920 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Chris Russell", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Author", 
                          next := 2955, root := ~, start := 2925, 
                          stop := 2954 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Finn Smith", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Author", 
                          next := 2986, root := ~, start := 2959, 
                          stop := 2985 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Murray White", 
                                  count := [ 0, 0, 0, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 0, 1 ], name := "Author", 
                          next := 3019, root := ~, start := 2990, 
                          stop := 3018 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( 
                                  content := "© 2014-20 by\n    Jan De Beule, \
Julius Jonušas, James D. Mitchell, Michael\n    Torpey, Wilf A. Wilson et al.\
", count := [ 0, 0, 1, 1 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 0, 0, 1, 2 ], mathmode := "Text",
                                  name := "P", next := 3169, root := ~, 
                                  start := 3165, stop := 3168 ), 
                              rec( content := "\n\n    ", 
                                  count := [ 0, 0, 1, 2 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 0, 0, 1, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 1, 2 ], mathmode := "Text",
                                  name := "Package", next := 28, root := ~, 
                                  start := 1, stop := 27 ), 
                              rec( 
                                  content := " is free software; you can redis\
tribute it and/or modify it\n    under the terms of the ", 
                                  count := [ 0, 0, 1, 2 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( Text := "GNU General Public License" 
                                     ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n    http://www.fsf.org/\
licenses/gpl.html", count := [ 0, 0, 1, 2 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 1, 2 ], mathmode := "Text",
                                  name := "URL", next := 3358, root := ~, 
                                  start := 3272, stop := 3357 ), 
                              rec( 
                                  content := " as published by the Free Softwa\
re\n    Foundation; either version 3 of the License, or (at your option) any l\
ater\n    version.\n  ", count := [ 0, 0, 1, 2 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 0, 0, 1, 1 ], name := "Copyright", 
                          next := 3499, root := ~, start := 3023, 
                          stop := 3498 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n    The ", 
                                  count := [ 0, 0, 2, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 0, 0, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 2, 1 ], mathmode := "Text",
                                  name := "Package", next := 28, root := ~, 
                                  start := 1, stop := 27 ), 
                              rec( content := " package is a ", 
                                  count := [ 0, 0, 2, 1 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "GAP", 
                                          count := [ 0, 0, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 2, 1 ], mathmode := "Text",
                                  name := "Package", next := 23, root := ~, 
                                  start := 1, stop := 22 ), 
                              rec( 
                                  content := " package containing methods for \
graphs,\n    digraphs, and multidigraphs.\n  ", count := [ 0, 0, 2, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 2, 1 ], 
                          name := "Abstract", next := 3637, root := ~, 
                          start := 3503, stop := 3636 ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( 
                                  content := "\n    We would like to thank Chri\
stopher Jefferson for his help in including \n    ", count := [ 0, 0, 3, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Not := "Text" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec( Text := "bliss" )
                                            , 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "http://www.tcs.tk\
k.fi/Software/bliss/", count := [ 0, 0, 3, 1 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 0, 0, 3, 1 ],
                                          mathmode := "Text", name := "URL", 
                                          next := 81, root := ~, start := 17, 
                                          stop := 80 ) ], 
                                  count := [ 0, 0, 3, 1 ], name := "Alt", 
                                  next := 87, root := ~, start := 1, 
                                  stop := 86 ), 
                              rec( attributes := rec( Only := "Text" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "bliss", 
                                                  count := [ 0, 0, 3, 1 ], 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 0, 0, 3, 1 ],
                                          name := "Package", next := 131, 
                                          root := ~, start := 107, 
                                          stop := 130 ) ], 
                                  count := [ 0, 0, 3, 1 ], mathmode := "Text",
                                  name := "Alt", next := 137, root := ~, 
                                  start := 87, stop := 136 ), 
                              rec( content := " in ", count := [ 0, 0, 3, 1 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 0, 0, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 0, 0, 3, 1 ], mathmode := "Text",
                                  name := "Package", next := 28, root := ~, 
                                  start := 1, stop := 27 ), 
                              rec( 
                                  content := ".\n\n    This package's methods \
for computing digraph homomorphisms are based on work\n    by Max Neunhöffer,\
 and independently Artur Schäfer.\n  ", count := [ 0, 0, 3, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 0, 0, 3, 1 ], 
                          name := "Acknowledgements", next := 3932, 
                          root := ~, start := 3641, stop := 3931 ) ], 
                  count := [ 0, 0, 0, 1 ], mathmode := "Text", 
                  name := "TitlePage", next := 3946, root := ~, 
                  start := 1985, stop := 3945 ), 
              rec( attributes := rec(  ), content := 0, 
                  count := [ 0, 0, 4, 1 ], mathmode := "Text", 
                  name := "TableOfContents", next := 3967, root := ~, 
                  start := 3949, stop := 3966 ), 
              rec( attributes := rec(  ), 
                  content := 
                    [ 
                      rec( content := "\n  ", count := [ 0, 0, 4, 1 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Label := "The Digraphs package" 
                             ), 
                          content := 
                            [ 
                              rec( content := "\n  ", count := [ 1, 0, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "\n    The ", 
                                          count := [ 1, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 1, 0, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 1, 0, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := " package\n  ", 
                                          count := [ 1, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 1, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 4068, root := ~, 
                                  start := 4019, stop := 4067 ), 
                              rec( content := "\n  ", count := [ 1, 0, 0, 3 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Key := "Digraphs" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 1, 0, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 1, 0, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := " package overview", 
                                          count := [ 1, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 1, 0, 0, 3 ], mathmode := "Text",
                                  name := "Index", next := 4128, root := ~, 
                                  start := 4071, stop := 4127 ), 
                              rec( content := "\n\n", count := [ 1, 0, 0, 3 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Introduction", 
                                                  count := [ 1, 1, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 1, 1, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 4170, 
                                          root := ~, start := 4139, 
                                          stop := 4169 ), 
                                      rec( 
                                          content := "\n\n  This is the manual\
 for version 1.4.0 of the ", count := [ 1, 1, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 1, 1, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 1, 1, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " package.\n  This packag\
e was developed at the University of St Andrews by:\n  ", 
                                          count := [ 1, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Jan De Be\
ule,", count := [ 1, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 4346, root := ~, 
                                                  start := 4320, stop := 4345 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Julius Jo\
nušas,", count := [ 1, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 4384, root := ~, 
                                                  start := 4351, stop := 4383 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "James D. \
Mitchell,", count := [ 1, 1, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 4420, root := ~, 
                                                  start := 4389, stop := 4419 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Michael C\
. Torpey, and", count := [ 1, 1, 0, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 4460, root := ~, 
                                                  start := 4425, stop := 4459 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Wilf A. W\
ilson.", count := [ 1, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 13 ], 
                                                  name := "Item", 
                                                  next := 4493, root := ~, 
                                                  start := 4465, stop := 4492 
                                                 ) ], count := [ 1, 1, 0, 4 ],
                                          mathmode := "Text", name := "List", 
                                          next := 4503, root := ~, 
                                          start := 4309, stop := 4502 ), 
                                      rec( 
                                          content := "\n  Additional contribut\
ions were made by:\n  ", count := [ 1, 1, 0, 15 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Stuart Bu\
rrell,", count := [ 1, 1, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 17 ], 
                                                  name := "Item", 
                                                  next := 4586, root := ~, 
                                                  start := 4558, stop := 4585 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Reinis Ci\
rpons,", count := [ 1, 1, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 19 ], 
                                                  name := "Item", 
                                                  next := 4619, root := ~, 
                                                  start := 4591, stop := 4618 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Luke Elli\
ott,", count := [ 1, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 21 ], 
                                                  name := "Item", 
                                                  next := 4650, root := ~, 
                                                  start := 4624, stop := 4649 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Max Horn,\
", count := [ 1, 1, 0, 23 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 1, 1, 0, 23 ], 
                                                  name := "Item", 
                                                  next := 4677, root := ~, 
                                                  start := 4655, stop := 4676 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Christoph\
er Jefferson,", count := [ 1, 1, 0, 25 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 25 ], 
                                                  name := "Item", 
                                                  next := 4717, root := ~, 
                                                  start := 4682, stop := 4716 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Markus Pf\
eiffer,", count := [ 1, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 27 ], 
                                                  name := "Item", 
                                                  next := 4751, root := ~, 
                                                  start := 4722, stop := 4750 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Chris Rus\
sell,", count := [ 1, 1, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 29 ], 
                                                  name := "Item", 
                                                  next := 4783, root := ~, 
                                                  start := 4756, stop := 4782 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Finn Smit\
h, and", count := [ 1, 1, 0, 31 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 31 ], 
                                                  name := "Item", 
                                                  next := 4816, root := ~, 
                                                  start := 4788, stop := 4815 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Maria Tsa\
lakou,", count := [ 1, 1, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 33 ], 
                                                  name := "Item", 
                                                  next := 4849, root := ~, 
                                                  start := 4821, stop := 4848 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Murray Wh\
yte.", count := [ 1, 1, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 35 ], 
                                                  name := "Item", 
                                                  next := 4880, root := ~, 
                                                  start := 4854, stop := 4879 
                                                 ) ], 
                                          count := [ 1, 1, 0, 16 ], 
                                          mathmode := "Text", name := "List", 
                                          next := 4890, root := ~, 
                                          start := 4547, stop := 4889 ), 
                                      rec( content := "\n\n  The ", 
                                          count := [ 1, 1, 0, 37 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 1, 1, 0, 37 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ 1, 1, 0, 37 ], 
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " package contains a vari\
ety of methods for efficiently creating\n  and storing mutable and immutable d\
igraphs and computing information about\n    them.  Full explanations of all t\
he functions contained in the package are\n    provided below. ", 
                                          count := [ 1, 1, 0, 37 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 5152, root := ~, 
                                          start := 5148, stop := 5151 ), 
                                      rec( content := "\n\n  If the ", 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "Grape" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://ww\
w.maths.qmul.ac.uk/~leonard/grape/", count := [ 1, 1, 0, 38 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 87, 
                                                  root := ~, start := 17, 
                                                  stop := 86 ) ], 
                                          count := [ 1, 1, 0, 38 ], 
                                          name := "Alt", next := 93, 
                                          root := ~, start := 1, stop := 92 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "Grape", 
                                                          count := 
                                                            [ 1, 1, 0, 38 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  name := "Package", 
                                                  next := 137, root := ~, 
                                                  start := 113, stop := 136 ) 
                                             ], count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 143, root := ~, 
                                          start := 93, stop := 142 ), 
                                      rec( 
                                          content := " package is available, i\
t will be loaded automatically.\n  Digraphs created with the ", 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " package can be converte\
d to ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "Grape" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://ww\
w.maths.qmul.ac.uk/~leonard/grape/", count := [ 1, 1, 0, 38 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 87, 
                                                  root := ~, start := 17, 
                                                  stop := 86 ) ], 
                                          count := [ 1, 1, 0, 38 ], 
                                          name := "Alt", next := 93, 
                                          root := ~, start := 1, stop := 92 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "Grape", 
                                                          count := 
                                                            [ 1, 1, 0, 38 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  name := "Package", 
                                                  next := 137, root := ~, 
                                                  start := 113, stop := 136 ) 
                                             ], count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 143, root := ~, 
                                          start := 93, stop := 142 ), 
                                      rec( content := "\n  graphs with ", 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := rec( Oper := "Graph" )
                                            , content := 0, 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", name := "Ref", 
                                          next := 5334, root := ~, 
                                          start := 5315, stop := 5333 ), 
                                      rec( content := ", and conversely ", 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "Grape" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://ww\
w.maths.qmul.ac.uk/~leonard/grape/", count := [ 1, 1, 0, 38 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 87, 
                                                  root := ~, start := 17, 
                                                  stop := 86 ) ], 
                                          count := [ 1, 1, 0, 38 ], 
                                          name := "Alt", next := 93, 
                                          root := ~, start := 1, stop := 92 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "Grape", 
                                                          count := 
                                                            [ 1, 1, 0, 38 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  name := "Package", 
                                                  next := 137, root := ~, 
                                                  start := 113, stop := 136 ) 
                                             ], count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 143, root := ~, 
                                          start := 93, stop := 142 ), 
                                      rec( 
                                          content := " graphs can be\n  conver\
ted to ", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := " objects with ", 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( Oper := "Digraph" ), 
                                          content := 0, 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", name := "Ref", 
                                          next := 5433, root := ~, 
                                          start := 5412, stop := 5432 ), 
                                      rec( content := ".  ", 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "Grape" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://ww\
w.maths.qmul.ac.uk/~leonard/grape/", count := [ 1, 1, 0, 38 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 87, 
                                                  root := ~, start := 17, 
                                                  stop := 86 ) ], 
                                          count := [ 1, 1, 0, 38 ], 
                                          name := "Alt", next := 93, 
                                          root := ~, start := 1, stop := 92 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "Grape", 
                                                          count := 
                                                            [ 1, 1, 0, 38 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  name := "Package", 
                                                  next := 137, root := ~, 
                                                  start := 113, stop := 136 ) 
                                             ], count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 143, root := ~, 
                                          start := 93, stop := 142 ), 
                                      rec( 
                                          content := " is not\n  required for \
", count := [ 1, 1, 0, 38 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                        , 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 1, 1, 0, 38 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := " to run. ", 
                                          count := [ 1, 1, 0, 38 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 5489, root := ~, 
                                          start := 5485, stop := 5488 ), 
                                      rec( content := "\n\n  The ", 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "bliss" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://ww\
w.tcs.tkk.fi/Software/bliss/", count := [ 1, 1, 0, 39 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 81, 
                                                  root := ~, start := 17, 
                                                  stop := 80 ) ], 
                                          count := [ 1, 1, 0, 39 ], 
                                          name := "Alt", next := 87, 
                                          root := ~, start := 1, stop := 86 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "bliss", 
                                                          count := 
                                                            [ 1, 1, 0, 39 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  name := "Package", 
                                                  next := 131, root := ~, 
                                                  start := 107, stop := 130 ) 
                                             ], count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 137, root := ~, 
                                          start := 87, stop := 136 ), 
                                      rec( content := " tool ", 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Key := "JK07" ),
                                          content := 0, 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", name := "Cite", 
                                          next := 5528, root := ~, 
                                          start := 5510, stop := 5527 ), 
                                      rec( 
                                          content := " is included in this pac\
kage.  It\n  is an open-source tool for computing automorphism groups and cano\
nical forms\n  of graphs, written by Tommi Junttila and Petteri Kaski. Several\
 of the methods\n  in the ", count := [ 1, 1, 0, 39 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := " package rely on ", 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "bliss" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://ww\
w.tcs.tkk.fi/Software/bliss/", count := [ 1, 1, 0, 39 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 81, 
                                                  root := ~, start := 17, 
                                                  stop := 80 ) ], 
                                          count := [ 1, 1, 0, 39 ], 
                                          name := "Alt", next := 87, 
                                          root := ~, start := 1, stop := 86 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "bliss", 
                                                          count := 
                                                            [ 1, 1, 0, 39 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  name := "Package", 
                                                  next := 131, root := ~, 
                                                  start := 107, stop := 130 ) 
                                             ], count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 137, root := ~, 
                                          start := 87, stop := 136 ), 
                                      rec( content := ". If the ", 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Text := "NautyTracesInte\
rface" ), content := [ rec( content := "https://github.com/gap-packages/NautyT\
racesInterface", count := [ 1, 1, 0, 39 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 111, 
                                                  root := ~, start := 17, 
                                                  stop := 110 ) ], 
                                          count := [ 1, 1, 0, 39 ], 
                                          name := "Alt", next := 117, 
                                          root := ~, start := 1, stop := 116 )
                                        , 
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "NautyTrac\
esInterface", count := [ 1, 1, 0, 39 ], name := "PCDATA", root := ~ ) ], 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  name := "Package", 
                                                  next := 176, root := ~, 
                                                  start := 137, stop := 175 ) 
                                             ], count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 182, root := ~, 
                                          start := 117, stop := 181 ), 
                                      rec( 
                                          content := "\n  package for GAP is a\
vailable then it is also possible to use ", count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "nauty" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://pa\
llini.di.uniroma1.it/", count := [ 1, 1, 0, 39 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 74, 
                                                  root := ~, start := 17, 
                                                  stop := 73 ) ], 
                                          count := [ 1, 1, 0, 39 ], 
                                          name := "Alt", next := 80, 
                                          root := ~, start := 1, stop := 79 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "nauty", 
                                                          count := 
                                                            [ 1, 1, 0, 39 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  name := "Package", 
                                                  next := 124, root := ~, 
                                                  start := 100, stop := 123 ) 
                                             ], count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 130, root := ~, 
                                          start := 80, stop := 129 ), 
                                      rec( content := " ", 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Key := "MP14" ),
                                          content := 0, 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", name := "Cite", 
                                          next := 5890, root := ~, 
                                          start := 5868, stop := 5889 ), 
                                      rec( 
                                          content := " for computing automorph\
ism groups and canonical forms\n  in ", count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 1, 1, 0, 39 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := ". See Section \n  ", 
                                          count := [ 1, 1, 0, 39 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( 
                                              Sect := "Isomorphisms and canoni\
cal labellings" ), content := 0, count := [ 1, 1, 0, 39 ], mathmode := "Text",
                                          name := "Ref", next := 6028, 
                                          root := ~, start := 5977, 
                                          stop := 6027 ), 
                                      rec( 
                                          content := " for more details.  \n  \
", count := [ 1, 1, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                        , 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 1, 1, 0, 40 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 6055, root := ~, 
                                          start := 6051, stop := 6054 ), 
                                      rec( 
                                          content := "\n\n  From version 1.0.0\
 of this package, digraphs can be either mutable or immutable.\n  Mutable digr\
aphs can be changed in-place by many of the methods in the\n  package, which a\
voids unnecessary copying. Immutable digraphs cannot be\n  changed in-place, b\
ut their advantage is that the value of an attribute of\n  an immutable digrap\
h is only ever computed once. Mutable digraphs can be\n  converted into immuta\
ble digraphs in-place using ", count := [ 1, 1, 0, 40 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( BookName := "ref", 
                                              Func := "MakeImmutable" ), 
                                          content := 0, 
                                          count := [ 1, 1, 0, 40 ], 
                                          mathmode := "Text", name := "Ref", 
                                          next := 6536, root := ~, 
                                          start := 6490, stop := 6535 ), 
                                      rec( 
                                          content := ".  One of the motivation\
s for introducing mutable\n  digraphs in version 1.0.0 was that in practice th\
e authors often wanted\n  to create a digraph and immediately modify it (remov\
ing certain edges,\n  loops, and so on). Before version 1.0.0, this involved c\
opying the digraph\n  several times, with each copy being discarded almost imm\
ediately.\n  From version 1.0.0, this unnecessary copying can be eliminated by\
\n  first creating a mutable digraph, then changing it in-place, and  finally\
\n  converting the mutable digraph to an immutable one in-place\n  (if desirab\
le).\n\n  ", count := [ 1, 1, 0, 40 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( Label := "Definitions" ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Definitio\
ns", count := [ 1, 1, 1, 2 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 1, 1, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Heading", 
                                                  next := 7167, root := ~, 
                                                  start := 7137, stop := 7166 
                                                 ), 
                                              rec( 
                                                  content := "\n\n    For the \
purposes of this package and its documentation, the following\n    definitions\
 apply: ", count := [ 1, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 7270, 
                                                  root := ~, start := 7266, 
                                                  stop := 7269 ), 
                                              rec( content := "\n\n    A ", 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "digraph",
                                                          count := 
                                                            [ 1, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 7292, 
                                                  root := ~, start := 7278, 
                                                  stop := 7291 ), 
                                              rec( content := " ", 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "E=(E^0,E^\
1,r,s)", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 7315, 
                                                  root := ~, start := 7293, 
                                                  stop := 7314 ), 
                                              rec( 
                                                  content := ", also known as \
a ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "directed\\
n      graph", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 7360, 
                                                  root := ~, start := 7333, 
                                                  stop := 7359 ), 
                                              rec( 
                                                  content := ", consists of a \
set of vertices ", count := [ 1, 1, 1, 4 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "E^0", 
                                                          count := 
                                                            [ 1, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 7402, 
                                                  root := ~, start := 7392, 
                                                  stop := 7401 ), 
                                              rec( 
                                                  content := " and a set of ed\
ges\n    ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "E^1", 
                                                          count := 
                                                            [ 1, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 7436, 
                                                  root := ~, start := 7426, 
                                                  stop := 7435 ), 
                                              rec( 
                                                  content := " together with f\
unctions ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "s, r: E^1\
 \\to E^0", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 7485, 
                                                  root := ~, start := 7461, 
                                                  stop := 7484 ), 
                                              rec( 
                                                  content := ", called the\n  \
  ", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "source",
                                                          count := 
                                                            [ 1, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 7515, 
                                                  root := ~, start := 7502, 
                                                  stop := 7514 ), 
                                              rec( content := " and ", 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "range", 
                                                          count := 
                                                            [ 1, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 7532, 
                                                  root := ~, start := 7520, 
                                                  stop := 7531 ), 
                                              rec( 
                                                  content := ", respectively.\\
n\n    The source and range of an edge is respectively the values of ", 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "s, r", 
                                                          count := 
                                                            [ 1, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 7626, 
                                                  root := ~, start := 7615, 
                                                  stop := 7625 ), 
                                              rec( 
                                                  content := " at\n    that ed\
ge.\n\n    An edge is called a ", count := [ 1, 1, 1, 4 ], mathmode := "Text",
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "loop", 
                                                          count := 
                                                            [ 1, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 7681, 
                                                  root := ~, start := 7670, 
                                                  stop := 7680 ), 
                                              rec( 
                                                  content := " if its source a\
nd range are the same.\n\n    A digraph is called a ", 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "multidigr\
aph", count := [ 1, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 7766, 
                                                  root := ~, start := 7747, 
                                                  stop := 7765 ), 
                                              rec( 
                                                  content := " if there exist \
two or more edges\n    with the same source and the same range. ", 
                                                  count := [ 1, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 7849, 
                                                  root := ~, start := 7845, 
                                                  stop := 7848 ), 
                                              rec( content := "\n\n    A ", 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "directed \
walk", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 7877, 
                                                  root := ~, start := 7857, 
                                                  stop := 7876 ), 
                                              rec( 
                                                  content := " on a digraph is\
 a sequence of alternating vertices\n    and edges ", count := [ 1, 1, 1, 5 ],
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "(v_1, e_1\
, v_2, e_2, ..., e_{n-1}, v_n)", count := [ 1, 1, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 7989, 
                                                  root := ~, start := 7943, 
                                                  stop := 7988 ), 
                                              rec( 
                                                  content := " such that each \
edge\n    ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "e_i", 
                                                          count := 
                                                            [ 1, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8024, 
                                                  root := ~, start := 8014, 
                                                  stop := 8023 ), 
                                              rec( content := " has source ", 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "v_i", 
                                                          count := 
                                                            [ 1, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8046, 
                                                  root := ~, start := 8036, 
                                                  stop := 8045 ), 
                                              rec( content := " and range ", 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "v_{i+1}",
                                                          count := 
                                                            [ 1, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8071, 
                                                  root := ~, start := 8057, 
                                                  stop := 8070 ), 
                                              rec( content := ". A ", 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "directed\\
n      path", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 8101, 
                                                  root := ~, start := 8075, 
                                                  stop := 8100 ), 
                                              rec( 
                                                  content := " is a directed w\
alk where no vertex (and hence no edge) is\n    repeated.  A ", 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "directed \
circuit", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 8200, 
                                                  root := ~, start := 8177, 
                                                  stop := 8199 ), 
                                              rec( 
                                                  content := " is a directed w\
alk where ", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "v_1 =\n  \
    v_n", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8248, 
                                                  root := ~, start := 8226, 
                                                  stop := 8247 ), 
                                              rec( content := ", and a ", 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "directed \
cycle", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 8277, 
                                                  root := ~, start := 8256, 
                                                  stop := 8276 ), 
                                              rec( 
                                                  content := " is a directed c\
ircuit where where no\n    vertex is repeated, except for ", 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "v_1 = v_n\
", count := [ 1, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8366, 
                                                  root := ~, start := 8350, 
                                                  stop := 8365 ), 
                                              rec( content := ".  ", 
                                                  count := [ 1, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 8373, 
                                                  root := ~, start := 8369, 
                                                  stop := 8372 ), 
                                              rec( content := "\n\n    The ", 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "length",
                                                          count := 
                                                            [ 1, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 8396, 
                                                  root := ~, start := 8383, 
                                                  stop := 8395 ), 
                                              rec( 
                                                  content := " of a directed w\
alk ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "(v_1, e_1\
, v_2, e_2, ..., e_{n-1},\n      v_n)", count := [ 1, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8468, 
                                                  root := ~, start := 8416, 
                                                  stop := 8467 ), 
                                              rec( content := " is equal to ",
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "n-1", 
                                                          count := 
                                                            [ 1, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8491, 
                                                  root := ~, start := 8481, 
                                                  stop := 8490 ), 
                                              rec( 
                                                  content := ", the number of \
edges it contains.  A\n    directed walk (or path) ", count := [ 1, 1, 1, 6 ],
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "(v_1, e_1\
, v_2, e_2, ..., e_{n-1}, v_n)", count := [ 1, 1, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8603, 
                                                  root := ~, start := 8557, 
                                                  stop := 8602 ), 
                                              rec( 
                                                  content := " is\n    sometim\
es called a directed walk (or path) ", count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "from vert\
ex ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
_1", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 1, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 8679, 
                                                          root := ~, 
                                                          start := 8669, 
                                                          stop := 8678 ), 
                                                      rec( 
                                                          content := " to\n   \
   vertex ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
_n", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 1, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 8706, 
                                                          root := ~, 
                                                          start := 8696, 
                                                          stop := 8705 ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 8710, 
                                                  root := ~, start := 8654, 
                                                  stop := 8709 ), 
                                              rec( 
                                                  content := ".  A directed wa\
lk of zero length, i.e. a sequence\n    ", count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "(v)", 
                                                          count := 
                                                            [ 1, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8775, 
                                                  root := ~, start := 8765, 
                                                  stop := 8774 ), 
                                              rec( 
                                                  content := " for some vertex\
 ", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                , 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "v", 
                                                          count := 
                                                            [ 1, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8800, 
                                                  root := ~, start := 8792, 
                                                  stop := 8799 ), 
                                              rec( content := ", is called ", 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "trivial",
                                                          count := 
                                                            [ 1, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 8826, 
                                                  root := ~, start := 8812, 
                                                  stop := 8825 ), 
                                              rec( 
                                                  content := ". A trivial\n   \
 directed walk is considered to be both a circuit and a cycle, as is the\n    \
empty directed walk ", count := [ 1, 1, 1, 6 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "()", 
                                                          count := 
                                                            [ 1, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "M", next := 8947, 
                                                  root := ~, start := 8938, 
                                                  stop := 8946 ), 
                                              rec( content := ". A ", 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "simple ci\
rcuit", count := [ 1, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "E", next := 8972, 
                                                  root := ~, start := 8951, 
                                                  stop := 8971 ), 
                                              rec( 
                                                  content := " is another name\
 for a\n    non-trivial and non-empty directed cycle.", 
                                                  count := [ 1, 1, 1, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 0, 
                                                  count := [ 1, 1, 1, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "P", next := 9044, 
                                                  root := ~, start := 9040, 
                                                  stop := 9043 ), 
                                              rec( content := "\n\n  ", 
                                                  count := [ 1, 1, 1, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 1, 1, 1, 1 ],
                                          mathmode := "Text", 
                                          name := "Subsection", next := 9061, 
                                          root := ~, start := 7105, 
                                          stop := 9060 ), 
                                      rec( content := "\n  ", 
                                          count := [ 1, 1, 1, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 1, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 9074, root := ~, 
                                  start := 4130, stop := 9073 ), 
                              rec( content := "\n", count := [ 1, 1, 1, 7 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 1, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 9085, root := ~, start := 3978, 
                          stop := 9084 ), 
                      rec( content := "\n ", count := [ 1, 1, 1, 7 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " intro ", count := [ 1, 1, 1, 7 ], 
                          mathmode := "Text", name := "XMLCOMMENT", root := ~ 
                         ), 
                      rec( content := "\n  ", count := [ 1, 1, 1, 7 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Label := "Installing Digraphs" )
                            , 
                          content := 
                            [ 
                              rec( content := "\n  ", count := [ 2, 0, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Installing ", 
                                          count := [ 2, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 0, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 0, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ) 
                                     ], count := [ 2, 0, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 9184, root := ~, start := 9144, 
                                  stop := 9183 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( Label := "For those in a hurry" ), 
                                  content := 
                                    [ 
                                      rec( content := "\n    ", 
                                          count := [ 2, 1, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "For those in a hu\
rry", count := [ 2, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 1, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 9270, 
                                          root := ~, start := 9231, 
                                          stop := 9269 ), 
                                      rec( 
                                          content := "\n    In this section we\
 give a brief description of how to start using\n    ", 
                                          count := [ 2, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 1, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 1, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := ".", 
                                          count := [ 2, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 2, 1, 0, 4 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 9360, root := ~, 
                                          start := 9356, stop := 9359 ), 
                                      rec( 
                                          content := "\n\n    It is assumed th\
at you have a working copy of ", count := [ 2, 1, 0, 4 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "GAP", 
                                                  count := [ 2, 1, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 1, 0, 4 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 23, 
                                          root := ~, start := 1, stop := 22 ),
                                      rec( 
                                          content := " with version number\n  \
  4.10.0 or higher. The most up-to-date version of ", count := [ 2, 1, 0, 4 ],
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "GAP", 
                                                  count := [ 2, 1, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 1, 0, 4 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 23, 
                                          root := ~, start := 1, stop := 22 ),
                                      rec( 
                                          content := " and instructions\n    o\
n how to install it can be obtained from the main ", count := [ 2, 1, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "GAP", 
                                                  count := [ 2, 1, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 1, 0, 4 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 23, 
                                          root := ~, start := 1, stop := 22 ),
                                      rec( content := " webpage\n    ", 
                                          count := [ 2, 1, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "http://www.gap-sy\
stem.org", count := [ 2, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 1, 0, 4 ], 
                                          mathmode := "Text", name := "URL", 
                                          next := 9626, root := ~, 
                                          start := 9590, stop := 9625 ), 
                                      rec( content := ".", 
                                          count := [ 2, 1, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 2, 1, 0, 5 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 9631, root := ~, 
                                          start := 9627, stop := 9630 ), 
                                      rec( 
                                          content := "\n\n    The following is\
 a summary of the steps that should lead to a\n    successful installation of \
", count := [ 2, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 1, 0, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 1, 0, 5 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := ":\n\n    ", 
                                          count := [ 2, 1, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 ensure that the ", count := [ 2, 1, 0, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "IO" ), content := [ rec( content := "\n     http://gap-packages\
.github.io/io/\n", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "URL",
                                                                  next := 78, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 77 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 7 ], 
                                                          name := "Alt", 
                                                          next := 84, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 83 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "IO", count := [ 2, 1, 0, 7 ], name := \
"PCDATA", root := ~ ) ], count := [ 2, 1, 0, 7 ], name := "Package", 
                                                                  next := 122,
                                                                  root := ~, 
                                                                  start := 101
                                                                    , 
                                                                  stop := 121 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 128, 
                                                          root := ~, 
                                                          start := 84, 
                                                          stop := 127 ), 
                                                      rec( 
                                                          content := " package\
 version 4.5.1 or higher is available.\n        ", count := [ 2, 1, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "IO" ), content := [ rec( content := "\n     http://gap-packages\
.github.io/io/\n", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "URL",
                                                                  next := 78, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 77 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 7 ], 
                                                          name := "Alt", 
                                                          next := 84, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 83 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "IO", count := [ 2, 1, 0, 7 ], name := \
"PCDATA", root := ~ ) ], count := [ 2, 1, 0, 7 ], name := "Package", 
                                                                  next := 122,
                                                                  root := ~, 
                                                                  start := 101
                                                                    , 
                                                                  stop := 121 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 128, 
                                                          root := ~, 
                                                          start := 84, 
                                                          stop := 127 ), 
                                                      rec( 
                                                          content := " must be\
 compiled before ", count := [ 2, 1, 0, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " can be \
loaded.\n      ", count := [ 2, 1, 0, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 9922, root := ~, 
                                                  start := 9761, stop := 9921 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 ensure that the ", count := [ 2, 1, 0, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Orb" ), content := [ rec( content := "\n     http://http://gap-\
packages.github.io/orb/", count := [ 2, 1, 0, 9 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 86, root := ~, start := 17, stop := 85 ), rec( content := "\n     "
                                                                    , 
                                                                  count := 
                                                                    [ 2, 1, 
                                                                      0, 9 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], 
                                                          name := "Alt", 
                                                          next := 98, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 97 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Orb", count := [ 2, 1, 0, 9 ], name :=\
 "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 115
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 98, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " package\
 version 4.8.2 or higher is available.\n        ", count := [ 2, 1, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Orb" ), content := [ rec( content := "\n     http://http://gap-\
packages.github.io/orb/", count := [ 2, 1, 0, 9 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 86, root := ~, start := 17, stop := 85 ), rec( content := "\n     "
                                                                    , 
                                                                  count := 
                                                                    [ 2, 1, 
                                                                      0, 9 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], 
                                                          name := "Alt", 
                                                          next := 98, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 97 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Orb", count := [ 2, 1, 0, 9 ], name :=\
 "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 9 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 115
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 98, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " has bet\
ter performance when compiled, but although compilation is\n        recommende\
d, it is not required to be compiled for ", count := [ 2, 1, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 1, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " to be\n\
        loaded.\n      ", count := [ 2, 1, 0, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 10202, root := ~, 
                                                  start := 9930, 
                                                  stop := 10201 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " ensure t\
hat the ", count := [ 2, 1, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "datastructures" ), content := [ rec( content := "https://github\
.com/gap-packages/datastructures", count := [ 2, 1, 0, 11 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 11 ], mathmode := "Tex\
t", name := "URL", next := 103, root := ~, start := 17, stop := 102 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 11 ], 
                                                          name := "Alt", 
                                                          next := 109, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 108 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "datastructures", count := [ 2, 1, 0, 1\
1 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 11 ], name := "Packa\
ge", next := 162, root := ~, start := 129, stop := 161 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 168, 
                                                          root := ~, 
                                                          start := 109, 
                                                          stop := 167 ), 
                                                      rec( 
                                                          content := " package\
 version\n        0.2.5 or higher is available. \n    ", count := 
                                                            [ 2, 1, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 10331, root := ~, 
                                                  start := 10210, 
                                                  stop := 10330 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 ", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "T\
his step is optional:", count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                          name := "B", 
                                                          next := 10383, 
                                                          root := ~, 
                                                          start := 10354, 
                                                          stop := 10382 ), 
                                                      rec( 
                                                          content := " certain\
 functions in ", count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " require\
\n        the ", count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ 2, 1, 0, 13 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ 2, 1, 0, 13 ], name\
 := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " package\
 to be available; see Section\n        ", count := [ 2, 1, 0, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Subsect := "The \
Grape package" ), content := 0, count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 10523, 
                                                          root := ~, 
                                                          start := 10489, 
                                                          stop := 10522 ), 
                                                      rec( 
                                                          content := " for ful\
l details.  To use these\n        functions make sure\n        that the ", 
                                                          count := 
                                                            [ 2, 1, 0, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ 2, 1, 0, 13 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ 2, 1, 0, 13 ], name\
 := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " package\
 version 4.8.1 or higher is available.\n        If ", count := [ 2, 1, 0, 13 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ 2, 1, 0, 13 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ 2, 1, 0, 13 ], name\
 := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 13 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " is not \
available, then ", count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 1, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " can be \
used as normal with\n        the exception that the functions listed in Subsec\
tion\n        ", count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Subsect := "The \
Grape package" ), content := 0, count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 10845, 
                                                          root := ~, 
                                                          start := 10811, 
                                                          stop := 10844 ), 
                                                      rec( 
                                                          content := " will no\
t work.\n      ", count := [ 2, 1, 0, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 0, 13 ], 
                                                  name := "Item", 
                                                  next := 10874, root := ~, 
                                                  start := 10339, 
                                                  stop := 10873 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "T\
his step is optional:", count := [ 2, 1, 0, 15 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], mathmode := "Text", 
                                                          name := "B", 
                                                          next := 10932, 
                                                          root := ~, 
                                                          start := 10903, 
                                                          stop := 10931 ), 
                                                      rec( 
                                                          content := " certain\
 functions in ", count := [ 2, 1, 0, 15 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " require\
\n          the ", count := [ 2, 1, 0, 15 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 2, 1, 0, 15 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 15 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 2, 1\
, 0, 15 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " package\
 to be available.\n        ", count := [ 2, 1, 0, 15 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          content := " TODO \n\
          see Section\n        <Ref Subsect=\"The Grape package\"/> for full d\
etails.  ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "XMLCOMMENT"
                                                            , root := ~ ), 
                                                      rec( 
                                                          content := "\n      \
  If you want to make use of these functions, please ensure that the\n        \
", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 2, 1, 0, 15 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 15 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 2, 1\
, 0, 15 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " package\
 version 0.2 or\n        higher is available.  If ", count := [ 2, 1, 0, 15 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 2, 1, 0, 15 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 15 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 2, 1\
, 0, 15 ], name := "PCDATA", root := ~ ) ], count := [ 2, 1, 0, 15 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 2, 1, 0, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " is not \
available,\n        then ", count := [ 2, 1, 0, 15 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " can be \
used as normal with the exception that \n          functions whose names conta\
in ", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "N\
auty", count := [ 2, 1, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "Q", 
                                                          next := 11491, 
                                                          root := ~, 
                                                          start := 11479, 
                                                          stop := 11490 ), 
                                                      rec( 
                                                          content := " will no\
t work.\n      ", count := [ 2, 1, 0, 15 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 0, 15 ], 
                                                  name := "Item", 
                                                  next := 11520, root := ~, 
                                                  start := 10888, 
                                                  stop := 11519 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 download the package archive ", count := [ 2, 1, 0, 17 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraphs-1.4.0.tar.gz", count := [ 2, 1, 0, 17 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 0, 17 ], mathmode := "Text", 
                                                          name := "F", 
                                                          next := 11599, 
                                                          root := ~, 
                                                          start := 11572, 
                                                          stop := 11598 ), 
                                                      rec( 
                                                          content := " from\n \
       ", count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Text := "the Dig\
raph package webpage" ), content := [ rec( content := "http://digraphs.github.\
io/Digraphs/", count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 11694, 
                                                          root := ~, 
                                                          start := 11613, 
                                                          stop := 11693 ), 
                                                      rec( 
                                                          content := ".\n     \
 ", count := [ 2, 1, 0, 17 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 2, 1, 0, 17 ], 
                                                  name := "Item", 
                                                  next := 11709, root := ~, 
                                                  start := 11528, 
                                                  stop := 11708 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 unzip and untar the file, this should create a directory called\n        ", 
                                                          count := 
                                                            [ 2, 1, 0, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraphs-1.4.0", count := [ 2, 1, 0, 19 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "F", 
                                                          next := 11824, 
                                                          root := ~, 
                                                          start := 11804, 
                                                          stop := 11823 ), 
                                                      rec( 
                                                          content := ".\n     \
 ", count := [ 2, 1, 0, 19 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 2, 1, 0, 19 ], 
                                                  name := "Item", 
                                                  next := 11839, root := ~, 
                                                  start := 11717, 
                                                  stop := 11838 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 locate the ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
kg", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "F", 
                                                          next := 11883, 
                                                          root := ~, 
                                                          start := 11873, 
                                                          stop := 11882 ), 
                                                      rec( 
                                                          content := " directo\
ry of your ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " directo\
ry, which contains\n        the directories ", count := [ 2, 1, 0, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ib", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "F", 
                                                          next := 11968, 
                                                          root := ~, 
                                                          start := 11958, 
                                                          stop := 11967 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 2, 1, 0, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
oc", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "F", 
                                                          next := 11980, 
                                                          root := ~, 
                                                          start := 11970, 
                                                          stop := 11979 ), 
                                                      rec( 
                                                          content := " and so \
on. Move the directory\n        ", count := [ 2, 1, 0, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraphs-1.4.0", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "F", 
                                                          next := 12039, 
                                                          root := ~, 
                                                          start := 12019, 
                                                          stop := 12038 ), 
                                                      rec( 
                                                          content := " into th\
e ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
kg", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "F", 
                                                          next := 12059, 
                                                          root := ~, 
                                                          start := 12049, 
                                                          stop := 12058 ), 
                                                      rec( 
                                                          content := " directo\
ry.\n      ", count := [ 2, 1, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 0, 21 ], 
                                                  name := "Item", 
                                                  next := 12084, root := ~, 
                                                  start := 11847, 
                                                  stop := 12083 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 it is necessary to compile the ", count := [ 2, 1, 0, 23 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 1, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 23 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " package\
.\n        Inside the ", count := [ 2, 1, 0, 23 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
kg/digraphs-1.4.0", count := [ 2, 1, 0, 23 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 0, 23 ], mathmode := "Text", 
                                                          name := "F", 
                                                          next := 12201, 
                                                          root := ~, 
                                                          start := 12177, 
                                                          stop := 12200 ), 
                                                      rec( 
                                                          content := " directo\
ry, type\n        ", count := [ 2, 1, 0, 23 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n./configure\nmake", count := [ 2, 1, 0, 24 ], name := "PCDATA", root := ~ ) ]
                                                            , 
                                                          count := 
                                                            [ 2, 1, 0, 24 ], 
                                                          mathmode := "Text", 
                                                          name := "Listing", 
                                                          next := 12274, 
                                                          root := ~, 
                                                          start := 12226, 
                                                          stop := 12273 ), 
                                                      rec( 
                                                          content := "\n      \
  Further information about this step can be found in Section\n        ", 
                                                          count := 
                                                            [ 2, 1, 0, 25 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Sect := "Compili\
ng the kernel module" ), content := 0, count := [ 2, 1, 0, 25 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 12392, 
                                                          root := ~, 
                                                          start := 12351, 
                                                          stop := 12391 ), 
                                                      rec( 
                                                          content := ".\n     \
 ", count := [ 2, 1, 0, 25 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 2, 1, 0, 23 ], 
                                                  name := "Item", 
                                                  next := 12407, root := ~, 
                                                  start := 12092, 
                                                  stop := 12406 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 start ", count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 27 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " in the \
usual way (i.e. type ", count := [ 2, 1, 0, 27 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ap", count := [ 2, 1, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 1, 0, 27 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 12480, 
                                                          root := ~, 
                                                          start := 12470, 
                                                          stop := 12479 ), 
                                                      rec( 
                                                          content := " at the \
command line).\n      ", count := [ 2, 1, 0, 27 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 1, 0, 27 ], 
                                                  name := "Item", 
                                                  next := 12516, root := ~, 
                                                  start := 12415, 
                                                  stop := 12515 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
 type ", count := [ 2, 1, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
oadPackage(\"digraphs\");", count := [ 2, 1, 0, 29 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 1, 0, 29 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 12575, 
                                                          root := ~, 
                                                          start := 12544, 
                                                          stop := 12574 ), 
                                                      rec( 
                                                          content := "\n      \
", count := [ 2, 1, 0, 29 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 2, 1, 0, 29 ], 
                                                  name := "Item", 
                                                  next := 12589, root := ~, 
                                                  start := 12524, 
                                                  stop := 12588 ) ], 
                                          count := [ 2, 1, 0, 6 ], 
                                          mathmode := "Text", name := "List", 
                                          next := 12601, root := ~, 
                                          start := 9747, stop := 12600 ), 
                                      rec( 
                                          content := "\n\n    If you want to c\
heck that the package is working correctly, you\n    should run some of the te\
sts described in Section\n    ", count := [ 2, 1, 0, 31 ], mathmode := "Text",
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( 
                                              Sect := "Testing your installati\
on" ), content := 0, count := [ 2, 1, 0, 31 ], mathmode := "Text", 
                                          name := "Ref", next := 12768, 
                                          root := ~, start := 12729, 
                                          stop := 12767 ), 
                                      rec( content := ".\n  ", 
                                          count := [ 2, 1, 0, 31 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 12782, 
                                  root := ~, start := 9188, stop := 12781 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 1, 0, 31 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 1, 0, 31 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n  ", 
                                  count := [ 2, 1, 0, 31 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 1, 0, 31 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 1, 0, 31 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( 
                                      Label := "Optional package dependencies"\
 ), content := [ rec( content := "\n    ", count := [ 2, 2, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Optional package \
dependencies", count := [ 2, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 2, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 13047, 
                                          root := ~, start := 12999, 
                                          stop := 13046 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 2, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          content := "************************\
********************************************", count := [ 2, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "XMLCOMMENT", root := ~ ), 
                                      rec( content := "\n\n    The ", 
                                          count := [ 2, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 2, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " package is written in "
                                            , count := [ 2, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "GAP", 
                                                  count := [ 2, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 2, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 23, 
                                          root := ~, start := 1, stop := 22 ),
                                      rec( 
                                          content := " and C code and requires\
 the\n    ", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "IO" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n     ht\
tp://gap-packages.github.io/io/\n", count := [ 2, 2, 0, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 78, 
                                                  root := ~, start := 17, 
                                                  stop := 77 ) ], 
                                          count := [ 2, 2, 0, 3 ], 
                                          name := "Alt", next := 84, 
                                          root := ~, start := 1, stop := 83 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "IO", 
                                                          count := 
                                                            [ 2, 2, 0, 3 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 0, 3 ], 
                                                  name := "Package", 
                                                  next := 122, root := ~, 
                                                  start := 101, stop := 121 ) 
                                             ], count := [ 2, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 128, root := ~, 
                                          start := 84, stop := 127 ), 
                                      rec( content := " package.  The ", 
                                          count := [ 2, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "IO" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n     ht\
tp://gap-packages.github.io/io/\n", count := [ 2, 2, 0, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 78, 
                                                  root := ~, start := 17, 
                                                  stop := 77 ) ], 
                                          count := [ 2, 2, 0, 3 ], 
                                          name := "Alt", next := 84, 
                                          root := ~, start := 1, stop := 83 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "IO", 
                                                          count := 
                                                            [ 2, 2, 0, 3 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 0, 3 ], 
                                                  name := "Package", 
                                                  next := 122, root := ~, 
                                                  start := 101, stop := 121 ) 
                                             ], count := [ 2, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 128, root := ~, 
                                          start := 84, stop := 127 ), 
                                      rec( 
                                          content := " package is used to read\
 and write transformations,\n    partial permutations, and bipartitions to a f\
ile. ", count := [ 2, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 2, 2, 0, 4 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 13342, root := ~, 
                                          start := 13338, stop := 13341 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 2, 2, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          content := "************************\
********************************************", count := [ 2, 2, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "XMLCOMMENT", root := ~ ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 2, 2, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( Label := "The Grape package" 
                                             ), 
                                          content := 
                                            [ 
                                              rec( content := "\n      ", 
                                                  count := [ 2, 2, 1, 1 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "The Grape\
 package", count := [ 2, 2, 1, 2 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Heading", 
                                                  next := 13510, root := ~, 
                                                  start := 13474, 
                                                  stop := 13509 ), 
                                              rec( 
                                                  content := "\n\n      The ",
                                                  count := [ 2, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Not := "Text" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Text := "Grape" 
                                                             ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ 2, 2, 1, 3 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 17, 
                                                          stop := 86 ) ], 
                                                  count := [ 2, 2, 1, 3 ], 
                                                  name := "Alt", next := 93, 
                                                  root := ~, start := 1, 
                                                  stop := 92 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Only := "Text" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
rape", count := [ 2, 2, 1, 3 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 2, 2, 1, 3 ], 
                                                          name := "Package", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 113, 
                                                          stop := 136 ) ], 
                                                  count := [ 2, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Alt", next := 143, 
                                                  root := ~, start := 93, 
                                                  stop := 142 ), 
                                              rec( 
                                                  content := " package must be\
 available for the following operations to be\n      available:\n\n      ", 
                                                  count := [ 2, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Oper := "Graph" ), content := 0, count := [ 2, 2, 1, 5 ], mathmode := "T\
ext", name := "Ref", next := 13655, root := ~, start := 13636, stop := 13654 )
                                                                , 
                                                              rec( 
                                                                  content := "\
 with a digraph argument", count := [ 2, 2, 1, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 2, 2, 1, 5 ], name := "Item", next := 13686, 
                                                          root := ~, 
                                                          start := 13630, 
                                                          stop := 13685 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Attr := "AsGraph" ), content := 0, count := [ 2, 2, 1, 7 ], mathmode := \
"Text", name := "Ref", next := 13722, root := ~, start := 13701, stop := 13721\
 ), rec( content := " with a digraph argument", count := [ 2, 2, 1, 7 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 7 ], 
                                                          name := "Item", 
                                                          next := 13753, 
                                                          root := ~, 
                                                          start := 13695, 
                                                          stop := 13752 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Oper := "Digraph" ), content := 0, count := [ 2, 2, 1, 9 ], mathmode := \
"Text", name := "Ref", next := 13789, root := ~, start := 13768, stop := 13788\
 ), rec( content := " with a ", count := [ 2, 2, 1, 9 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( content := "http://www.math\
s.qmul.ac.uk/~leonard/grape/", count := [ 2, 2, 1, 9 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 9 ], mathmode := "Text", 
                                                                          name\
 := "URL", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                                    [ 2, 2, 
                                                                      1, 9 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( content :\
= "Grape", count := [ 2, 2, 1, 9 ], name := "PCDATA", root := ~ ) ], count := 
                                                                            [ \
2, 2, 1, 9 ], name := "Package", next := 137, root := ~, start := 113, stop :=\
 136 ) ], count := [ 2, 2, 1, 9 ], mathmode := "Text", name := "Alt", 
                                                                  next := 143,
                                                                  root := ~, 
                                                                  start := 93,
                                                                  stop := 142 
                                                                 ), 
                                                              rec( 
                                                                  content := "\
 graph argument", count := [ 2, 2, 1, 9 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 2, 2, 1, 9 ], name := "Item", next := 13826, 
                                                          root := ~, 
                                                          start := 13762, 
                                                          stop := 13825 ) ], 
                                                  count := [ 2, 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "List", 
                                                  next := 13840, root := ~, 
                                                  start := 13615, 
                                                  stop := 13839 ), 
                                              rec( content := "\n\n      If ",
                                                  count := [ 2, 2, 1, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Not := "Text" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Text := "Grape" 
                                                             ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ 2, 2, 1, 11 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 2, 2, 1, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 17, 
                                                          stop := 86 ) ], 
                                                  count := [ 2, 2, 1, 11 ], 
                                                  name := "Alt", next := 93, 
                                                  root := ~, start := 1, 
                                                  stop := 92 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Only := "Text" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
rape", count := [ 2, 2, 1, 11 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 2, 2, 1, 11 ], 
                                                          name := "Package", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 113, 
                                                          stop := 136 ) ], 
                                                  count := [ 2, 2, 1, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "Alt", next := 143, 
                                                  root := ~, start := 93, 
                                                  stop := 142 ), 
                                              rec( 
                                                  content := " is not availabl\
e, then ", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Digraphs"
                                                            , 
                                                          count := 
                                                            [ 2, 2, 1, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 2, 1, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "Package", 
                                                  next := 28, root := ~, 
                                                  start := 1, stop := 27 ), 
                                              rec( 
                                                  content := " can be used as \
normal with\n      the exception that the functions above will not work.\n    \
", count := [ 2, 2, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 2, 1, 1 ],
                                          mathmode := "Text", 
                                          name := "Subsection", 
                                          next := 13997, root := ~, 
                                          start := 13429, stop := 13996 ), 
                                      rec( content := "\n  ", 
                                          count := [ 2, 2, 1, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 14010, 
                                  root := ~, start := 12947, stop := 14009 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 2, 1, 11 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 2, 1, 11 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n  ", 
                                  count := [ 2, 2, 1, 11 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 2, 1, 11 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 2, 1, 11 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( 
                                      Label := "Compiling the kernel module" )
                                    , 
                                  content := 
                                    [ 
                                      rec( content := "\n    ", 
                                          count := [ 2, 3, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Compiling the ker\
nel module", count := [ 2, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 3, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 14271, 
                                          root := ~, start := 14225, 
                                          stop := 14270 ), 
                                      rec( content := "\n    The ", 
                                          count := [ 2, 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 3, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 3, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := " package has a ", 
                                          count := [ 2, 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "GAP", 
                                                  count := [ 2, 3, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 3, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 23, 
                                          root := ~, start := 1, stop := 22 ),
                                      rec( 
                                          content := " kernel component in\n  \
  C which should be compiled. This component contains certain low-level\n    f\
unctions required by ", count := [ 2, 3, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 3, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 3, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := ".\n    ", 
                                          count := [ 2, 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 2, 3, 0, 4 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 14451, root := ~, 
                                          start := 14447, stop := 14450 ), 
                                      rec( 
                                          content := "\n\n    It is not possib\
le to use the ", count := [ 2, 3, 0, 4 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 3, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 3, 0, 4 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " package without compili\
ng it.", count := [ 2, 3, 0, 4 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 2, 3, 0, 5 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 14531, root := ~, 
                                          start := 14527, stop := 14530 ), 
                                      rec( 
                                          content := "\n\n    To compile the k\
ernel component inside the ", count := [ 2, 3, 0, 5 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "pkg/digraphs-1.4.\
0", count := [ 2, 3, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 3, 0, 5 ],
                                          mathmode := "Text", name := "F", 
                                          next := 14604, root := ~, 
                                          start := 14580, stop := 14603 ), 
                                      rec( 
                                          content := "\n    directory, type\n"
                                            , count := [ 2, 3, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n\n./configure\n\
make", count := [ 2, 3, 0, 6 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ 2, 3, 0, 6 ], 
                                          mathmode := "Text", 
                                          name := "Listing", next := 14674, 
                                          root := ~, start := 14625, 
                                          stop := 14673 ), 
                                      rec( content := "\n    ", 
                                          count := [ 2, 3, 0, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 2, 3, 0, 8 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 14683, root := ~, 
                                          start := 14679, stop := 14682 ), 
                                      rec( 
                                          content := "\n\n    If you installed\
 the package in another 'pkg' directory than the standard 'pkg'\n    directory\
 in your ", count := [ 2, 3, 0, 8 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "GAP", 
                                                  count := [ 2, 3, 0, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 3, 0, 8 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 23, 
                                          root := ~, start := 1, stop := 22 ),
                                      rec( 
                                          content := " installation, then you \
have to do two things. Firstly\n    during compilation you have to use the opt\
ion '--with-gaproot=PATH' of the\n    'configure' script where 'PATH' is a pat\
h to the main GAP root directory (if\n    not given the default '../..' is ass\
umed).", count := [ 2, 3, 0, 8 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 2, 3, 0, 9 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 15061, root := ~, 
                                          start := 15057, stop := 15060 ), 
                                      rec( 
                                          content := "\n\n    If you installed\
 ", count := [ 2, 3, 0, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                        , 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "GAP", 
                                                  count := [ 2, 3, 0, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 3, 0, 9 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 23, 
                                          root := ~, start := 1, stop := 22 ),
                                      rec( 
                                          content := " on several architecture\
s, you must execute the\n    configure/make step for each of the architectures\
. You can either do this\n    immediately after configuring and compiling GAP \
itself on this architecture, or\n    alternatively set the environment\n    va\
riable 'CONFIGNAME' to the name of the configuration you used when compiling\n\
    GAP before running './configure'.  Note however that your compiler choice \
and\n    flags (environment variables 'CC' and 'CFLAGS') need to be chosen to \
match the\n    setup of the original GAP compilation. For example you have to \
specify 32-bit\n    or 64-bit mode correctly!\n  ", count := [ 2, 3, 0, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 3, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 15709, 
                                  root := ~, start := 14175, stop := 15708 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 3, 0, 9 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 3, 0, 9 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n  ", count := [ 2, 3, 0, 9 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 3, 0, 9 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 3, 0, 9 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( 
                                      Label := "Rebuilding the documentation" 
                                     ), 
                                  content := 
                                    [ 
                                      rec( content := "\n    ", 
                                          count := [ 2, 4, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Rebuilding the do\
cumentation", count := [ 2, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 4, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 15972, 
                                          root := ~, start := 15925, 
                                          stop := 15971 ), 
                                      rec( content := "\n    The ", 
                                          count := [ 2, 4, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 4, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 4, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " package comes complete \
with pdf, html, and text versions of\n    the documentation. However, you migh\
t find it necessary, at some point, to\n    rebuild the documentation. To rebu\
ild the documentation, please use the\n    function ", 
                                          count := [ 2, 4, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( Func := "DigraphsMakeDoc" ), 
                                          content := 0, 
                                          count := [ 2, 4, 0, 3 ], 
                                          mathmode := "Text", name := "Ref", 
                                          next := 16249, root := ~, 
                                          start := 16220, stop := 16248 ), 
                                      rec( content := ".\n\n    ", 
                                          count := [ 2, 4, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "", 
                                                      Name := "DigraphsMakeDoc\
" ), content := 0, count := [ 2, 4, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 16308, root := ~, 
                                                  start := 16271, 
                                                  stop := 16307 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Nothing",
                                                          count := 
                                                            [ 2, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 4, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 16337, root := ~, 
                                                  start := 16311, 
                                                  stop := 16336 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function should be called with no argument to compile the ", 
                                                          count := 
                                                            [ 2, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := "\n    do\
cumentation.\n  ", count := [ 2, 4, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 4, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 16467, root := ~, 
                                                  start := 16340, 
                                                  stop := 16466 ) ], 
                                          count := [ 2, 4, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 16481, root := ~, 
                                          start := 16256, stop := 16480 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 2, 4, 1, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 4, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 16495, 
                                  root := ~, start := 15874, stop := 16494 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 4, 1, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 4, 1, 3 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n  ", count := [ 2, 4, 1, 3 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 4, 1, 3 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 4, 1, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( Label := "Testing your installation" 
                                     ), 
                                  content := 
                                    [ 
                                      rec( content := "\n    ", 
                                          count := [ 2, 5, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Testing your inst\
allation", count := [ 2, 5, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 2, 5, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 16752, 
                                          root := ~, start := 16708, 
                                          stop := 16751 ), 
                                      rec( 
                                          content := "\n\n    In this section \
we describe how to test that ", count := [ 2, 5, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 5, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 5, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " is working as\n    inte\
nded.  To test that ", count := [ 2, 5, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 5, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 5, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " is installed correctly \
use\n    ", count := [ 2, 5, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( 
                                              Func := "DigraphsTestInstall" ),
                                          content := 0, 
                                          count := [ 2, 5, 0, 3 ], 
                                          mathmode := "Text", name := "Ref", 
                                          next := 16931, root := ~, 
                                          start := 16898, stop := 16930 ), 
                                      rec( 
                                          content := " or for more extensive t\
ests use\n    ", count := [ 2, 5, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( 
                                              Func := "DigraphsTestStandard" )
                                            , content := 0, 
                                          count := [ 2, 5, 0, 3 ], 
                                          mathmode := "Text", name := "Ref", 
                                          next := 17002, root := ~, 
                                          start := 16968, stop := 17001 ), 
                                      rec( content := ". ", 
                                          count := [ 2, 5, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ 2, 5, 0, 4 ], 
                                          mathmode := "Text", name := "P", 
                                          next := 17008, root := ~, 
                                          start := 17004, stop := 17007 ), 
                                      rec( 
                                          content := "\n\n    If something goe\
s wrong, then please review the instructions in Section ", 
                                          count := [ 2, 5, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( 
                                              Sect := "For those in a hurry" )
                                            , content := 0, 
                                          count := [ 2, 5, 0, 4 ], 
                                          mathmode := "Text", name := "Ref", 
                                          next := 17126, root := ~, 
                                          start := 17086, stop := 17125 ), 
                                      rec( content := " and ensure that ", 
                                          count := [ 2, 5, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 2, 5, 0, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 5, 0, 4 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " has been\n    properly \
installed.  If you continue having problems, please use the ", 
                                          count := [ 2, 5, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( 
                                          attributes := 
                                            rec( Text := "issue tracker" ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "https://github.co\
m/digraphs/Digraphs/issues", count := [ 2, 5, 0, 4 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 2, 5, 0, 4 ],
                                          mathmode := "Text", name := "URL", 
                                          next := 17317, root := ~, 
                                          start := 17236, stop := 17316 ), 
                                      rec( 
                                          content := "\n    to report the issu\
es you are having.\n\n    ", count := [ 2, 5, 0, 4 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "", 
                                                      Name := "DigraphsTestIns\
tall" ), content := 0, count := [ 2, 5, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 17420, root := ~, 
                                                  start := 17379, 
                                                  stop := 17419 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 17443, 
                                                          root := ~, 
                                                          start := 17432, 
                                                          stop := 17442 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 17459, 
                                                          root := ~, 
                                                          start := 17447, 
                                                          stop := 17458 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 17470, root := ~, 
                                                  start := 17423, 
                                                  stop := 17469 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function can be called without arguments to test your installation of\n    "
                                                            , 
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " is work\
ing correctly. These tests should take no more than a\n    few seconds to comp\
lete.  To test more comprehensively that\n    ", count := [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " is work\
ing correctly, use ", count := [ 2, 5, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sTestStandard" ), content := 0, count := [ 2, 5, 1, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 17781, 
                                                          root := ~, 
                                                          start := 17747, 
                                                          stop := 17780 ), 
                                                      rec( content := ".\n  ",
                                                          count := 
                                                            [ 2, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 17799, root := ~, 
                                                  start := 17473, 
                                                  stop := 17798 ) ], 
                                          count := [ 2, 5, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 17813, root := ~, 
                                          start := 17364, stop := 17812 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 2, 5, 1, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "", 
                                                      Name := "DigraphsTestSta\
ndard" ), content := 0, count := [ 2, 5, 2, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 17876, root := ~, 
                                                  start := 17834, 
                                                  stop := 17875 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 17899, 
                                                          root := ~, 
                                                          start := 17888, 
                                                          stop := 17898 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 17915, 
                                                          root := ~, 
                                                          start := 17903, 
                                                          stop := 17914 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 17926, root := ~, 
                                                  start := 17879, 
                                                  stop := 17925 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function can be called without arguments to test all of the methods\n    inc\
luded in ", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := ".\n    T\
hese tests should take less than a minute to complete. ", count := 
                                                            [ 2, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 2, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 18112, 
                                                          root := ~, 
                                                          start := 18108, 
                                                          stop := 18111 ), 
                                                      rec( 
                                                          content := "\n\n    \
To quickly test that ", count := [ 2, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " is inst\
alled correctly use ", count := [ 2, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sTestInstall" ), content := 0, count := [ 2, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 18214, 
                                                          root := ~, 
                                                          start := 18177, 
                                                          stop := 18213 ), 
                                                      rec( 
                                                          content := ".  For a\
 more thorough test, use ", count := [ 2, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sTestExtreme" ), content := 0, count := [ 2, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 18284, 
                                                          root := ~, 
                                                          start := 18247, 
                                                          stop := 18283 ), 
                                                      rec( content := ".\n  ",
                                                          count := 
                                                            [ 2, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 18302, root := ~, 
                                                  start := 17929, 
                                                  stop := 18301 ) ], 
                                          count := [ 2, 5, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 18316, root := ~, 
                                          start := 17819, stop := 18315 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 2, 5, 2, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "", 
                                                      Name := "DigraphsTestExt\
reme" ), content := 0, count := [ 2, 5, 3, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 18378, root := ~, 
                                                  start := 18337, 
                                                  stop := 18377 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Nothing."
                                                            , 
                                                          count := 
                                                            [ 2, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 18408, root := ~, 
                                                  start := 18381, 
                                                  stop := 18407 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function should be called with no argument. It executes a series of\n    ver\
y demanding tests, which measure the performance of a variety of\n    function\
s on large examples.  These tests take a long time to\n    complete, at least \
several minutes. ", count := [ 2, 5, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 2, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 18684, 
                                                          root := ~, 
                                                          start := 18680, 
                                                          stop := 18683 ), 
                                                      rec( 
                                                          content := "\n\n    \
For these tests to complete, the digraphs library ", count := [ 2, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraphs-lib", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 18759, 
                                                          root := ~, 
                                                          start := 18740, 
                                                          stop := 18758 ), 
                                                      rec( 
                                                          content := " must\n \
   be downloaded and placed in the ", count := [ 2, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraphs", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 18816, 
                                                          root := ~, 
                                                          start := 18801, 
                                                          stop := 18815 ), 
                                                      rec( 
                                                          content := " directo\
ry in a subfolder\n    named ", count := [ 2, 5, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraphs-lib", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "F", 
                                                          next := 18871, 
                                                          root := ~, 
                                                          start := 18852, 
                                                          stop := 18870 ), 
                                                      rec( 
                                                          content := ".\n    T\
his library can be found on the ", count := [ 2, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 2, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " website\
.\n  ", count := [ 2, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 2, 5, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 18946, root := ~, 
                                                  start := 18411, 
                                                  stop := 18945 ) ], 
                                          count := [ 2, 5, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 18960, root := ~, 
                                          start := 18322, stop := 18959 ), 
                                      rec( content := "\n\n\n  ", 
                                          count := [ 2, 5, 3, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 2, 5, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 18975, 
                                  root := ~, start := 16660, stop := 18974 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 2, 5, 3, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 5, 3, 4 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n  ", count := [ 2, 5, 3, 4 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  content := "********************************\
**************************************", count := [ 2, 5, 3, 4 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n\n\n", 
                                  count := [ 2, 5, 3, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 2, 0, 0, 1 ], mathmode := "Text", 
                          name := "Chapter", next := 19149, root := ~, 
                          start := 9104, stop := 19148 ), 
                      rec( content := "\n ", count := [ 2, 5, 3, 4 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " installing ", count := [ 2, 5, 3, 4 ],
                          mathmode := "Text", name := "XMLCOMMENT", root := ~ 
                         ), 
                      rec( content := "\n  ", count := [ 2, 5, 3, 4 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Label := "Creating digraphs" ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Creating digraphs", 
                                          count := [ 3, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 19244, 
                                  root := ~, start := 19208, stop := 19243 ), 
                              rec( 
                                  content := "\n\n  In this chapter we describ\
e how to create digraphs.", count := [ 3, 0, 0, 3 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 3, 0, 0, 4 ], mathmode := "Text",
                                  name := "P", next := 19303, root := ~, 
                                  start := 19299, stop := 19302 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 3, 0, 0, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Creating digraphs\
", count := [ 3, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                             ], count := [ 3, 1, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 19352, 
                                          root := ~, start := 19316, 
                                          stop := 19351 ), 
                                      rec( content := "\n    ", 
                                          count := [ 3, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Name := "IsDigraph", 
                                                      Type := "Category" ), 
                                                  content := 0, 
                                                  count := [ 3, 1, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Filt", 
                                                  next := 19412, root := ~, 
                                                  start := 19372, 
                                                  stop := 19411 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Eve\
ry  digraph in  ", count := [ 3, 1, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := "  belong\
s  to  the  category\n    ", count := [ 3, 1, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraph", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 19511, 
                                                          root := ~, 
                                                          start := 19495, 
                                                          stop := 19510 ), 
                                                      rec( 
                                                          content := ".  Some \
basic attributes and operations for digraphs\n    are ", count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Vertices" ), content := 0, count := [ 3, 1, 1, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 19601, 
                                                          root := ~, 
                                                          start := 19572, 
                                                          stop := 19600 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Edges" ), content := 0, count := [ 3, 1, 1, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 19629, 
                                                          root := ~, 
                                                          start := 19603, 
                                                          stop := 19628 ), 
                                                      rec( 
                                                          content := ", and\n \
   ", count := [ 3, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "OutNeig\
hbours" ), content := 0, count := [ 3, 1, 1, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 19666, 
                                                          root := ~, 
                                                          start := 19639, 
                                                          stop := 19665 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 19686, root := ~, 
                                                  start := 19415, 
                                                  stop := 19685 ) ], 
                                          count := [ 3, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 19700, root := ~, 
                                          start := 19357, stop := 19699 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 1, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Name := "IsMutableDigrap\
h", Type := "Category" ), content := 0, count := [ 3, 1, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Filt", 
                                                  next := 19768, root := ~, 
                                                  start := 19721, 
                                                  stop := 19767 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sMutableDigraph", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "C", 
                                                          next := 19812, 
                                                          root := ~, 
                                                          start := 19789, 
                                                          stop := 19811 ), 
                                                      rec( 
                                                          content := " is a sy\
nonym for ", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsDigra\
ph" ), content := 0, count := [ 3, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 19854, 
                                                          root := ~, 
                                                          start := 19830, 
                                                          stop := 19853 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Filt := "IsMutable" ), content := 0, count := [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 19902, 
                                                          root := ~, 
                                                          start := 19859, 
                                                          stop := 19901 ), 
                                                      rec( 
                                                          content := ".  A mut\
able digraph may be changed\n    in-place by methods in the ", 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 3, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " package\
, and is not attribute-storing\n    – see ", count := [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Filt := "IsAttributeStoringRep" ), content := 0, count := [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 20081, 
                                                          root := ~, 
                                                          start := 20030, 
                                                          stop := 20080 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 20091, 
                                                          root := ~, 
                                                          start := 20087, 
                                                          stop := 20090 ), 
                                                      rec( 
                                                          content := "\n\n    \
A mutable digraph may be converted into an immutable attribute-storing\n    di\
graph by calling ", count := [ 3, 1, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Func := "MakeImmutable" ), content := 0, count := [ 3, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 20233, 
                                                          root := ~, 
                                                          start := 20191, 
                                                          stop := 20232 ), 
                                                      rec( 
                                                          content := " on the\\
n    digraph.\n    ", count := [ 3, 1, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 20272, root := ~, 
                                                  start := 19771, 
                                                  stop := 20271 ) ], 
                                          count := [ 3, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 20286, root := ~, 
                                          start := 19706, stop := 20285 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 2, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Name := "IsImmutableDigr\
aph", Type := "Category" ), content := 0, count := [ 3, 1, 3, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Filt", 
                                                  next := 20356, root := ~, 
                                                  start := 20307, 
                                                  stop := 20355 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 3, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sImmutableDigraph", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "C", 
                                                          next := 20402, 
                                                          root := ~, 
                                                          start := 20377, 
                                                          stop := 20401 ), 
                                                      rec( 
                                                          content := " is a su\
bcategory of ", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsDigra\
ph" ), content := 0, count := [ 3, 1, 3, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 20447, 
                                                          root := ~, 
                                                          start := 20423, 
                                                          stop := 20446 ), 
                                                      rec( 
                                                          content := ".\n    D\
igraphs that lie in ", count := [ 3, 1, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sImmutableDigraph", count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 3, 1, 3, 3 ], mathmode := "Text", name := "C", 
                                                          next := 20499, 
                                                          root := ~, 
                                                          start := 20474, 
                                                          stop := 20498 ), 
                                                      rec( 
                                                          content := " are imm\
utable and\n    attribute-storing. In particular, they lie in\n    ", 
                                                          count := 
                                                            [ 3, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Filt := "IsAttributeStoringRep" ), content := 0, count := [ 3, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 20623, 
                                                          root := ~, 
                                                          start := 20572, 
                                                          stop := 20622 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 20629, 
                                                          root := ~, 
                                                          start := 20625, 
                                                          stop := 20628 ), 
                                                      rec( 
                                                          content := "\n\n    \
A mutable digraph may be converted to an immutable\n    digraph that lies in t\
he category ", count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sImmutableDigraph", count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "C", 
                                                          next := 20749, 
                                                          root := ~, 
                                                          start := 20724, 
                                                          stop := 20748 ), 
                                                      rec( 
                                                          content := " by call\
ing\n    ", count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Func := "MakeImmutable" ), content := 0, count := [ 3, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 20807, 
                                                          root := ~, 
                                                          start := 20765, 
                                                          stop := 20806 ), 
                                                      rec( 
                                                          content := " on the \
digraph.", count := [ 3, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 20827, 
                                                          root := ~, 
                                                          start := 20823, 
                                                          stop := 20826 ), 
                                                      rec( 
                                                          content := "\n\n    \
The operation ", count := [ 3, 1, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
MutableCopy" ), content := 0, count := [ 3, 1, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 20879, 
                                                          root := ~, 
                                                          start := 20847, 
                                                          stop := 20878 ), 
                                                      rec( 
                                                          content := " can be \
used\n    to construct a mutable copy of an immutable digraph. It is however n\
ot\n    possible to convert an immutable digraph into a mutable digraph in-pla\
ce.\n  ", count := [ 3, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 21061, root := ~, 
                                                  start := 20359, 
                                                  stop := 21060 ) ], 
                                          count := [ 3, 1, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 21075, root := ~, 
                                          start := 20292, stop := 21074 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 3, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Name := "IsCayleyDigraph\
", Type := "Category" ), content := 0, count := [ 3, 1, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Filt", 
                                                  next := 21142, root := ~, 
                                                  start := 21096, 
                                                  stop := 21141 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 3, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sCayleyDigraph", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 21185, 
                                                          root := ~, 
                                                          start := 21163, 
                                                          stop := 21184 ), 
                                                      rec( 
                                                          content := " is a su\
bcategory of ", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraph", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 21222, 
                                                          root := ~, 
                                                          start := 21206, 
                                                          stop := 21221 ), 
                                                      rec( 
                                                          content := ". Digrap\
hs that\n    are Cayley digraphs of a group and that are constructed by the op\
eration\n    ", count := [ 3, 1, 4, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "CayleyD\
igraph" ), content := 0, count := [ 3, 1, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 21346, 
                                                          root := ~, 
                                                          start := 21319, 
                                                          stop := 21345 ), 
                                                      rec( 
                                                          content := " are con\
structed in this category, and are\n    always immutable.\n    ", 
                                                          count := 
                                                            [ 3, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 21429, root := ~, 
                                                  start := 21145, 
                                                  stop := 21428 ) ], 
                                          count := [ 3, 1, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 21443, root := ~, 
                                          start := 21081, stop := 21442 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 4, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Name := "IsDigraphWithAd\
jacencyFunction", Type := "Category" ), content := 0, count := [ 3, 1, 5, 2 ],
                                                  mathmode := "Text", 
                                                  name := "Filt", 
                                                  next := 21525, root := ~, 
                                                  start := 21464, 
                                                  stop := 21524 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 3, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphWithAdjacencyFunction", count := [ 3, 1, 5, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 1, 5, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 21583, 
                                                          root := ~, 
                                                          start := 21546, 
                                                          stop := 21582 ), 
                                                      rec( 
                                                          content := " is a su\
bcategory of ", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraph", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 21620, 
                                                          root := ~, 
                                                          start := 21604, 
                                                          stop := 21619 ), 
                                                      rec( 
                                                          content := ".\n    D\
igraphs that are ", count := [ 3, 1, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
reated", count := [ 3, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 21658, 
                                                          root := ~, 
                                                          start := 21644, 
                                                          stop := 21657 ), 
                                                      rec( 
                                                          content := " using a\
n adjacency function are constructed\n    in this category.\n  ", 
                                                          count := 
                                                            [ 3, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 21741, root := ~, 
                                                  start := 21528, 
                                                  stop := 21740 ) ], 
                                          count := [ 3, 1, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 21755, root := ~, 
                                          start := 21449, stop := 21754 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 5, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Name := "DigraphByOutNei\
ghboursType" ), content := 0, count := [ 3, 1, 6, 2 ], mathmode := "Text", 
                                                  name := "Var", 
                                                  next := 21816, root := ~, 
                                                  start := 21776, 
                                                  stop := 21815 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Name := "DigraphFamily" 
                                                     ), content := 0, 
                                                  count := [ 3, 1, 6, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Fam", 
                                                  next := 21846, root := ~, 
                                                  start := 21819, 
                                                  stop := 21845 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
 type of all digraphs is ", count := [ 3, 1, 6, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphByOutNeighboursType", count := [ 3, 1, 6, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 1, 6, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 21928, 
                                                          root := ~, 
                                                          start := 21895, 
                                                          stop := 21927 ), 
                                                      rec( 
                                                          content := ".\n    T\
he family of all digraphs is ", count := [ 3, 1, 6, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphFamily", count := [ 3, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 21984, 
                                                          root := ~, 
                                                          start := 21964, 
                                                          stop := 21983 ), 
                                                      rec( content := ".\n  ",
                                                          count := 
                                                            [ 3, 1, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 6, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 22002, root := ~, 
                                                  start := 21849, 
                                                  stop := 22001 ) ], 
                                          count := [ 3, 1, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 22016, root := ~, 
                                          start := 21761, stop := 22015 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 6, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt,] obj[, so\
urce, range]", Name := "Digraph" ), content := 0, count := [ 3, 1, 7, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 22098, root := ~, 
                                                  start := 22037, 
                                                  stop := 22097 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt,] list, fu\
nc", Label := "for a list and function", Name := "Digraph" ), content := 0, 
                                                  count := [ 3, 1, 7, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 22191, root := ~, 
                                                  start := 22101, 
                                                  stop := 22190 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt,] G, list,\
 act, adj", Label := "for a group, list, function, and function", 
                                                      Name := "Digraph" ), 
                                                  content := 0, 
                                                  count := [ 3, 1, 7, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 22308, root := ~, 
                                                  start := 22194, 
                                                  stop := 22307 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 1, 7, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 22340, root := ~, 
                                                  start := 22311, 
                                                  stop := 22339 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
the optional first argument ", count := [ 3, 1, 7, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 22403, 
                                                          root := ~, 
                                                          start := 22392, 
                                                          stop := 22402 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 1, 7, 7 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 22549, 
                                                          root := ~, 
                                                          start := 22538, 
                                                          stop := 22548 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 1, 7, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 22583, 
                                                          root := ~, 
                                                          start := 22553, 
                                                          stop := 22582 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 22651, 
                                                          root := ~, 
                                                          start := 22640, 
                                                          stop := 22650 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 1, 7, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 22691, 
                                                          root := ~, 
                                                          start := 22655, 
                                                          stop := 22690 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 22776, 
                                                          root := ~, 
                                                          start := 22765, 
                                                          stop := 22775 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 1, 7, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 1, 7, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 22834, 
                                                          root := ~, 
                                                          start := 22798, 
                                                          stop := 22833 ), 
                                                      rec( 
                                                          content := " is used\
 by default.\n    ", count := [ 3, 1, 7, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "for a list (i.e. an adjacency list)", 
                                                                          coun\
t := [ 3, 1, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 3, 1, 
                                                                      7, 8 ], 
                                                                  name := "Mar\
k", next := 22920, root := ~, start := 22872, stop := 22919 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        if ", count := [ 3, 1, 7, 9\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
  ), content := [ rec( content := "obj", count := [ 3, 1, 7, 9 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmode := \
"Text", name := "A", next := 22955, root := ~, start := 22945, stop := 22954 )
                                                                        , 
                                                                      rec( 
                                                                          cont\
ent := " is a list of lists of positive integers in\n        the range from ",
                                                                          coun\
t := [ 3, 1, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "1", count := [ 3, 1, 7, 9 ], \
mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], 
                                                                          math\
mode := "Text", name := "C", next := 23030, root := ~, start := 23022, stop :=\
 23029 ), rec( content := " to ", count := [ 3, 1, 7, 9 ], mathmode := "Text",
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "Length(", count := [ 3, 1, 7, 9 ], mathmode := "Text", name := "PCDATA"\
, root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "obj",\
 count := [ 3, 1, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ],\
 count := [ 3, 1, 7, 9 ], mathmode := "Text", name := "A", next := 23054, root\
 := ~, start := 23044, stop := 23053 ), rec( content := ")", count := [ 3, 1, \
7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, \
7, 9 ], mathmode := "Text", name := "C", next := 23059, root := ~, start := 23\
034, stop := 23058 ), rec( content := ", then this function\n        returns t\
he digraph with vertices\n        ", count := [ 3, 1, 7, 9 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ re\
c( content := "E ^ 0 = ", count := [ 3, 1, 7, 9 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmode := "Text", name :=\
 "M", next := 23145, root := ~, start := 23130, stop := 23144 ), rec( attribut\
es := rec(  ), content := [ rec( content := "[1 .. Length(", count := [ 3, 1, \
7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := \
rec(  ), content := [ rec( content := "obj", count := [ 3, 1, 7, 9 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmode\
 := "Text", name := "A", next := 23171, root := ~, start := 23161, stop := 231\
70 ), rec( content := ")]", count := [ 3, 1, 7, 9 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmode := "Text", name \
:= "C", next := 23177, root := ~, start := 23145, stop := 23176 ), rec( conten\
t := ",\n        and edges corresponding to the entries of ", count := [ 3, 1,\
 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\
 rec(  ), content := [ rec( content := "obj", count := [ 3, 1, 7, 9 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], mathmod\
e := "Text", name := "A", next := 23239, root := ~, start := 23229, stop := 23\
238 ), rec( content := ". ", count := [ 3, 1, 7, 9 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 0, count := 
                                                                            [ \
3, 1, 7, 10 ], mathmode := "Text", name := "P", next := 23245, root := ~, star\
t := 23241, stop := 23244 ), rec( content := "\n\n        More precisely, ther\
e is an edge from vertex ", count := [ 3, 1, 7, 10 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "i", count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "C", next :=\
 23308, root := ~, start := 23300, stop := 23307 ), rec( content := " to ", 
                                                                          coun\
t := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "j", count := [ 3, 1, 7, 10 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 23320, root := ~, start := 23312, stop :=\
 23319 ), rec( content := " if and\n        only if ", count := [ 3, 1, 7, 10 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "j", count := [ 3, 1, 7, 10 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 23352, root := ~, start := 23344, stop := 23351 ), rec( conte\
nt := " is in ", count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA\
", root := ~ ), rec( attributes := rec(  ), content := [ rec( attributes := re\
c(  ), content := [ rec( content := "obj", count := [ 3, 1, 7, 10 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode\
 := "Text", name := "A", next := 23372, root := ~, start := 23362, stop := 233\
71 ), rec( content := "[i]", count := [ 3, 1, 7, 10 ], mathmode := "Text", nam\
e := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 23379, root := ~, start := 23359, stop := 23378 ), rec( conte\
nt := "; the source of this edge is\n        ", count := [ 3, 1, 7, 10 ], math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "i", count := [ 3, 1, 7, 10 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 23424, root := ~, start := 23416, stop := 23423 ), rec( conte\
nt := " and the range is ", count := [ 3, 1, 7, 10 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "j", count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "C", next :=\
 23450, root := ~, start := 23442, stop := 23449 ), rec( content := ". If ", 
                                                                          coun\
t := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "j", count := [ 3, 1, 7, 10 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 23463, root := ~, start := 23455, stop :=\
 23462 ), rec( content := " occurs in\n        ", count := [ 3, 1, 7, 10 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( attributes := rec(  ), content := [ rec( content := "obj", count\
 := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 3, 1, 7, 10 ], mathmode := "Text", name := "A", next := 23495, root := \
~, start := 23485, stop := 23494 ), rec( content := "[i]", count := [ 3, 1, 7,\
 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7\
, 10 ], mathmode := "Text", name := "C", next := 23502, root := ~, start := 23\
482, stop := 23501 ), rec( content := " with multiplicity ", count := [ 3, 1, \
7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\
 rec(  ), content := [ rec( content := "k", count := [ 3, 1, 7, 10 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmod\
e := "Text", name := "C", next := 23529, root := ~, start := 23521, stop := 23\
528 ), rec( content := ", then there are ", count := [ 3, 1, 7, 10 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content\
 := [ rec( content := "k", count := [ 3, 1, 7, 10 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name\
 := "C", next := 23554, root := ~, start := 23546, stop := 23553 ), rec( conte\
nt := "\n        edges from ", count := [ 3, 1, 7, 10 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "i", count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 3, 1, 7, 10 ], mathmode := "Text", name := "C", next :=\
 23582, root := ~, start := 23574, stop := 23581 ), rec( content := " to ", 
                                                                          coun\
t := [ 3, 1, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "j", count := [ 3, 1, 7, 10 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 10 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 23594, root := ~, start := 23586, stop :=\
 23593 ), rec( content := ".\n      ", count := [ 3, 1, 7, 10 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 9 ], name := "Item\
", next := 23609, root := ~, start := 22927, stop := 23608 ), rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "for three lists", count := [ 3, 1, 7,\
 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 3, 1, 
                                                                      7, 11 ],
                                                                  name := "Mar\
k", next := 23645, root := ~, start := 23617, stop := 23644 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        if ", count := [ 3, 1, 7, 1\
2 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\
(  ), content := [ rec( content := "obj", count := [ 3, 1, 7, 12 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode \
:= "Text", name := "A", next := 23680, root := ~, start := 23670, stop := 2367\
9 ), rec( content := " is a duplicate-free list, and ", count := [ 3, 1, 7, 12\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
  ), content := [ rec( content := "source", count := [ 3, 1, 7, 12 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmod\
e := "Text", name := "A", next := 23724, root := ~, start := 23711, stop := 23\
723 ), rec( content := " and\n        ", count := [ 3, 1, 7, 12 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :=\
 [ rec( content := "range", count := [ 3, 1, 7, 12 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", 
                                                                          name\
 := "A", next := 23749, root := ~, start := 23737, stop := 23748 ), rec( conte\
nt := " are lists of equal length consisting of positive integers\n        in \
the list ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "[1 .. Lengt\
h(", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~\
 ), rec( attributes := rec(  ), content := [ rec( content := "obj", count := [\
 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := \
[ 3, 1, 7, 12 ], mathmode := "Text", name := "A", next := 23854, root := ~, st\
art := 23844, stop := 23853 ), rec( content := ")]", count := [ 3, 1, 7, 12 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 23860, root := ~, start := 23828, stop :=\
 23859 ), rec( content := ", then this function\n        returns a digraph wit\
h vertices\n        ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :=\
 "E ^ 0 = ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "M", next \
:= 23944, root := ~, start := 23929, stop := 23943 ), rec( attributes := rec( \
 ), content := [ rec( content := "[1 .. Length(", count := [ 3, 1, 7, 12 ], ma\
thmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), c\
ontent := [ rec( content := "obj", count := [ 3, 1, 7, 12 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Tex\
t", name := "A", next := 23970, root := ~, start := 23960, stop := 23969 ), re\
c( content := ")]", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "C"
                                                                            , 
                                                                          next\
 := 23976, root := ~, start := 23944, stop := 23975 ), rec( content := ", and\
\n        ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "Length(", c\
ount := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), re\
c( attributes := rec(  ), content := [ rec( content := "source", count := [ 3,\
 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3\
, 1, 7, 12 ], mathmode := "Text", name := "A", next := 24013, root := ~, start\
 := 24000, stop := 24012 ), rec( content := ")", count := [ 3, 1, 7, 12 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], 
                                                                          math\
mode := "Text", name := "C", next := 24018, root := ~, start := 23990, stop :=\
 24017 ), rec( content := " edges.  For each ", count := [ 3, 1, 7, 12 ], math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "i", count := [ 3, 1, 7, 12 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 24044, root := ~, start := 24036, stop := 24043 ), rec( conte\
nt := " in\n        ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :=\
 "[1 .. Length(", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "sou\
rce", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := \
~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "A", next := 2408\
5, root := ~, start := 24072, stop := 24084 ), rec( content := ")]", count := \
[ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\
 [ 3, 1, 7, 12 ], mathmode := "Text", name := "C", next := 24091, root := ~, 
                                                                          star\
t := 24056, stop := 24090 ), rec( content := " there exists an edge with sourc\
e\n        vertex ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PC\
DATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\
source[i]", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", ro\
ot := ~ ) ], count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "C", next :\
= 24156, root := ~, start := 24140, stop := 24155 ), rec( content := " and ran\
ge vertex ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "range[i]", \
count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ],
                                                                          coun\
t := [ 3, 1, 7, 12 ], mathmode := "Text", name := "C", next := 24189, root := \
~, start := 24174, stop := 24188 ), rec( content := ".\n        See ", count :\
= [ 3, 1, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( 
                                                                          attr\
ibutes := rec( Attr := "DigraphSource" ), content := 0, count := [ 3, 1, 7, 12\
 ], mathmode := "Text", name := "Ref", next := 24230, root := ~, start := 2420\
3, stop := 24229 ), rec( content := " and ", count := [ 3, 1, 7, 12 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "D\
igraphRange" ), content := 0, count := [ 3, 1, 7, 12 ], mathmode := "Text", 
                                                                          name\
 := "Ref", next := 24261, root := ~, start := 24235, stop := 24260 ), rec( 
                                                                          cont\
ent := ".\n        ", count := [ 3, 1, 7, 12 ], mathmode := "Text", name := "P\
CDATA", root := ~ ), rec( attributes := rec(  ), content := 0, count := [ 3, 1\
, 7, 13 ], mathmode := "Text", name := "P", next := 24275, root := ~, start :=\
 24271, stop := 24274 ), rec( content := "\n\n        The vertices of the digr\
aph will be labelled by the elements of\n        ", count := [ 3, 1, 7, 13 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "obj", count := [ 3, 1, 7, 13 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 13 ], mathmode := "Text",
                                                                          name\
 := "A", next := 24367, root := ~, start := 24357, stop := 24366 ), rec( conte\
nt := ".\n      ", count := [ 3, 1, 7, 13 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 3, 1, 7, 12 ], name := "Item", next := 24382, 
                                                                  root := ~, 
                                                                  start := 236\
52, stop := 24381 ), rec( attributes := rec(  ), content := [ rec( content := \
"for an integer, and two lists", count := [ 3, 1, 7, 14 ], mathmode := "Text",
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 14 ], name := "Mark", 
                                                                  next := 2443\
2, root := ~, start := 24390, stop := 24431 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n        if ", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := \
"PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :\
= "obj", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "A", next := 2\
4467, root := ~, start := 24457, stop := 24466 ), rec( content := " is an inte\
ger, and ", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "source", co\
unt := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 3, 1, 7, 15 ], mathmode := "Text", name := "A", next := 24500, root := \
~, start := 24487, stop := 24499 ), rec( content := " and\n        ", count :=\
 [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\
ibutes := rec(  ), content := [ rec( content := "range", count := [ 3, 1, 7, 1\
5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, \
15 ], mathmode := "Text", name := "A", next := 24525, root := ~, start := 2451\
3, stop := 24524 ), rec( content := " are lists of equal length consisting of \
positive integers\n        in the list ", count := [ 3, 1, 7, 15 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :\
= [ rec( content := "[1 .. ", count := [ 3, 1, 7, 15 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( con\
tent := "obj", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA",\
 root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "A", nex\
t := 24623, root := ~, start := 24613, stop := 24622 ), rec( content := "]", c\
ount := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 3, 1, 7, 15 ], mathmode := "Text", name := "C", next := 24628, root := \
~, start := 24604, stop := 24627 ), rec( content := ", then this function\n   \
     returns a digraph with vertices\n        ", count := [ 3, 1, 7, 15 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "E ^ 0 = ", count := [ 3, 1, 7, 15 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "T\
ext", name := "M", next := 24712, root := ~, start := 24697, stop := 24711 ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[1 .. ", count := [ 3, 1, 7, \
15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\
c(  ), content := [ rec( content := "obj", count := [ 3, 1, 7, 15 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode\
 := "Text", name := "A", next := 24731, root := ~, start := 24721, stop := 247\
30 ), rec( content := "]", count := [ 3, 1, 7, 15 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name\
 := "C", next := 24736, root := ~, start := 24712, stop := 24735 ), rec( conte\
nt := ", and\n        ", count := [ 3, 1, 7, 15 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "Length(", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", \
root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "source"\
, count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) \
], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "A", next := 24773, r\
oot := ~, start := 24760, stop := 24772 ), rec( content := ")", count := [ 3, \
1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3,\
 1, 7, 15 ], mathmode := "Text", name := "C", next := 24778, root := ~, start \
:= 24750, stop := 24777 ), rec( content := " edges.  For each ", count := [ 3,\
 1, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\
s := rec(  ), content := [ rec( content := "i", count := [ 3, 1, 7, 15 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], 
                                                                          math\
mode := "Text", name := "C", next := 24804, root := ~, start := 24796, stop :=\
 24803 ), rec( content := " in\n        ", count := [ 3, 1, 7, 15 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content \
:= [ rec( content := "[1 .. Length(", count := [ 3, 1, 7, 15 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ \
rec( content := "source", count := [ 3, 1, 7, 15 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name \
:= "A", next := 24845, root := ~, start := 24832, stop := 24844 ), rec( conten\
t := ")]", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "C", next :=\
 24851, root := ~, start := 24816, stop := 24850 ), rec( content := " there ex\
ists an edge with source\n        vertex ", count := [ 3, 1, 7, 15 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content\
 := [ rec( content := "source[i]", count := [ 3, 1, 7, 15 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Tex\
t", name := "C", next := 24916, root := ~, start := 24900, stop := 24915 ), 
                                                                      rec( 
                                                                          cont\
ent := " and range vertex ", count := [ 3, 1, 7, 15 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "range[i]", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 24949, root := ~, start := 24934, stop := 24948 ), rec( content := ".\n   \
     See ", count := [ 3, 1, 7, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec( Attr := "DigraphSource" ), content := 0, coun\
t := [ 3, 1, 7, 15 ], mathmode := "Text", name := "Ref", next := 24990, root :\
= ~, start := 24963, stop := 24989 ), rec( content := " and ", count := [ 3, 1\
, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \
:= rec( Attr := "DigraphRange" ), content := 0, count := [ 3, 1, 7, 15 ], math\
mode := "Text", name := "Ref", next := 25021, root := ~, start := 24995, stop \
:= 25020 ), rec( content := ".\n      ", count := [ 3, 1, 7, 15 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 15 ], 
                                                                  name := "Ite\
m", next := 25036, root := ~, start := 24439, stop := 25035 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "for a list and a function", count := 
                                                                            [ \
3, 1, 7, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 3, 1, 
                                                                      7, 16 ],
                                                                  name := "Mar\
k", next := 25082, root := ~, start := 25044, stop := 25081 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        if ", count := [ 3, 1, 7, 1\
7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\
(  ), content := [ rec( content := "list", count := [ 3, 1, 7, 17 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode\
 := "Text", name := "A", next := 25118, root := ~, start := 25107, stop := 251\
17 ), rec( content := " is a list and ", count := [ 3, 1, 7, 17 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :=\
 [ rec( content := "func", count := [ 3, 1, 7, 17 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name\
 := "A", next := 25144, root := ~, start := 25133, stop := 25143 ), rec( conte\
nt := " is a function taking 2\n        arguments that are elements of ", coun\
t := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "list", count := [ 3, 1, 7, 17\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 1\
7 ], mathmode := "Text", name := "A", next := 25218, root := ~, start := 25207
                                                                            , 
                                                                          stop\
 := 25217 ), rec( content := ", and ", count := [ 3, 1, 7, 17 ], mathmode := "\
Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                            [ \
rec( content := "func", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name :=\
 "A", next := 25235, root := ~, start := 25224, stop := 25234 ), rec( content \
:= " returns\n        ", count := [ 3, 1, 7, 17 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "true", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "K", next :=\
 25263, root := ~, start := 25252, stop := 25262 ), rec( content := " or ", 
                                                                          coun\
t := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "false", count := [ 3, 1, 7, 1\
7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, \
17 ], mathmode := "Text", name := "K", next := 25279, root := ~, start := 2526\
7, stop := 25278 ), rec( content := ", then this operation creates a digraph w\
ith\n        vertices ", count := [ 3, 1, 7, 17 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "[1 .. Length(", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "l\
ist", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := \
~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "A", next := 2536\
8, root := ~, start := 25357, stop := 25367 ), rec( content := ")]", count := \
[ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\
 [ 3, 1, 7, 17 ], mathmode := "Text", name := "C", next := 25374, root := ~, 
                                                                          star\
t := 25341, stop := 25373 ), rec( content := " and an edge from vertex\n      \
  ", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~\
 ), rec( attributes := rec(  ), content := [ rec( content := "i", count := [ 3\
, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \
3, 1, 7, 17 ], mathmode := "Text", name := "C", next := 25415, root := ~, star\
t := 25407, stop := 25414 ), rec( content := " to vertex ", count := [ 3, 1, 7\
, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := "j", count := [ 3, 1, 7, 17 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode :\
= "Text", name := "C", next := 25434, root := ~, start := 25426, stop := 25433\
 ), rec( content := " if and only if\n        ", count := [ 3, 1, 7, 17 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( attributes := rec(  ), content := [ rec( content := "func", coun\
t := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], cou\
nt := [ 3, 1, 7, 17 ], mathmode := "Text", name := "A", next := 25472, root :=\
 ~, start := 25461, stop := 25471 ), rec( content := "(", count := [ 3, 1, 7, \
17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\
c(  ), content := [ rec( content := "list", count := [ 3, 1, 7, 17 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmod\
e := "Text", name := "A", next := 25484, root := ~, start := 25473, stop := 25\
483 ), rec( content := "[i], ", count := [ 3, 1, 7, 17 ], mathmode := "Text", \
name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( c\
ontent := "list", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "A", \
next := 25500, root := ~, start := 25489, stop := 25499 ), rec( content := "[j\
])", count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~\
 ) ], count := [ 3, 1, 7, 17 ], mathmode := "Text", name := "C", next := 25508
                                                                            , 
                                                                          root\
 := ~, start := 25458, stop := 25507 ), rec( content := " returns ", count := 
                                                                            [ \
3, 1, 7, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "true", count := [ 3, 1, 7, 17 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "K", next := 25528, root := ~, start := 25517, stop :=\
 25527 ), rec( content := ".\n      ", count := [ 3, 1, 7, 17 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 17 ], name := "Ite\
m", next := 25543, root := ~, start := 25089, stop := 25542 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "for a group, a list, and two function\
s", count := [ 3, 1, 7, 18 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 3, 1, 
                                                                      7, 18 ],
                                                                  name := "Mar\
k", next := 25602, root := ~, start := 25551, stop := 25601 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        The arguments will be ", 
                                                                          coun\
t := [ 3, 1, 7, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "G, list, act, adj", count := \
[ 3, 1, 7, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\
 [ 3, 1, 7, 19 ], mathmode := "Text", name := "A", next := 25670, root := ~, 
                                                                          star\
t := 25646, stop := 25669 ), rec( content := ". ", count := [ 3, 1, 7, 19 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := 0, count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "P", next := 2\
5676, root := ~, start := 25672, stop := 25675 ), rec( content := "\n\n       \
 Let ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ), rec( attributes := rec(  ), content := [ rec( content := "G", count := \
[ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\
 [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next := 25698, root := ~, 
                                                                          star\
t := 25690, stop := 25697 ), rec( content := " be a group acting on the object\
s in ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ), rec( attributes := rec(  ), content := [ rec( content := "list", count \
:= [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\
 := [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next := 25746, root := ~
                                                                            , 
                                                                          star\
t := 25735, stop := 25745 ), rec( content := " via\n        the action ", coun\
t := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "act", count := [ 3, 1, 7, 20 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20\
 ], mathmode := "Text", name := "A", next := 25780, root := ~, start := 25770,
                                                                          stop\
 := 25779 ), rec( content := ", and let ", count := [ 3, 1, 7, 20 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content \
:= [ rec( content := "adj", count := [ 3, 1, 7, 20 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", 
                                                                          name\
 := "A", next := 25800, root := ~, start := 25790, stop := 25799 ), rec( conte\
nt := " be a function taking\n        two objects from ", count := [ 3, 1, 7, \
20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\
c(  ), content := [ rec( content := "list", count := [ 3, 1, 7, 20 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmod\
e := "Text", name := "A", next := 25858, root := ~, start := 25847, stop := 25\
857 ), rec( content := " as arguments and returning ", count := [ 3, 1, 7, 20 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "true", count := [ 3, 1, 7, 20 ], mathmode := "Text",\
 name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "C", next := 25897, root := ~, start := 25886, stop := 25896 ), rec( conte\
nt := " or\n        ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :=\
 "false", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "C", next := \
25921, root := ~, start := 25909, stop := 25920 ), rec( content := ". The func\
tion ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ), rec( attributes := rec(  ), content := [ rec( content := "adj", count :\
= [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \
:= [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next := 25946, root := ~,
                                                                          star\
t := 25936, stop := 25945 ), rec( content := " will describe the adjacency\n  \
      between objects from ", count := [ 3, 1, 7, 20 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "list", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next\
 := 26015, root := ~, start := 26004, stop := 26014 ), rec( content := ", whic\
h is invariant under the action of\n        ", count := [ 3, 1, 7, 20 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), cont\
ent := [ rec( content := "G", count := [ 3, 1, 7, 20 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", 
                                                                          name\
 := "A", next := 26072, root := ~, start := 26064, stop := 26071 ), rec( conte\
nt := ". This variant of the constructor returns a digraph with\n        verti\
ces the objects of ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "P\
CDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := \
"list", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "A", next := 26\
172, root := ~, start := 26161, stop := 26171 ), rec( content := " and directe\
d edges ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "[x, y]", co\
unt := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 3, 1, 7, 20 ], mathmode := "Text", name := "C", next := 26205, root := \
~, start := 26192, stop := 26204 ), rec( content := "\n        when ", count :\
= [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "f(x, y)", count := [ 3, 1, 7,\
 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7\
, 20 ], mathmode := "Text", name := "C", next := 26233, root := ~, start := 26\
219, stop := 26232 ), rec( content := " is ", count := [ 3, 1, 7, 20 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conte\
nt := [ rec( content := "true", count := [ 3, 1, 7, 20 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 20 ], mathmode := "Text",
                                                                          name\
 := "C", next := 26248, root := ~, start := 26237, stop := 26247 ), rec( conte\
nt := ". ", count := [ 3, 1, 7, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := 0, count := [ 3, 1, 7, 21 ], 
                                                                          math\
mode := "Text", name := "P", next := 26254, root := ~, start := 26250, stop :=\
 26253 ), rec( content := "\n\n        The action of the group ", count := [ 3\
, 1, 7, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := [ rec( content := "G", count := [ 3, 1, 7, 21 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 21 ], 
                                                                          math\
mode := "Text", name := "A", next := 26296, root := ~, start := 26288, stop :=\
 26295 ), rec( content := " on the objects in ", count := [ 3, 1, 7, 21 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "list", count := [ 3, 1, 7, 21 ], mathmode := "Text",\
 name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 21 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "A", next := 26326, root := ~, start := 26315, stop := 26325 ), rec( conte\
nt := " is stored\n        in the attribute ", count := [ 3, 1, 7, 21 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := \
"DigraphGroup" ), content := 0, count := [ 3, 1, 7, 21 ], mathmode := "Text", 
                                                                          name\
 := "Ref", next := 26388, root := ~, start := 26362, stop := 26387 ), rec( 
                                                                          cont\
ent := ", and is used to speed up\n        operations like ", count := [ 3, 1,\
 7, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec( Attr := "DigraphDiameter" ), content := 0, count := [ 3, 1, 7, 21 ], 
                                                                          math\
mode := "Text", name := "Ref", next := 26467, root := ~, start := 26438, stop \
:= 26466 ), rec( content := ".\n      ", count := [ 3, 1, 7, 21 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 19 ], 
                                                                  name := "Ite\
m", next := 26482, root := ~, start := 25609, stop := 26481 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "for a Grape package graph", count := 
                                                                            [ \
3, 1, 7, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 3, 1, 
                                                                      7, 22 ],
                                                                  name := "Mar\
k", next := 26528, root := ~, start := 26490, stop := 26527 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        if ", count := [ 3, 1, 7, 2\
3 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\
(  ), content := [ rec( content := "obj", count := [ 3, 1, 7, 23 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 23 ], mathmode \
:= "Text", name := "A", next := 26563, root := ~, start := 26553, stop := 2656\
2 ), rec( content := " is a ", count := [ 3, 1, 7, 23 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content :=\
 [ rec( attributes := rec( Text := "Grape" ), content := [ rec( content := "ht\
tp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ 3, 1, 7, 23 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 23 ], mathmod\
e := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 ) ]
                                                                            , 
                                                                          coun\
t := [ 3, 1, 7, 23 ], name := "Alt", next := 93, root := ~, start := 1, stop :\
= 92 ), rec( attributes := rec( Only := "Text" ), content := [ rec( attributes\
 := rec(  ), content := [ rec( content := "Grape", count := [ 3, 1, 7, 23 ], n\
ame := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 23 ], name := "Package", n\
ext := 137, root := ~, start := 113, stop := 136 ) ], count := [ 3, 1, 7, 23 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "Alt", next := 143, root := ~, start := 93, stop := 14\
2 ), rec( content := " package graph (i.e. a record for which the\n        fun\
ction ", count := [ 3, 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ), rec( attributes := rec(  ), content := [ rec( content := "IsGraph", co\
unt := [ 3, 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 3, 1, 7, 23 ], mathmode := "Text", name := "C", next := 26651, root := \
~, start := 26637, stop := 26650 ), rec( content := " returns ", count := [ 3,\
 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\
s := rec(  ), content := [ rec( content := "true", count := [ 3, 1, 7, 23 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 23 ], 
                                                                          math\
mode := "Text", name := "K", next := 26671, root := ~, start := 26660, stop :=\
 26670 ), rec( content := "), then this function returns\n        a digraph is\
omorphic to ", count := [ 3, 1, 7, 23 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "obj", count\
 := [ 3, 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 3, 1, 7, 23 ], mathmode := "Text", name := "A", next := 26743, root := \
~, start := 26733, stop := 26742 ), rec( content := ".\n      ", count := [ 3,\
 1, 7, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 3, 1, 
                                                                      7, 23 ],
                                                                  name := "Ite\
m", next := 26758, root := ~, start := 26535, stop := 26757 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "for a binary relation", count := [ 3,\
 1, 7, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 3, 1, 
                                                                      7, 24 ],
                                                                  name := "Mar\
k", next := 26800, root := ~, start := 26766, stop := 26799 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        if ", count := [ 3, 1, 7, 2\
5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\
(  ), content := [ rec( content := "obj", count := [ 3, 1, 7, 25 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], mathmode \
:= "Text", name := "A", next := 26835, root := ~, start := 26825, stop := 2683\
4 ), rec( content := " is a binary relation on the points ", count := [ 3, 1, \
7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\
 rec(  ), content := [ rec( content := "[1 .. n]", count := [ 3, 1, 7, 25 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], 
                                                                          math\
mode := "Text", name := "C", next := 26886, root := ~, start := 26871, stop :=\
 26885 ), rec( content := " for\n        some posititve integer ", count := [ \
3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "n", count := [ 3, 1, 7, 25 ], ma\
thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], 
                                                                          math\
mode := "Text", name := "M", next := 26930, root := ~, start := 26922, stop :=\
 26929 ), rec( content := ", then this function returns the digraph\n        d\
efined by ", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "obj", count\
 := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 3, 1, 7, 25 ], mathmode := "Text", name := "A", next := 27000, root := \
~, start := 26990, stop := 26999 ), rec( content := ". Specifically, this func\
tion returns a digraph\n        which has ", count := [ 3, 1, 7, 25 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conten\
t := [ rec( content := "n", count := [ 3, 1, 7, 25 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], mathmode := "Text", 
                                                                          name\
 := "M", next := 27074, root := ~, start := 27066, stop := 27073 ), rec( conte\
nt := " vertices, and which has an edge with source ", count := [ 3, 1, 7, 25 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "i", count := [ 3, 1, 7, 25 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 3, 1, 7, 25 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 27127, root := ~, start := 27119, stop := 27126 ), rec( conte\
nt := "\n        and range ", count := [ 3, 1, 7, 25 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "j", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "C", next :=\
 27154, root := ~, start := 27146, stop := 27153 ), rec( content := " if and o\
nly if ", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "[i,j]", cou\
nt := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 3, 1, 7, 25 ], mathmode := "Text", name := "C", next := 27182, root := \
~, start := 27170, stop := 27181 ), rec( content := " is a pair in\n        th\
e binary relation ", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PC\
DATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\
obj", count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := \
~ ) ], count := [ 3, 1, 7, 25 ], mathmode := "Text", name := "A", next := 2723\
4, root := ~, start := 27224, stop := 27233 ), rec( content := ".\n      ", 
                                                                          coun\
t := [ 3, 1, 7, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 3, 1, 
                                                                      7, 25 ],
                                                                  name := "Ite\
m", next := 27249, root := ~, start := 26807, stop := 27248 ) ], 
                                                          count := 
                                                            [ 3, 1, 7, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 27261, 
                                                          root := ~, 
                                                          start := 22859, 
                                                          stop := 27260 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 1, 7, 27 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([\n> [2, 5, 8, 10], [2, 3, 4, 2, 5, 6, 8, 9, 10], [1],\n> \
[3, 5, 7, 8, 10], [2, 5, 7], [3, 6, 7, 9, 10], [1, 4],\n> [1, 5, 9], [1, 2, 7,\
 8], [3, 5]]);\n<immutable multidigraph with 10 vertices, 38 edges>\ngap> gr :\
= Digraph([\"a\", \"b\", \"c\"], [\"a\"], [\"b\"]);\n<immutable digraph with 3\
 vertices, 1 edge>\ngap> gr := Digraph(5, [1, 2, 2, 4, 1, 1], [2, 3, 5, 5, 1, \
1]);\n<immutable multidigraph with 5 vertices, 6 edges>\ngap> Petersen := Grap\
h(SymmetricGroup(5), [[1, 2]], OnSets,\n> function(x, y) return Intersection(x\
, y) = []; end);;\ngap> Digraph(Petersen);\n<immutable digraph with 10 vertice\
s, 30 edges>\ngap> gr := Digraph([1 .. 10], ReturnTrue);\n<immutable digraph w\
ith 10 vertices, 100 edges>", count := [ 3, 1, 7, 28 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 7, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 28003, 
                                                          root := ~, 
                                                          start := 27267, 
                                                          stop := 28002 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The next example illustrates the uses of the fourth and fifth variants of\n \
     this constructor. The resulting digraph is a strongly regular graph, and\
\n      it is actually the point graph of the van Lint-Schrijver partial\n    \
  geometry, ", count := [ 3, 1, 7, 29 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "vLS81" )
                                                            , content := 0, 
                                                          count := 
                                                            [ 3, 1, 7, 29 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 28270, 
                                                          root := ~, 
                                                          start := 28251, 
                                                          stop := 28269 ), 
                                                      rec( 
                                                          content := ".  The a\
lgebraic description\n      is taken from the seminal paper of Calderbank and \
Kantor ", count := [ 3, 1, 7, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "CK86" ),
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 7, 29 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 28388, 
                                                          root := ~, 
                                                          start := 28362, 
                                                          stop := 28387 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 3, 1, 7, 29 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> f := GF(3 ^ 4);\nGF(3^4)\ngap> gamma := First(f, x -> Order(x) = 5);\nZ(\
3^4)^64\ngap> L := Union([Zero(f)], List(Group(gamma)));\n[ 0*Z(3), Z(3)^0, Z(\
3^4)^16, Z(3^4)^32, Z(3^4)^48, Z(3^4)^64 ]\ngap> omega := Union(List(L, x -> L\
ist(Difference(L, [x]), y -> x - y)));\n[ Z(3)^0, Z(3), Z(3^4)^5, Z(3^4)^7, Z(\
3^4)^8, Z(3^4)^13, Z(3^4)^15, \n  Z(3^4)^16, Z(3^4)^21, Z(3^4)^23, Z(3^4)^24, \
Z(3^4)^29, Z(3^4)^31, \n  Z(3^4)^32, Z(3^4)^37, Z(3^4)^39, Z(3^4)^45, Z(3^4)^4\
7, Z(3^4)^48, \n  Z(3^4)^53, Z(3^4)^55, Z(3^4)^56, Z(3^4)^61, Z(3^4)^63, Z(3^4\
)^64, \n  Z(3^4)^69, Z(3^4)^71, Z(3^4)^72, Z(3^4)^77, Z(3^4)^79 ]\ngap> adj :=\
 function(x, y)\n>   return x - y in omega;\n> end;\nfunction( x, y ) ... end\
\ngap> digraph := Digraph(AsList(f), adj);\n<immutable digraph with 81 vertice\
s, 2430 edges>\ngap> group := Group(Z(3));;\ngap> act := \\*;\n<Operation \"*\
\">\ngap> digraph := Digraph(group, List(f), act, adj);\n<immutable digraph wi\
th 81 vertices, 2430 edges>\n", count := [ 3, 1, 7, 30 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 7, 30 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 29358, 
                                                          root := ~, 
                                                          start := 28390, 
                                                          stop := 29357 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 1, 7, 31 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 7, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 29375, root := ~, 
                                                  start := 22343, 
                                                  stop := 29374 ) ], 
                                          count := [ 3, 1, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 29389, root := ~, 
                                          start := 22022, stop := 29388 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 7, 31 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]list", 
                                                      Name := "DigraphByAdjace\
ncyMatrix" ), content := 0, count := [ 3, 1, 8, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 29468, root := ~, 
                                                  start := 29410, 
                                                  stop := 29467 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 29500, root := ~, 
                                                  start := 29471, 
                                                  stop := 29499 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
the optional first argument ", count := [ 3, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 29563, 
                                                          root := ~, 
                                                          start := 29552, 
                                                          stop := 29562 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 1, 8, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 29709, 
                                                          root := ~, 
                                                          start := 29698, 
                                                          stop := 29708 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 29743, 
                                                          root := ~, 
                                                          start := 29713, 
                                                          stop := 29742 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 29811, 
                                                          root := ~, 
                                                          start := 29800, 
                                                          stop := 29810 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 29851, 
                                                          root := ~, 
                                                          start := 29815, 
                                                          stop := 29850 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 29936, 
                                                          root := ~, 
                                                          start := 29925, 
                                                          stop := 29935 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 29994, 
                                                          root := ~, 
                                                          start := 29958, 
                                                          stop := 29993 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 30018, 
                                                          root := ~, 
                                                          start := 30014, 
                                                          stop := 30017 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 30038, 
                                                          root := ~, 
                                                          start := 30027, 
                                                          stop := 30037 ), 
                                                      rec( 
                                                          content := " is the \
adjacency matrix of a digraph in the sense of\n    ", count := [ 3, 1, 8, 4 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Adjacen\
cyMatrix" ), content := 0, count := [ 3, 1, 8, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 30125, 
                                                          root := ~, 
                                                          start := 30096, 
                                                          stop := 30124 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns the digraph\n    which is defined by ", 
                                                          count := 
                                                            [ 3, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 30202, 
                                                          root := ~, 
                                                          start := 30191, 
                                                          stop := 30201 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 30208, 
                                                          root := ~, 
                                                          start := 30204, 
                                                          stop := 30207 ), 
                                                      rec( 
                                                          content := "\n\n    \
Alternatively, if ", count := [ 3, 1, 8, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 30243, 
                                                          root := ~, 
                                                          start := 30232, 
                                                          stop := 30242 ), 
                                                      rec( 
                                                          content := " is a sq\
uare boolean matrix, then this\n    operation returns the digraph with ", 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
ength(", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 30335, 
                                                          root := ~, 
                                                          start := 30321, 
                                                          stop := 30334 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 30346, 
                                                          root := ~, 
                                                          start := 30335, 
                                                          stop := 30345 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 30354, 
                                                          root := ~, 
                                                          start := 30346, 
                                                          stop := 30353 ), 
                                                      rec( 
                                                          content := "\n    ve\
rtices which has the edge ", count := [ 3, 1, 8, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i,j]", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 30399, 
                                                          root := ~, 
                                                          start := 30387, 
                                                          stop := 30398 ), 
                                                      rec( 
                                                          content := " if and \
only if\n    ", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 30430, 
                                                          root := ~, 
                                                          start := 30419, 
                                                          stop := 30429 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i][j]", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 30443, 
                                                          root := ~, 
                                                          start := 30430, 
                                                          stop := 30442 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 3, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 30458, 
                                                          root := ~, 
                                                          start := 30447, 
                                                          stop := 30457 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 30464, 
                                                          root := ~, 
                                                          start := 30460, 
                                                          stop := 30463 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 1, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> DigraphByAdjacencyMatrix([\n> [0, 1, 0, 2, 0],\n> [1, 1, 1, 0, 1],\n> [0\
, 3, 2, 1, 1],\n> [0, 0, 1, 0, 1],\n> [2, 0, 0, 0, 0]]);\n<immutable multidigr\
aph with 5 vertices, 18 edges>\ngap> D := DigraphByAdjacencyMatrix([\n> [true,\
 false, true],\n> [false, false, true],\n> [false, true, false]]);\n<immutable\
 digraph with 3 vertices, 4 edges>\ngap> OutNeighbours(D);\n[ [ 1, 3 ], [ 3 ],\
 [ 2 ] ]\ngap> D := DigraphByAdjacencyMatrix(IsMutableDigraph, \n> [[true, fal\
se, true],\n>  [false, false, true],\n>  [false, true, false]]);\n<mutable dig\
raph with 3 vertices, 4 edges>\n", count := [ 3, 1, 8, 7 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 31060, 
                                                          root := ~, 
                                                          start := 30470, 
                                                          stop := 31059 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 1, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 31077, root := ~, 
                                                  start := 29503, 
                                                  stop := 31076 ) ], 
                                          count := [ 3, 1, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 31091, root := ~, 
                                          start := 29395, stop := 31090 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 8, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]list[, n\
]", Name := "DigraphByEdges" ), content := 0, count := [ 3, 1, 9, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 31165, root := ~, 
                                                  start := 31112, 
                                                  stop := 31164 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 1, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 31197, root := ~, 
                                                  start := 31168, 
                                                  stop := 31196 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
the optional first argument ", count := [ 3, 1, 9, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 31260, 
                                                          root := ~, 
                                                          start := 31249, 
                                                          stop := 31259 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 1, 9, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 31406, 
                                                          root := ~, 
                                                          start := 31395, 
                                                          stop := 31405 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 1, 9, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 31440, 
                                                          root := ~, 
                                                          start := 31410, 
                                                          stop := 31439 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 31508, 
                                                          root := ~, 
                                                          start := 31497, 
                                                          stop := 31507 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 1, 9, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 31548, 
                                                          root := ~, 
                                                          start := 31512, 
                                                          stop := 31547 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 31633, 
                                                          root := ~, 
                                                          start := 31622, 
                                                          stop := 31632 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 1, 9, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 1, 9, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 31691, 
                                                          root := ~, 
                                                          start := 31655, 
                                                          stop := 31690 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 31715, 
                                                          root := ~, 
                                                          start := 31711, 
                                                          stop := 31714 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 31735, 
                                                          root := ~, 
                                                          start := 31724, 
                                                          stop := 31734 ), 
                                                      rec( 
                                                          content := " is list\
 of pairs of positive integers, then this function\n    returns the digraph wi\
th the minimum number of vertices ", count := [ 3, 1, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 31862, 
                                                          root := ~, 
                                                          start := 31854, 
                                                          stop := 31861 ), 
                                                      rec( 
                                                          content := " such th\
at\n    its list equal ", count := [ 3, 1, 9, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 31903, 
                                                          root := ~, 
                                                          start := 31892, 
                                                          stop := 31902 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 1, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 31908, 
                                                          root := ~, 
                                                          start := 31904, 
                                                          stop := 31907 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional second argument ", count := [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 31954, 
                                                          root := ~, 
                                                          start := 31946, 
                                                          stop := 31953 ), 
                                                      rec( 
                                                          content := " is a po\
sitive integer with\n    ", count := [ 3, 1, 9, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "n", count := [ 3, 1, 9, 5 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 9, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 31997, root := ~, start := 31989, stop := 31996 )
                                                                , 
                                                              rec( 
                                                                  content := "\
 >= m", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 32006, 
                                                          root := ~, 
                                                          start := 31986, 
                                                          stop := 32005 ), 
                                                      rec( 
                                                          content := " (with "
                                                            , 
                                                          count := 
                                                            [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 32021, 
                                                          root := ~, 
                                                          start := 32013, 
                                                          stop := 32020 ), 
                                                      rec( 
                                                          content := " defined\
 as above),\n    then this function returns the digraph with ", 
                                                          count := 
                                                            [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 32097, 
                                                          root := ~, 
                                                          start := 32089, 
                                                          stop := 32096 ), 
                                                      rec( 
                                                          content := " vertice\
s and list\n    ", count := [ 3, 1, 9, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 32131, 
                                                          root := ~, 
                                                          start := 32120, 
                                                          stop := 32130 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 32137, 
                                                          root := ~, 
                                                          start := 32133, 
                                                          stop := 32136 ), 
                                                      rec( 
                                                          content := "\n\n    \
See ", count := [ 3, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Edges" ), content := 0, count := [ 3, 1, 9, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 32173, 
                                                          root := ~, 
                                                          start := 32147, 
                                                          stop := 32172 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> DigraphByEdges(\n> [[1, 3], [2, 1], [2, 3], [2, 5], [3, 6],\n>  [4, 6], \
[5, 2], [5, 4], [5, 6], [6, 6]]);\n<immutable digraph with 6 vertices, 10 edge\
s>\ngap> DigraphByEdges(\n> [[1, 3], [2, 1], [2, 3], [2, 5], [3, 6],\n>  [4, 6\
], [5, 2], [5, 4], [5, 6], [6, 6]], 12);\n<immutable digraph with 12 vertices,\
 10 edges>\ngap> DigraphByEdges(IsMutableDigraph, \n> [[1, 3], [2, 1], [2, 3],\
 [2, 5], [3, 6],\n>  [4, 6], [5, 2], [5, 4], [5, 6], [6, 6]], 12);\n<mutable d\
igraph with 12 vertices, 10 edges>\n", count := [ 3, 1, 9, 7 ], name := "PCDAT\
A", root := ~ ) ], count := [ 3, 1, 9, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 32703, 
                                                          root := ~, 
                                                          start := 32180, 
                                                          stop := 32702 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 1, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 32720, root := ~, 
                                                  start := 31200, 
                                                  stop := 32719 ) ], 
                                          count := [ 3, 1, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 32734, root := ~, 
                                          start := 31097, stop := 32733 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 9, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "G, edges[, n]", 
                                                      Name := "EdgeOrbitsDigra\
ph" ), content := 0, count := [ 3, 1, 10, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 32807, root := ~, 
                                                  start := 32755, 
                                                  stop := 32806 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    An \
immutable digraph.\n  ", count := [ 3, 1, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 32858, root := ~, 
                                                  start := 32810, 
                                                  stop := 32857 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 32890, 
                                                          root := ~, 
                                                          start := 32882, 
                                                          stop := 32889 ), 
                                                      rec( 
                                                          content := " is a pe\
rmutation group, ", count := [ 3, 1, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 32927, 
                                                          root := ~, 
                                                          start := 32915, 
                                                          stop := 32926 ), 
                                                      rec( 
                                                          content := " is an e\
dge or list of\n    edges, and ", count := [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 32973, 
                                                          root := ~, 
                                                          start := 32965, 
                                                          stop := 32972 ), 
                                                      rec( 
                                                          content := " is a no\
n-negative integer such that ", count := [ 3, 1, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 33018, 
                                                          root := ~, 
                                                          start := 33010, 
                                                          stop := 33017 ), 
                                                      rec( 
                                                          content := " fixes\n\
    ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 1, 10, 3 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 10, 3 ], 
                                                                  mathmode := \
"Text", name := "A", next := 33046, root := ~, start := 33038, stop := 33045 )
                                                                , 
                                                              rec( 
                                                                  content := "\
]", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 33051, 
                                                          root := ~, 
                                                          start := 33029, 
                                                          stop := 33050 ), 
                                                      rec( 
                                                          content := " setwise\
, then\n    this operation returns an immutable digraph with ", 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 33127, 
                                                          root := ~, 
                                                          start := 33119, 
                                                          stop := 33126 ), 
                                                      rec( 
                                                          content := " vertice\
s and the union\n    of the orbits of the edges in ", count := [ 3, 1, 10, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
edges ", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 33199, 
                                                          root := ~, 
                                                          start := 33185, 
                                                          stop := 33198 ), 
                                                      rec( 
                                                          content := " under t\
he action of the\n    permutation group ", count := [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 33254, 
                                                          root := ~, 
                                                          start := 33246, 
                                                          stop := 33253 ), 
                                                      rec( 
                                                          content := ".  An ed\
ge in this context is simply a pair of\n    positive integers.\n    ", 
                                                          count := 
                                                            [ 3, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 33332, 
                                                          root := ~, 
                                                          start := 33328, 
                                                          stop := 33331 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional third argument ", count := [ 3, 1, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 33377, 
                                                          root := ~, 
                                                          start := 33369, 
                                                          stop := 33376 ), 
                                                      rec( 
                                                          content := " is not \
present, then the largest\n    moved point of the permutation group ", 
                                                          count := 
                                                            [ 3, 1, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 33460, 
                                                          root := ~, 
                                                          start := 33452, 
                                                          stop := 33459 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 1, 10, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 33484, 
                                                          root := ~, 
                                                          start := 33480, 
                                                          stop := 33483 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph := EdgeOrbitsDigraph(Group((1, 3), (1, 2)(3, 4)),\n>            \
                     [[1, 2], [4, 5]], 5);\n<immutable digraph with 5 vertices\
, 12 edges>\ngap> OutNeighbours(digraph);\n[ [ 2, 4, 5 ], [ 1, 3, 5 ], [ 2, 4,\
 5 ], [ 1, 3, 5 ], [  ] ]\ngap> RepresentativeOutNeighbours(digraph);\n[ [ 2, \
4, 5 ], [  ] ]\n", count := [ 3, 1, 10, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 1, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 33842, 
                                                          root := ~, 
                                                          start := 33490, 
                                                          stop := 33841 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 1, 10, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 33859, root := ~, 
                                                  start := 32861, 
                                                  stop := 33858 ) ], 
                                          count := [ 3, 1, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 33873, root := ~, 
                                          start := 32740, stop := 33872 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 10, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]list", 
                                                      Name := "DigraphByInNeig\
hbours" ), content := 0, count := [ 3, 1, 11, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 33949, root := ~, 
                                                  start := 33894, 
                                                  stop := 33948 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]list", 
                                                      Name := "DigraphByInNeig\
hbors" ), content := 0, count := [ 3, 1, 11, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 34006, root := ~, 
                                                  start := 33952, 
                                                  stop := 34005 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 1, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 34038, root := ~, 
                                                  start := 34009, 
                                                  stop := 34037 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n  If th\
e optional first argument ", count := [ 3, 1, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 34099, 
                                                          root := ~, 
                                                          start := 34088, 
                                                          stop := 34098 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n  specify the category or representation the digraph be\
ing created will\n  belong to. For example, if ", count := [ 3, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 34241, 
                                                          root := ~, 
                                                          start := 34230, 
                                                          stop := 34240 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 1, 11, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 34275, 
                                                          root := ~, 
                                                          start := 34245, 
                                                          stop := 34274 ), 
                                                      rec( 
                                                          content := ",\n  the\
n the digraph being created will be mutable, if ", count := [ 3, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 34341, 
                                                          root := ~, 
                                                          start := 34330, 
                                                          stop := 34340 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 1, 11, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 34379, 
                                                          root := ~, 
                                                          start := 34345, 
                                                          stop := 34378 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n  If the optional first argument ", 
                                                          count := 
                                                            [ 3, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 34462, 
                                                          root := ~, 
                                                          start := 34451, 
                                                          stop := 34461 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 1, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 1, 11, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 34518, 
                                                          root := ~, 
                                                          start := 34484, 
                                                          stop := 34517 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 1, 11, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 34542, 
                                                          root := ~, 
                                                          start := 34538, 
                                                          stop := 34541 ), 
                                                      rec( 
                                                          content := "\n\n  If\
 ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 34560, 
                                                          root := ~, 
                                                          start := 34549, 
                                                          stop := 34559 ), 
                                                      rec( 
                                                          content := " is a li\
st of lists of positive integers list the range\n  ", count := [ 3, 1, 11, 6 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. Length(", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "list", count := [ 3, 1, 11, 6 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 34645, root := ~, start := 34634, stop := 34644 )
                                                                , 
                                                              rec( 
                                                                  content := "\
)]", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 34651, 
                                                          root := ~, 
                                                          start := 34618, 
                                                          stop := 34650 ), 
                                                      rec( 
                                                          content := ", then t\
his function returns the\n  digraph with vertices ", count := [ 3, 1, 11, 6 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "E\
^0=", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 34719, 
                                                          root := ~, 
                                                          start := 34708, 
                                                          stop := 34718 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. Length(", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "list", count := [ 3, 1, 11, 6 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 34746, root := ~, start := 34735, stop := 34745 )
                                                                , 
                                                              rec( 
                                                                  content := "\
)]", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 34752, 
                                                          root := ~, 
                                                          start := 34719, 
                                                          stop := 34751 ), 
                                                      rec( 
                                                          content := ", and\n \
 edges corresponding to the entries of ", count := [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 34809, 
                                                          root := ~, 
                                                          start := 34798, 
                                                          stop := 34808 ), 
                                                      rec( 
                                                          content := ". More p\
recisely, there is an\n  edge with source vertex ", count := [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 34873, 
                                                          root := ~, 
                                                          start := 34865, 
                                                          stop := 34872 ), 
                                                      rec( 
                                                          content := " and ran\
ge vertex ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 34899, 
                                                          root := ~, 
                                                          start := 34891, 
                                                          stop := 34898 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 34911, 
                                                          root := ~, 
                                                          start := 34903, 
                                                          stop := 34910 ), 
                                                      rec( 
                                                          content := " is list\
\n  ", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "list", count := [ 3, 1, 11, 6 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 34936, root := ~, start := 34925, stop := 34935 )
                                                                , 
                                                              rec( 
                                                                  content := "\
[j]", count := [ 3, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 34943, 
                                                          root := ~, 
                                                          start := 34922, 
                                                          stop := 34942 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 34949, 
                                                          root := ~, 
                                                          start := 34945, 
                                                          stop := 34948 ), 
                                                      rec( 
                                                          content := "\n\n  If\
 ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 34964, 
                                                          root := ~, 
                                                          start := 34956, 
                                                          stop := 34963 ), 
                                                      rec( 
                                                          content := " occurs \
list ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "list", count := [ 3, 1, 11, 7 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 1, 11, 7 ], 
                                                                  mathmode := \
"Text", name := "A", next := 34991, root := ~, start := 34980, stop := 34990 )
                                                                , 
                                                              rec( 
                                                                  content := "\
[j]", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 34998, 
                                                          root := ~, 
                                                          start := 34977, 
                                                          stop := 34997 ), 
                                                      rec( 
                                                          content := " with mu\
ltiplicity ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 35025, 
                                                          root := ~, 
                                                          start := 35017, 
                                                          stop := 35024 ), 
                                                      rec( 
                                                          content := ",\n  the\
n there are ", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 35052, 
                                                          root := ~, 
                                                          start := 35044, 
                                                          stop := 35051 ), 
                                                      rec( 
                                                          content := " multipl\
e edges from ", count := [ 3, 1, 11, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 35081, 
                                                          root := ~, 
                                                          start := 35073, 
                                                          stop := 35080 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 3, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 35093, 
                                                          root := ~, 
                                                          start := 35085, 
                                                          stop := 35092 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 11, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 35099, 
                                                          root := ~, 
                                                          start := 35095, 
                                                          stop := 35098 ), 
                                                      rec( 
                                                          content := "\n\n  Se\
e ", count := [ 3, 1, 11, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "InNeigh\
bours" ), content := 0, count := [ 3, 1, 11, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 35133, 
                                                          root := ~, 
                                                          start := 35107, 
                                                          stop := 35132 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 1, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphByInNeighbours([\n> [2, 5, 8, 10], [2, 3, 4, 5, 6, 8, 9, 10]\
,\n> [1], [3, 5, 7, 8, 10], [2, 5, 7], [3, 6, 7, 9, 10], [1, 4],\n> [1, 5, 9],\
 [1, 2, 7, 8], [3, 5]]);\n<immutable digraph with 10 vertices, 37 edges>\ngap>\
 D := DigraphByInNeighbours([[2, 3, 2], [1], [1, 2, 3]]);\n<immutable multidig\
raph with 3 vertices, 7 edges>\ngap> D := DigraphByInNeighbours(IsMutableDigra\
ph, \n>                               [[2, 3, 2], [1], [1, 2, 3]]);\n<mutable \
multidigraph with 3 vertices, 7 edges>\n", count := [ 3, 1, 11, 9 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 1, 11, 9 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 35669, 
                                                          root := ~, 
                                                          start := 35140, 
                                                          stop := 35668 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 1, 11, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 35686, root := ~, 
                                                  start := 34041, 
                                                  stop := 35685 ) ], 
                                          count := [ 3, 1, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 35700, root := ~, 
                                          start := 33879, stop := 35699 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 1, 11, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "G[, gens]", 
                                                      Name := "CayleyDigraph" 
                                                     ), content := 0, 
                                                  count := [ 3, 1, 12, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 35765, root := ~, 
                                                  start := 35721, 
                                                  stop := 35764 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An immuta\
ble digraph.", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 35808, root := ~, 
                                                  start := 35768, 
                                                  stop := 35807 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Let\
 ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 35841, 
                                                          root := ~, 
                                                          start := 35833, 
                                                          stop := 35840 ), 
                                                      rec( 
                                                          content := " be any \
group and let ", count := [ 3, 1, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ens", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 35874, 
                                                          root := ~, 
                                                          start := 35863, 
                                                          stop := 35873 ), 
                                                      rec( 
                                                          content := " be a li\
st of elements of\n    ", count := [ 3, 1, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 35912, 
                                                          root := ~, 
                                                          start := 35904, 
                                                          stop := 35911 ), 
                                                      rec( 
                                                          content := ". This o\
peration returns an immutable digraph that corresponds to\n    the Cayley grap\
h of ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 36010, 
                                                          root := ~, 
                                                          start := 36002, 
                                                          stop := 36009 ), 
                                                      rec( 
                                                          content := " with re\
spect\n    ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ens", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 36039, 
                                                          root := ~, 
                                                          start := 36028, 
                                                          stop := 36038 ), 
                                                      rec( 
                                                          content := ". The ve\
rtices are the elements of ", count := [ 3, 1, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 36082, 
                                                          root := ~, 
                                                          start := 36074, 
                                                          stop := 36081 ), 
                                                      rec( 
                                                          content := ". There \
exists an edge\n    from the vertex ", count := [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 36133, 
                                                          root := ~, 
                                                          start := 36125, 
                                                          stop := 36132 ), 
                                                      rec( 
                                                          content := " to the \
vertex ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 36156, 
                                                          root := ~, 
                                                          start := 36148, 
                                                          stop := 36155 ), 
                                                      rec( 
                                                          content := " if and \
only if there exists\n    a generator ", count := [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 36209, 
                                                          root := ~, 
                                                          start := 36201, 
                                                          stop := 36208 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ens", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 36224, 
                                                          root := ~, 
                                                          start := 36213, 
                                                          stop := 36223 ), 
                                                      rec( 
                                                          content := " such th\
at ", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
 * g = y", count := [ 3, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 36251, 
                                                          root := ~, 
                                                          start := 36235, 
                                                          stop := 36250 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 36257, 
                                                          root := ~, 
                                                          start := 36253, 
                                                          stop := 36256 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          content := " FIXME W\
hat is the correspondence between vertices and elements? ", 
                                                          count := 
                                                            [ 3, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "XMLCOMMENT"
                                                            , root := ~ ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional second argument ", count := [ 3, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ens", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 36384, 
                                                          root := ~, 
                                                          start := 36373, 
                                                          stop := 36383 ), 
                                                      rec( 
                                                          content := " is not \
present, then the\n    generators of ", count := [ 3, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 36436, 
                                                          root := ~, 
                                                          start := 36428, 
                                                          stop := 36435 ), 
                                                      rec( 
                                                          content := " are use\
d by default.", count := [ 3, 1, 12, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 36461, 
                                                          root := ~, 
                                                          start := 36457, 
                                                          stop := 36460 ), 
                                                      rec( 
                                                          content := "\n\n    \
The digraph created by this operation belongs to the category ", 
                                                          count := 
                                                            [ 3, 1, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsCayle\
yDigraph" ), content := 0, count := [ 3, 1, 12, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 36564, 
                                                          root := ~, 
                                                          start := 36529, 
                                                          stop := 36563 ), 
                                                      rec( 
                                                          content := ", the gr\
oup ", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 1, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 36584, 
                                                          root := ~, 
                                                          start := 36576, 
                                                          stop := 36583 ), 
                                                      rec( 
                                                          content := " can be \
recovered from the\n    digraph using ", count := [ 3, 1, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "GroupOf\
CayleyDigraph" ), content := 0, count := [ 3, 1, 12, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 36663, 
                                                          root := ~, 
                                                          start := 36629, 
                                                          stop := 36662 ), 
                                                      rec( 
                                                          content := ", and th\
e generators\n    ", count := [ 3, 1, 12, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ens", count := [ 3, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 1, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 36699, 
                                                          root := ~, 
                                                          start := 36688, 
                                                          stop := 36698 ), 
                                                      rec( 
                                                          content := " can be \
obtained using ", count := [ 3, 1, 12, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Generat\
orsOfCayleyDigraph" ), content := 0, count := [ 3, 1, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 36761, 
                                                          root := ~, 
                                                          start := 36722, 
                                                          stop := 36760 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 1, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 1, 12, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 36766, 
                                                          root := ~, 
                                                          start := 36762, 
                                                          stop := 36765 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that this function can only return an immutable digraph.\n\n    ", 
                                                          count := 
                                                            [ 3, 1, 12, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> G := DihedralGroup(8);\n<pc group of size 8 with 3 generators>\ngap> Cay\
leyDigraph(G);\n<immutable digraph with 8 vertices, 24 edges>\ngap> G := Dihed\
ralGroup(IsPermGroup, 8);\nGroup([ (1,2,3,4), (2,4) ])\ngap> CayleyDigraph(G);\
\n<immutable digraph with 8 vertices, 16 edges>\ngap> digraph := CayleyDigraph\
(G, [()]);\n<immutable digraph with 8 vertices, 8 edges>\ngap> GroupOfCayleyDi\
graph(digraph) = G;\ntrue\ngap> GeneratorsOfCayleyDigraph(digraph);\n[ () ]", 
                                                                  count := 
                                                                    [ 3, 1, 
                                                                      12, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 1, 12, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 37322, 
                                                          root := ~, 
                                                          start := 36839, 
                                                          stop := 37321 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 1, 12, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 1, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 37339, root := ~, 
                                                  start := 35811, 
                                                  stop := 37338 ) ], 
                                          count := [ 3, 1, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 37353, root := ~, 
                                          start := 35706, stop := 37352 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 3, 1, 12, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 37367, 
                                  root := ~, start := 19307, stop := 37366 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 3, 1, 12, 8 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Changing represen\
tations", count := [ 3, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 3, 2, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 37423, 
                                          root := ~, start := 37380, 
                                          stop := 37422 ), 
                                      rec( content := "\n    ", 
                                          count := [ 3, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "AsBinaryRelatio\
n" ), content := 0, count := [ 3, 2, 1, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 37488, root := ~, 
                                                  start := 37443, 
                                                  stop := 37487 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A binary \
relation.", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 37528, root := ~, 
                                                  start := 37491, 
                                                  stop := 37527 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 37566, 
                                                          root := ~, 
                                                          start := 37552, 
                                                          stop := 37565 ), 
                                                      rec( 
                                                          content := " is a di\
graph with a positive number of vertices\n    ", count := [ 3, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 37627, 
                                                          root := ~, 
                                                          start := 37619, 
                                                          stop := 37626 ), 
                                                      rec( 
                                                          content := ", and no\
 multiple edges, then this operation returns a binary\n    relation on the poi\
nts ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1..n]", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 37729, 
                                                          root := ~, 
                                                          start := 37716, 
                                                          stop := 37728 ), 
                                                      rec( 
                                                          content := ".\n    T\
he pair ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i,j]", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 37756, 
                                                          root := ~, 
                                                          start := 37744, 
                                                          stop := 37755 ), 
                                                      rec( 
                                                          content := " is in t\
he binary relation if and only if\n    ", count := [ 3, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i,j]", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 37814, 
                                                          root := ~, 
                                                          start := 37802, 
                                                          stop := 37813 ), 
                                                      rec( 
                                                          content := " is an e\
dge in ", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 37843, 
                                                          root := ~, 
                                                          start := 37829, 
                                                          stop := 37842 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 37853, 
                                                          root := ~, 
                                                          start := 37849, 
                                                          stop := 37852 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 3, 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3, 2], [1, 2], [2], [3, 4]]);\n<immutable digraph with 4 \
vertices, 7 edges>\ngap> AsBinaryRelation(D);\nBinary Relation on 4 points\n",
                                                                  count := 
                                                                    [ 3, 2, 
                                                                      1, 5 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 2, 1, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 38035, 
                                                          root := ~, 
                                                          start := 37854, 
                                                          stop := 38034 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 38052, root := ~, 
                                                  start := 37531, 
                                                  stop := 38051 ) ], 
                                          count := [ 3, 2, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 38066, root := ~, 
                                          start := 37428, stop := 38065 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 2, 1, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]trans[, \
n]", Name := "AsDigraph" ), content := 0, count := [ 3, 2, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 38136, root := ~, 
                                                  start := 38087, 
                                                  stop := 38135 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
, or ", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 38173, 
                                                          root := ~, 
                                                          start := 38162, 
                                                          stop := 38172 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 38184, root := ~, 
                                                  start := 38139, 
                                                  stop := 38183 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
the optional first argument ", count := [ 3, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 38247, 
                                                          root := ~, 
                                                          start := 38236, 
                                                          stop := 38246 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 2, 2, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 38393, 
                                                          root := ~, 
                                                          start := 38382, 
                                                          stop := 38392 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 38427, 
                                                          root := ~, 
                                                          start := 38397, 
                                                          stop := 38426 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 38495, 
                                                          root := ~, 
                                                          start := 38484, 
                                                          stop := 38494 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 38535, 
                                                          root := ~, 
                                                          start := 38499, 
                                                          stop := 38534 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 38620, 
                                                          root := ~, 
                                                          start := 38609, 
                                                          stop := 38619 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 38678, 
                                                          root := ~, 
                                                          start := 38642, 
                                                          stop := 38677 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 38702, 
                                                          root := ~, 
                                                          start := 38698, 
                                                          stop := 38701 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rans", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 38723, 
                                                          root := ~, 
                                                          start := 38711, 
                                                          stop := 38722 ), 
                                                      rec( 
                                                          content := " is a tr\
ansformation, and ", count := [ 3, 2, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 38757, 
                                                          root := ~, 
                                                          start := 38749, 
                                                          stop := 38756 ), 
                                                      rec( 
                                                          content := " is a no\
n-negative integer\n    such that the restriction of ", count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rans", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 38829, 
                                                          root := ~, 
                                                          start := 38817, 
                                                          stop := 38828 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 2, 2, 4 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], 
                                                                  mathmode := \
"Text", name := "A", next := 38850, root := ~, start := 38842, stop := 38849 )
                                                                , 
                                                              rec( 
                                                                  content := "\
]", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 38855, 
                                                          root := ~, 
                                                          start := 38833, 
                                                          stop := 38854 ), 
                                                      rec( 
                                                          content := " defines\
\n    a transformation of ", count := [ 3, 2, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. ", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 2, 2, 4 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 4 ], 
                                                                  mathmode := \
"Text", name := "A", next := 38905, root := ~, start := 38897, stop := 38904 )
                                                                , 
                                                              rec( 
                                                                  content := "\
]", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 38910, 
                                                          root := ~, 
                                                          start := 38888, 
                                                          stop := 38909 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sDigraph", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 38933, 
                                                          root := ~, 
                                                          start := 38917, 
                                                          stop := 38932 ), 
                                                      rec( 
                                                          content := "\n    re\
turns the functional digraph with ", count := [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 38982, 
                                                          root := ~, 
                                                          start := 38974, 
                                                          stop := 38981 ), 
                                                      rec( 
                                                          content := " vertice\
s defined by\n    ", count := [ 3, 2, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rans", count := [ 3, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 39019, 
                                                          root := ~, 
                                                          start := 39007, 
                                                          stop := 39018 ), 
                                                      rec( 
                                                          content := ". See ",
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsFunct\
ionalDigraph" ), content := 0, count := [ 3, 2, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 39058, 
                                                          root := ~, 
                                                          start := 39025, 
                                                          stop := 39057 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 39068, 
                                                          root := ~, 
                                                          start := 39064, 
                                                          stop := 39067 ), 
                                                      rec( 
                                                          content := "\n\n    \
Specifically, the digraph returned by ", count := [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sDigraph", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 39128, 
                                                          root := ~, 
                                                          start := 39112, 
                                                          stop := 39127 ), 
                                                      rec( 
                                                          content := " has  ",
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 39142, 
                                                          root := ~, 
                                                          start := 39134, 
                                                          stop := 39141 ), 
                                                      rec( 
                                                          content := " edges:\\
n    for each vertex ", count := [ 3, 2, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 39178, 
                                                          root := ~, 
                                                          start := 39170, 
                                                          stop := 39177 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. ", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 2, 2, 5 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 39199, root := ~, start := 39191, stop := 39198 )
                                                                , 
                                                              rec( 
                                                                  content := "\
]", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 39204, 
                                                          root := ~, 
                                                          start := 39182, 
                                                          stop := 39203 ), 
                                                      rec( 
                                                          content := ", there \
is a unique edge\n    with source ", count := [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 39253, 
                                                          root := ~, 
                                                          start := 39245, 
                                                          stop := 39252 ), 
                                                      rec( 
                                                          content := "; this e\
dge has range ", count := [ 3, 2, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
^", count := [ 3, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                                , 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "trans", count := [ 3, 2, 2, 5 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 39292, root := ~, start := 39280, stop := 39291 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 39296, 
                                                          root := ~, 
                                                          start := 39275, 
                                                          stop := 39295 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 39306, 
                                                          root := ~, 
                                                          start := 39302, 
                                                          stop := 39305 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional second argument ", count := [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 39352, 
                                                          root := ~, 
                                                          start := 39344, 
                                                          stop := 39351 ), 
                                                      rec( 
                                                          content := " is not \
supplied, then the degree of\n    the transformation ", count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rans", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 39424, 
                                                          root := ~, 
                                                          start := 39412, 
                                                          stop := 39423 ), 
                                                      rec( 
                                                          content := " is used\
 by default.  If the restriction of\n    ", count := [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rans", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 39484, 
                                                          root := ~, 
                                                          start := 39472, 
                                                          stop := 39483 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 2, 2, 6 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 39505, root := ~, start := 39497, stop := 39504 )
                                                                , 
                                                              rec( 
                                                                  content := "\
]", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 39510, 
                                                          root := ~, 
                                                          start := 39488, 
                                                          stop := 39509 ), 
                                                      rec( 
                                                          content := " does no\
t define a transformation of\n    ", count := [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 2, 2, 6 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 39568, root := ~, start := 39560, stop := 39567 )
                                                                , 
                                                              rec( 
                                                                  content := "\
]", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 39573, 
                                                          root := ~, 
                                                          start := 39551, 
                                                          stop := 39572 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sDigraph(", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "trans", count := [ 3, 2, 2, 6 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 39605, root := ~, start := 39593, stop := 39604 )
                                                                , 
                                                              rec( 
                                                                  content := "\
, ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 2, 2, 6 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 2, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 39615, root := ~, start := 39607, stop := 39614 )
                                                                , 
                                                              rec( 
                                                                  content := "\
)", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 39620, 
                                                          root := ~, 
                                                          start := 39580, 
                                                          stop := 39619 ), 
                                                      rec( 
                                                          content := "\n    re\
turns ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 39644, 
                                                          root := ~, 
                                                          start := 39633, 
                                                          stop := 39643 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> f := Transformation([4, 3, 3, 1, 7, 9, 10, 4, 2, 3]);\nTransformation( [\
 4, 3, 3, 1, 7, 9, 10, 4, 2, 3 ] )\ngap> AsDigraph(f);\n<immutable functional \
digraph with 10 vertices>\ngap> AsDigraph(f, 4);\n<immutable functional digrap\
h with 4 vertices>\ngap> AsDigraph(f, 5);\nfail\ngap> b := BinaryRelationOnPoi\
nts(\n> [[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\nBinary Relation on 5 po\
ints\ngap> D := AsDigraph(b);\n<immutable digraph with 5 vertices, 11 edges>\n\
", count := [ 3, 2, 2, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 2, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 40137, 
                                                          root := ~, 
                                                          start := 39651, 
                                                          stop := 40136 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 2, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 40154, root := ~, 
                                                  start := 38187, 
                                                  stop := 40153 ) ], 
                                          count := [ 3, 2, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 40168, root := ~, 
                                          start := 38072, stop := 40167 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 2, 2, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "Graph" ), 
                                                  content := 0, 
                                                  count := [ 3, 2, 3, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 40223, root := ~, 
                                                  start := 40189, 
                                                  stop := 40222 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "A ", 
                                                          count := 
                                                            [ 3, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 3, 2, 3, 3 ]
                                                            , name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ 3, 2, 3, 3 ], name \
:= "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " package\
 graph.", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 2, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 40269, root := ~, 
                                                  start := 40226, 
                                                  stop := 40268 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 40307, 
                                                          root := ~, 
                                                          start := 40293, 
                                                          stop := 40306 ), 
                                                      rec( 
                                                          content := " is a mu\
table or immutable digraph without multiple edges, then this operation\n    re\
turns a ", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 3, 2, 3, 3 ]
                                                            , name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ 3, 2, 3, 3 ], name \
:= "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 3 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " package\
 graph that is isomorphic to ", count := [ 3, 2, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 40458, 
                                                          root := ~, 
                                                          start := 40444, 
                                                          stop := 40457 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 2, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 40464, 
                                                          root := ~, 
                                                          start := 40460, 
                                                          stop := 40463 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 40487, 
                                                          root := ~, 
                                                          start := 40473, 
                                                          stop := 40486 ), 
                                                      rec( 
                                                          content := " is a mu\
ltidigraph, then since ", count := [ 3, 2, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 3, 2, 3, 4 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 3, 2, 3, 4 ]
                                                            , name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ 3, 2, 3, 4 ], name \
:= "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 4 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " does no\
t support\n    multiple edges, the multiple edges will be reduced to a single \
edge in the\n    result. In order words, for a multidigraph this operation wil\
l return the\n    same as ", count := [ 3, 2, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
raph(DigraphRemoveAllMultipleEdges(", count := [ 3, 2, 3, 4 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 3, 2, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 40755, 
                                                          root := ~, 
                                                          start := 40712, 
                                                          stop := 40754 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 40769, 
                                                          root := ~, 
                                                          start := 40755, 
                                                          stop := 40768 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
)", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 40778, 
                                                          root := ~, 
                                                          start := 40769, 
                                                          stop := 40777 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> Petersen := Graph(SymmetricGroup(5), [[1, 2]], OnSets,\n> function(x, y)\
 return Intersection(x, y) = []; end);;\ngap> Display(Petersen);\nrec(\n  adja\
cencies := [ [ 3, 5, 8 ] ],\n  group := \n   Group( [ ( 1, 2, 3, 5, 7)( 4, 6, \
8, 9,10), ( 2, 4)( 6, 9)( 7,10) \n     ] ),\n  isGraph := true,\n  names := [ \
[ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 1, 3 ], [ 4, 5 ], \n      [ 2, 4 ], [ 1, 5 ], \
[ 3, 5 ], [ 1, 4 ], [ 2, 5 ] ],\n  order := 10,\n  representatives := [ 1 ],\n\
  schreierVector := [ -1, 1, 1, 2, 1, 1, 1, 1, 2, 2 ] )\ngap> Digraph(Petersen\
);\n<immutable digraph with 10 vertices, 30 edges>\ngap> Graph(last) = Peterse\
n;\ntrue", count := [ 3, 2, 3, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 41431, 
                                                          root := ~, 
                                                          start := 40785, 
                                                          stop := 41430 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 2, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 2, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 41448, root := ~, 
                                                  start := 40272, 
                                                  stop := 41447 ) ], 
                                          count := [ 3, 2, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 41462, root := ~, 
                                          start := 40174, stop := 41461 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 2, 3, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "AsGraph" ), 
                                                  content := 0, 
                                                  count := [ 3, 2, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 41519, root := ~, 
                                                  start := 41483, 
                                                  stop := 41518 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "A ", 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := [ 3, 2, 4, 3 ]
                                                            , name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ 3, 2, 4, 3 ], name \
:= "PCDATA", root := ~ ) ], count := [ 3, 2, 4, 3 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " package\
 graph.", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 41565, root := ~, 
                                                  start := 41522, 
                                                  stop := 41564 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 41603, 
                                                          root := ~, 
                                                          start := 41589, 
                                                          stop := 41602 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then this method returns the same as\n    ", count := [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Graph" 
                                                             ), content := 0, 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 41678, 
                                                          root := ~, 
                                                          start := 41659, 
                                                          stop := 41677 ), 
                                                      rec( 
                                                          content := ", except\
 that if ", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 41709, 
                                                          root := ~, 
                                                          start := 41695, 
                                                          stop := 41708 ), 
                                                      rec( 
                                                          content := " is immu\
table, then the\n    result will be stored as a mutable attribute of ", 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 41799, 
                                                          root := ~, 
                                                          start := 41785, 
                                                          stop := 41798 ), 
                                                      rec( 
                                                          content := ".\n    I\
n this latter case, when ", count := [ 3, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sGraph(", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 41846, 
                                                          root := ~, 
                                                          start := 41831, 
                                                          stop := 41845 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 41860, 
                                                          root := ~, 
                                                          start := 41846, 
                                                          stop := 41859 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 41868, 
                                                          root := ~, 
                                                          start := 41860, 
                                                          stop := 41867 ), 
                                                      rec( 
                                                          content := " is call\
ed\n    subsequently, the same ", count := [ 3, 2, 4, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 3, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " object \
will be returned as before.\n\n    ", count := [ 3, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2], [3], []]);\n<immutable digraph with 3 vertices, 3 \
edges>\ngap> G := AsGraph(D);\nrec( adjacencies := [ [ 1, 2 ], [ 3 ], [  ] ], \
group := Group(()), \n  isGraph := true, names := [ 1 .. 3 ], order := 3, \n  \
representatives := [ 1, 2, 3 ], schreierVector := [ -1, -2, -3 ] )\n", 
                                                                  count := 
                                                                    [ 3, 2, 
                                                                      4, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 2, 4, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 42279, 
                                                          root := ~, 
                                                          start := 41952, 
                                                          stop := 42278 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 42296, root := ~, 
                                                  start := 41568, 
                                                  stop := 42295 ) ], 
                                          count := [ 3, 2, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 42310, root := ~, 
                                          start := 41468, stop := 42309 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 2, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "AsTransformatio\
n" ), content := 0, count := [ 3, 2, 5, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 42376, root := ~, 
                                                  start := 42331, 
                                                  stop := 42375 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A transfo\
rmation, or ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 42420, 
                                                          root := ~, 
                                                          start := 42409, 
                                                          stop := 42419 ) ], 
                                                  count := [ 3, 2, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 42430, root := ~, 
                                                  start := 42379, 
                                                  stop := 42429 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 42468, 
                                                          root := ~, 
                                                          start := 42454, 
                                                          stop := 42467 ), 
                                                      rec( 
                                                          content := " is a fu\
nctional digraph, then ", count := [ 3, 2, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sTransformation", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "C", 
                                                          next := 42522, 
                                                          root := ~, 
                                                          start := 42499, 
                                                          stop := 42521 ), 
                                                      rec( 
                                                          content := "\n    re\
turns the transformation which is defined by ", count := [ 3, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 42588, 
                                                          root := ~, 
                                                          start := 42574, 
                                                          stop := 42587 ), 
                                                      rec( 
                                                          content := ".  See "
                                                            , 
                                                          count := 
                                                            [ 3, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsFunct\
ionalDigraph" ), content := 0, count := [ 3, 2, 5, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 42634, 
                                                          root := ~, 
                                                          start := 42595, 
                                                          stop := 42633 ), 
                                                      rec( 
                                                          content := ". Otherw\
ise,\n    ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sTransformation(", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "C", 
                                                          next := 42675, 
                                                          root := ~, 
                                                          start := 42651, 
                                                          stop := 42674 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 42689, 
                                                          root := ~, 
                                                          start := 42675, 
                                                          stop := 42688 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 42697, 
                                                          root := ~, 
                                                          start := 42689, 
                                                          stop := 42696 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 3, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 42717, 
                                                          root := ~, 
                                                          start := 42706, 
                                                          stop := 42716 ), 
                                                      rec( content := ".  ", 
                                                          count := 
                                                            [ 3, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 42724, 
                                                          root := ~, 
                                                          start := 42720, 
                                                          stop := 42723 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 42747, 
                                                          root := ~, 
                                                          start := 42733, 
                                                          stop := 42746 ), 
                                                      rec( 
                                                          content := " is a fu\
nctional digraph with ", count := [ 3, 2, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 42785, 
                                                          root := ~, 
                                                          start := 42777, 
                                                          stop := 42784 ), 
                                                      rec( 
                                                          content := " vertice\
s, then\n    ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sTransformation(", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "C", 
                                                          next := 42829, 
                                                          root := ~, 
                                                          start := 42805, 
                                                          stop := 42828 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 42843, 
                                                          root := ~, 
                                                          start := 42829, 
                                                          stop := 42842 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 42851, 
                                                          root := ~, 
                                                          start := 42843, 
                                                          stop := 42850 ), 
                                                      rec( 
                                                          content := " will re\
turn the\n    transformation ", count := [ 3, 2, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 42895, 
                                                          root := ~, 
                                                          start := 42887, 
                                                          stop := 42894 ), 
                                                      rec( 
                                                          content := " of degr\
ee at most ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 42922, 
                                                          root := ~, 
                                                          start := 42914, 
                                                          stop := 42921 ), 
                                                      rec( 
                                                          content := " where f\
or each ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
\n      \\leq i \\leq n", count := [ 3, 2, 5, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 2, 5, 4 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 42966, 
                                                          root := ~, 
                                                          start := 42938, 
                                                          stop := 42965 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 ^ f", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 42980, 
                                                          root := ~, 
                                                          start := 42968, 
                                                          stop := 42979 ), 
                                                      rec( 
                                                          content := " is equa\
l to the unique out-neighbour of\n    vertex ", count := [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 43040, 
                                                          root := ~, 
                                                          start := 43032, 
                                                          stop := 43039 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 43058, 
                                                          root := ~, 
                                                          start := 43044, 
                                                          stop := 43057 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1], [3], [2]]);\n<immutable digraph with 3 vertices, 3 ed\
ges>\ngap> AsTransformation(D);\nTransformation( [ 1, 3, 2 ] )\ngap> D := Cycl\
eDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\nga\
p> AsTransformation(D);\nTransformation( [ 2, 3, 1 ] )\ngap> AsPermutation(las\
t);\n(1,2,3)\ngap> D := Digraph([[2, 3], [], []]);\n<immutable digraph with 3 \
vertices, 2 edges>\ngap> AsTransformation(D);\nfail", count := [ 3, 2, 5, 5 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 2, 5, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 43524, 
                                                          root := ~, 
                                                          start := 43065, 
                                                          stop := 43523 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 2, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 43541, root := ~, 
                                                  start := 42433, 
                                                  stop := 43540 ) ], 
                                          count := [ 3, 2, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 43555, root := ~, 
                                          start := 42316, stop := 43554 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 3, 2, 5, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 43569, 
                                  root := ~, start := 37371, stop := 43568 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 3, 2, 5, 6 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "New digraphs from\
 old", count := [ 3, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 3, 3, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 43622, 
                                          root := ~, start := 43582, 
                                          stop := 43621 ), 
                                      rec( content := "\n    ", 
                                          count := [ 3, 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphImmutabl\
eCopy" ), content := 0, count := [ 3, 3, 1, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 43691, root := ~, 
                                                  start := 43642, 
                                                  stop := 43690 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMutableC\
opy" ), content := 0, count := [ 3, 3, 1, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 43741, root := ~, 
                                                  start := 43694, 
                                                  stop := 43740 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphCopySame\
Mutability" ), content := 0, count := [ 3, 3, 1, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 43798, root := ~, 
                                                  start := 43744, 
                                                  stop := 43797 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphCopy" ),
                                                  content := 0, 
                                                  count := [ 3, 3, 1, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 43841, root := ~, 
                                                  start := 43801, 
                                                  stop := 43840 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 1, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 43873, root := ~, 
                                                  start := 43844, 
                                                  stop := 43872 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Eac\
h of these operations returns a new copy of ", count := [ 3, 3, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 43955, 
                                                          root := ~, 
                                                          start := 43941, 
                                                          stop := 43954 ), 
                                                      rec( 
                                                          content := ",\n    o\
f the appropriate mutability, retaining none of the attributes or\n    propert\
ies of ", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 1, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 44060, 
                                                          root := ~, 
                                                          start := 44046, 
                                                          stop := 44059 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 3, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 1, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 44066, 
                                                          root := ~, 
                                                          start := 44062, 
                                                          stop := 44065 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphCopy", count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 1, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 44090, 
                                                          root := ~, 
                                                          start := 44072, 
                                                          stop := 44089 ), 
                                                      rec( 
                                                          content := " is a sy\
nonym for ", count := [ 3, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphCopySameMutability", count := [ 3, 3, 1, 10 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 1, 10 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 44140, 
                                                          root := ~, 
                                                          start := 44108, 
                                                          stop := 44139 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 3, 3, 1, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(10);\n<immutable cycle digraph with 10 vertices>\ngap>\
 DigraphCopy(D) = D;\ntrue\ngap> IsIdenticalObj(DigraphCopy(D), D);\nfalse\nga\
p> DigraphMutableCopy(D);\n<mutable digraph with 10 vertices, 10 edges>\n", 
                                                                  count := 
                                                                    [ 3, 3, 
                                                                      1, 11 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 1, 11 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 44394, 
                                                          root := ~, 
                                                          start := 44142, 
                                                          stop := 44393 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 1, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 1, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 44411, root := ~, 
                                                  start := 43876, 
                                                  stop := 44410 ) ], 
                                          count := [ 3, 3, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 44425, root := ~, 
                                          start := 43627, stop := 44424 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 1, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphImmutabl\
eCopyIfImmutable" ), content := 0, count := [ 3, 3, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 44506, root := ~, 
                                                  start := 44446, 
                                                  stop := 44505 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphImmutabl\
eCopyIfMutable" ), content := 0, count := [ 3, 3, 2, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 44567, root := ~, 
                                                  start := 44509, 
                                                  stop := 44566 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMutableC\
opyIfMutable" ), content := 0, count := [ 3, 3, 2, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 44626, root := ~, 
                                                  start := 44570, 
                                                  stop := 44625 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMutableC\
opyIfImmutable" ), content := 0, count := [ 3, 3, 2, 8 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 44687, root := ~, 
                                                  start := 44629, 
                                                  stop := 44686 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 2, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 44719, root := ~, 
                                                  start := 44690, 
                                                  stop := 44718 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Eac\
h of these operations returns either the original argument\n    ", 
                                                          count := 
                                                            [ 3, 3, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 44820, 
                                                          root := ~, 
                                                          start := 44806, 
                                                          stop := 44819 ), 
                                                      rec( 
                                                          content := ", or a n\
ew copy of ", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 44853, 
                                                          root := ~, 
                                                          start := 44839, 
                                                          stop := 44852 ), 
                                                      rec( 
                                                          content := " of the \
appropriate\n    mutability, according to the mutability of ", 
                                                          count := 
                                                            [ 3, 3, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 44934, 
                                                          root := ~, 
                                                          start := 44920, 
                                                          stop := 44933 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 3, 3, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> C := CycleDigraph(10);\n<immutable cycle digraph with 10 vertices>\ngap>\
 D := DigraphImmutableCopyIfImmutable(C);\n<immutable digraph with 10 vertices\
, 10 edges>\ngap> IsIdenticalObj(C, D);\nfalse\ngap> C = D;\ntrue\ngap> D := D\
igraphImmutableCopyIfMutable(C);\n<immutable cycle digraph with 10 vertices>\n\
gap> IsIdenticalObj(C, D);\ntrue\ngap> C = D;\ntrue\ngap> D := DigraphMutableC\
opyIfMutable(C);\n<immutable cycle digraph with 10 vertices>\ngap> IsMutableDi\
graph(D);\nfalse\ngap> D := DigraphMutableCopyIfImmutable(C);\n<mutable digrap\
h with 10 vertices, 10 edges>\ngap> IsMutableDigraph(D);\ntrue\ngap> C := Cycl\
eDigraph(IsMutableDigraph, 10);\n<mutable digraph with 10 vertices, 10 edges>\
\ngap> D := DigraphImmutableCopyIfImmutable(C);\n<mutable digraph with 10 vert\
ices, 10 edges>\ngap> IsIdenticalObj(C, D);\ntrue\ngap> C = D;\ntrue\ngap> D :\
= DigraphImmutableCopyIfMutable(C);\n<immutable digraph with 10 vertices, 10 e\
dges>\ngap> IsIdenticalObj(C, D);\nfalse\ngap> C = D;\ntrue\ngap> D := Digraph\
MutableCopyIfMutable(C);\n<mutable digraph with 10 vertices, 10 edges>\ngap> I\
sMutableDigraph(D);\ntrue\ngap> D := DigraphMutableCopyIfImmutable(C);\n<mutab\
le digraph with 10 vertices, 10 edges>\ngap> IsIdenticalObj(C, D);\ntrue\ngap>\
 IsMutableDigraph(D);\ntrue", count := [ 3, 3, 2, 10 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 46196, 
                                                          root := ~, 
                                                          start := 44936, 
                                                          stop := 46195 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 2, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 2, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 46213, root := ~, 
                                                  start := 44722, 
                                                  stop := 46212 ) ], 
                                          count := [ 3, 3, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 46227, root := ~, 
                                          start := 44431, stop := 46226 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 2, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, verts",
                                                      Name := "InducedSubdigra\
ph" ), content := 0, count := [ 3, 3, 3, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 46301, root := ~, 
                                                  start := 46248, 
                                                  stop := 46300 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 46333, root := ~, 
                                                  start := 46304, 
                                                  stop := 46332 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46371, 
                                                          root := ~, 
                                                          start := 46357, 
                                                          stop := 46370 ), 
                                                      rec( 
                                                          content := " is a di\
graph, and ", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
erts", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46402, 
                                                          root := ~, 
                                                          start := 46390, 
                                                          stop := 46401 ), 
                                                      rec( 
                                                          content := " is a su\
bset of the\n    vertices of ", count := [ 3, 3, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46452, 
                                                          root := ~, 
                                                          start := 46438, 
                                                          stop := 46451 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns a digraph\n    constructed from ", count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46527, 
                                                          root := ~, 
                                                          start := 46513, 
                                                          stop := 46526 ), 
                                                      rec( 
                                                          content := " by reta\
ining precisely those vertices in\n    ", count := [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
erts", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46585, 
                                                          root := ~, 
                                                          start := 46573, 
                                                          stop := 46584 ), 
                                                      rec( 
                                                          content := ", and th\
ose edges whose source and range vertices are both\n    contained in ", 
                                                          count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
erts", count := [ 3, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46673, 
                                                          root := ~, 
                                                          start := 46661, 
                                                          stop := 46672 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 46679, 
                                                          root := ~, 
                                                          start := 46675, 
                                                          stop := 46678 ), 
                                                      rec( 
                                                          content := "\n\n    \
The vertices of the induced subdigraph are\n    ", count := [ 3, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1..Length(verts)]", count := [ 3, 3, 3, 4 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 3, 3, 3, 4 ], mathmode := "Text", name := "C", 
                                                          next := 46757, 
                                                          root := ~, 
                                                          start := 46732, 
                                                          stop := 46756 ), 
                                                      rec( 
                                                          content := " but the\
 original vertex labels can be\n    accessed via ", count := [ 3, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 3, 3, 3, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 46846, 
                                                          root := ~, 
                                                          start := 46813, 
                                                          stop := 46845 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 46852, 
                                                          root := ~, 
                                                          start := 46848, 
                                                          stop := 46851 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46875, 
                                                          root := ~, 
                                                          start := 46861, 
                                                          stop := 46874 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 46917, 
                                                          root := ~, 
                                                          start := 46887, 
                                                          stop := 46916 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46942, 
                                                          root := ~, 
                                                          start := 46928, 
                                                          stop := 46941 ), 
                                                      rec( 
                                                          content := " is modi\
fied in place. If ", count := [ 3, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 46982, 
                                                          root := ~, 
                                                          start := 46968, 
                                                          stop := 46981 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 47032, 
                                                          root := ~, 
                                                          start := 46994, 
                                                          stop := 47031 ), 
                                                      rec( 
                                                          content := ", a new \
immutable digraph containing the\n    appropriate\n    vertices and edges is r\
eturned.", count := [ 3, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 47128, 
                                                          root := ~, 
                                                          start := 47124, 
                                                          stop := 47127 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 1, 2, 3, 4, 4], [1, 3, 4], [3, 1], [1, 1]]);\n<immutab\
le multidigraph with 4 vertices, 13 edges>\ngap> InducedSubdigraph(D, [1, 3, 4\
]);\n<immutable multidigraph with 3 vertices, 9 edges>\ngap> DigraphVertices(l\
ast);\n[ 1 .. 3 ]\ngap> D := DigraphMutableCopy(D);\n<mutable multidigraph wit\
h 4 vertices, 13 edges>\ngap> new := InducedSubdigraph(D, [1, 3, 4]);\n<mutabl\
e multidigraph with 3 vertices, 9 edges>\ngap> D = new;\ntrue\n", count := 
                                                                    [ 3, 3, 
                                                                      3, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 3, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 47606, 
                                                          root := ~, 
                                                          start := 47134, 
                                                          stop := 47605 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 3, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 47623, root := ~, 
                                                  start := 46336, 
                                                  stop := 47622 ) ], 
                                          count := [ 3, 3, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 47637, root := ~, 
                                          start := 46233, stop := 47636 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 3, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "ReducedDigraph"\
 ), content := 0, count := [ 3, 3, 4, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 47701, root := ~, 
                                                  start := 47658, 
                                                  stop := 47700 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "ReducedDigraphA\
ttr" ), content := 0, count := [ 3, 3, 4, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 47751, root := ~, 
                                                  start := 47704, 
                                                  stop := 47750 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 4, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 47783, root := ~, 
                                                  start := 47754, 
                                                  stop := 47782 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns a digraph isomorphic to the subdigraph of\n    ", 
                                                          count := 
                                                            [ 3, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 47886, 
                                                          root := ~, 
                                                          start := 47872, 
                                                          stop := 47885 ), 
                                                      rec( 
                                                          content := " induced\
 by the set of non-isolated vertices,\n    i.e. the set of those vertices of "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 47984, 
                                                          root := ~, 
                                                          start := 47970, 
                                                          stop := 47983 ), 
                                                      rec( 
                                                          content := " which a\
re the source or\n    range of some edge in ", count := [ 3, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 48049, 
                                                          root := ~, 
                                                          start := 48035, 
                                                          stop := 48048 ), 
                                                      rec( 
                                                          content := ".\n    S\
ee ", count := [ 3, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Induced\
Subdigraph" ), content := 0, count := [ 3, 3, 4, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 48090, 
                                                          root := ~, 
                                                          start := 48059, 
                                                          stop := 48089 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 48100, 
                                                          root := ~, 
                                                          start := 48096, 
                                                          stop := 48099 ), 
                                                      rec( 
                                                          content := "\n\n    \
The ordering of the remaining vertices of ", count := [ 3, 3, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 48162, 
                                                          root := ~, 
                                                          start := 48148, 
                                                          stop := 48161 ), 
                                                      rec( 
                                                          content := " is pres\
erved, as are\n    the labels of the remaining vertices and edges;\n    see ",
                                                          count := 
                                                            [ 3, 3, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 3, 3, 4, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 48277, 
                                                          root := ~, 
                                                          start := 48244, 
                                                          stop := 48276 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 3, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
EdgeLabels" ), content := 0, count := [ 3, 3, 4, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 48313, 
                                                          root := ~, 
                                                          start := 48282, 
                                                          stop := 48312 ), 
                                                      rec( 
                                                          content := ".\n    T\
his can allow one to match a vertex in the reduced digraph to the\n    corresp\
onding vertex in ", count := [ 3, 3, 4, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 48428, 
                                                          root := ~, 
                                                          start := 48414, 
                                                          stop := 48427 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 48438, 
                                                          root := ~, 
                                                          start := 48434, 
                                                          stop := 48437 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 48461, 
                                                          root := ~, 
                                                          start := 48447, 
                                                          stop := 48460 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the isolated \
vertices of the mutable digraph ", count := [ 3, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 48592, 
                                                          root := ~, 
                                                          start := 48578, 
                                                          stop := 48591 ), 
                                                      rec( 
                                                          content := " are\n  \
  removed in-place.\n    ", count := [ 3, 3, 4, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2], [], [], [1, 4], []]);\n<immutable digraph with 5 v\
ertices, 4 edges>\ngap> R := ReducedDigraph(D);\n<immutable digraph with 3 ver\
tices, 4 edges>\ngap> OutNeighbours(R);\n[ [ 1, 2 ], [  ], [ 1, 3 ] ]\ngap> Di\
graphEdges(D);\n[ [ 1, 1 ], [ 1, 2 ], [ 4, 1 ], [ 4, 4 ] ]\ngap> DigraphEdges(\
R);\n[ [ 1, 1 ], [ 1, 2 ], [ 3, 1 ], [ 3, 3 ] ]\ngap> DigraphVertexLabel(R, 3)\
;\n4\ngap> DigraphVertexLabel(R, 2);\n2\ngap> D := Digraph(IsMutableDigraph, [\
[], [3], [2]]);\n<mutable digraph with 3 vertices, 2 edges>\ngap> ReducedDigra\
ph(D);\n<mutable digraph with 2 vertices, 2 edges>\ngap> D;\n<mutable digraph \
with 2 vertices, 2 edges>\n", count := [ 3, 3, 4, 8 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 4, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 49285, 
                                                          root := ~, 
                                                          start := 48623, 
                                                          stop := 49284 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 4, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 4, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 49302, root := ~, 
                                                  start := 47786, 
                                                  stop := 49301 ) ], 
                                          count := [ 3, 3, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 49316, root := ~, 
                                          start := 47643, stop := 49315 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 4, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "MaximalSymmetri\
cSubdigraph" ), content := 0, count := [ 3, 3, 5, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 49392, root := ~, 
                                                  start := 49337, 
                                                  stop := 49391 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "MaximalSymmetri\
cSubdigraphAttr" ), content := 0, count := [ 3, 3, 5, 4 ], mathmode := "Text",
                                                  name := "Attr", 
                                                  next := 49454, root := ~, 
                                                  start := 49395, 
                                                  stop := 49453 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "MaximalSymmetri\
cSubdigraphWithoutLoops" ), content := 0, count := [ 3, 3, 5, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 49524, root := ~, 
                                                  start := 49457, 
                                                  stop := 49523 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "MaximalSymmetri\
cSubdigraphWithoutLoopsAttr" ), content := 0, count := [ 3, 3, 5, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 49598, root := ~, 
                                                  start := 49527, 
                                                  stop := 49597 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 5, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 49630, root := ~, 
                                                  start := 49601, 
                                                  stop := 49629 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 49668, 
                                                          root := ~, 
                                                          start := 49654, 
                                                          stop := 49667 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "M\
aximalSymmetricSubdigraph", count := [ 3, 3, 5, 9 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 5, 9 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 49721, 
                                                          root := ~, 
                                                          start := 49688, 
                                                          stop := 49720 ), 
                                                      rec( 
                                                          content := "\n    re\
turns a symmetric digraph without multiple edges which has the same\n    verte\
x set as ", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 49828, 
                                                          root := ~, 
                                                          start := 49814, 
                                                          stop := 49827 ), 
                                                      rec( 
                                                          content := ", and wh\
ose edge list is formed from\n    ", count := [ 3, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 49883, 
                                                          root := ~, 
                                                          start := 49869, 
                                                          stop := 49882 ), 
                                                      rec( 
                                                          content := " by igno\
ring the multiplicity of edges, and by ignoring\n    edges ", 
                                                          count := 
                                                            [ 3, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u,v]", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 49961, 
                                                          root := ~, 
                                                          start := 49949, 
                                                          stop := 49960 ), 
                                                      rec( 
                                                          content := " for whi\
ch there does not exist an edge ", count := [ 3, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
v,u]", count := [ 3, 3, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 50013, 
                                                          root := ~, 
                                                          start := 50001, 
                                                          stop := 50012 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 50023, 
                                                          root := ~, 
                                                          start := 50019, 
                                                          stop := 50022 ), 
                                                      rec( 
                                                          content := "\n\n    \
The digraph returned by ", count := [ 3, 3, 5, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "M\
aximalSymmetricSubdigraphWithoutLoops", count := [ 3, 3, 5, 10 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 50098, 
                                                          root := ~, 
                                                          start := 50053, 
                                                          stop := 50097 ), 
                                                      rec( 
                                                          content := " is\n   \
 the same, except that loops are removed.", count := [ 3, 3, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 50150, 
                                                          root := ~, 
                                                          start := 50146, 
                                                          stop := 50149 ), 
                                                      rec( 
                                                          content := "\n    \n\
    If ", count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 50177, 
                                                          root := ~, 
                                                          start := 50163, 
                                                          stop := 50176 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the mutable d\
igraph ", count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 5, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 50283, 
                                                          root := ~, 
                                                          start := 50269, 
                                                          stop := 50282 ), 
                                                      rec( 
                                                          content := " is chan\
ged in-place into such\n    a digraph described above.", count := 
                                                            [ 3, 3, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 50348, 
                                                          root := ~, 
                                                          start := 50344, 
                                                          stop := 50347 ), 
                                                      rec( 
                                                          content := "\n\n    \
See ", count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsSymme\
tricDigraph" ), content := 0, count := [ 3, 3, 5, 12 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 50390, 
                                                          root := ~, 
                                                          start := 50358, 
                                                          stop := 50389 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsMulti\
Digraph" ), content := 0, count := [ 3, 3, 5, 12 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 50420, 
                                                          root := ~, 
                                                          start := 50392, 
                                                          stop := 50419 ), 
                                                      rec( 
                                                          content := ", and\n \
   ", count := [ 3, 3, 5, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ 3, 3, 5, 12 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 50459, 
                                                          root := ~, 
                                                          start := 50430, 
                                                          stop := 50458 ), 
                                                      rec( 
                                                          content := " for mor\
e information.\n    ", count := [ 3, 3, 5, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 2], [1, 3], [4], [3, 1]]);\n<immutable multidigraph wi\
th 4 vertices, 7 edges>\ngap> not IsSymmetricDigraph(D) and IsMultiDigraph(D);\
\ntrue\ngap> OutNeighbours(D);\n[ [ 2, 2 ], [ 1, 3 ], [ 4 ], [ 3, 1 ] ]\ngap> \
S := MaximalSymmetricSubdigraph(D);\n<immutable symmetric digraph with 4 verti\
ces, 4 edges>\ngap> IsSymmetricDigraph(S) and not IsMultiDigraph(S);\ntrue\nga\
p> OutNeighbours(S);\n[ [ 2 ], [ 1 ], [ 4 ], [ 3 ] ]\ngap> D := CycleDigraph(I\
sMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> Maximal\
SymmetricSubdigraph(D);\n<mutable empty digraph with 3 vertices>\ngap> D;\n<mu\
table empty digraph with 3 vertices>\n", count := [ 3, 3, 5, 13 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 5, 13 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 51161, 
                                                          root := ~, 
                                                          start := 50486, 
                                                          stop := 51160 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 5, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 5, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 51178, root := ~, 
                                                  start := 49633, 
                                                  stop := 51177 ) ], 
                                          count := [ 3, 3, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 51192, root := ~, 
                                          start := 49322, stop := 51191 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 5, 14 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "MaximalAntiSymm\
etricSubdigraph" ), content := 0, count := [ 3, 3, 6, 2 ], mathmode := "Text",
                                                  name := "Oper", 
                                                  next := 51272, root := ~, 
                                                  start := 51213, 
                                                  stop := 51271 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "MaximalAntiSymm\
etricSubdigraphAttr" ), content := 0, count := [ 3, 3, 6, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 51338, root := ~, 
                                                  start := 51275, 
                                                  stop := 51337 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 6, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 51370, root := ~, 
                                                  start := 51341, 
                                                  stop := 51369 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 51408, 
                                                          root := ~, 
                                                          start := 51394, 
                                                          stop := 51407 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "M\
aximalAntiSymmetricSubdigraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 51465, 
                                                          root := ~, 
                                                          start := 51428, 
                                                          stop := 51464 ), 
                                                      rec( 
                                                          content := "\n    re\
turns an anti-symmetric subdigraph of ", count := [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 51524, 
                                                          root := ~, 
                                                          start := 51510, 
                                                          stop := 51523 ), 
                                                      rec( 
                                                          content := " formed \
by\n    retaining the vertices of ", count := [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 51579, 
                                                          root := ~, 
                                                          start := 51565, 
                                                          stop := 51578 ), 
                                                      rec( 
                                                          content := ", discar\
ding any duplicate edges,\n    and discarding any edge ", count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i,j]", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 51653, 
                                                          root := ~, 
                                                          start := 51641, 
                                                          stop := 51652 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 51671, 
                                                          root := ~, 
                                                          start := 51657, 
                                                          stop := 51670 ), 
                                                      rec( 
                                                          content := " where "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 > j", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 51690, 
                                                          root := ~, 
                                                          start := 51678, 
                                                          stop := 51689 ), 
                                                      rec( 
                                                          content := "\n    an\
d the reverse edge ", count := [ 3, 3, 6, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
j,i]", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 51728, 
                                                          root := ~, 
                                                          start := 51716, 
                                                          stop := 51727 ), 
                                                      rec( 
                                                          content := " is an e\
dge of ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 51757, 
                                                          root := ~, 
                                                          start := 51743, 
                                                          stop := 51756 ), 
                                                      rec( 
                                                          content := ".\n    I\
n other words, for every\n    symmetric pair of edges ", count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i,j]", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 51829, 
                                                          root := ~, 
                                                          start := 51817, 
                                                          stop := 51828 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
j,i]", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 51846, 
                                                          root := ~, 
                                                          start := 51834, 
                                                          stop := 51845 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 51864, 
                                                          root := ~, 
                                                          start := 51850, 
                                                          stop := 51863 ), 
                                                      rec( 
                                                          content := ", where \
\n    ", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 51885, 
                                                          root := ~, 
                                                          start := 51877, 
                                                          stop := 51884 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 3, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 51898, 
                                                          root := ~, 
                                                          start := 51890, 
                                                          stop := 51897 ), 
                                                      rec( 
                                                          content := " are dis\
tinct, it discards the the edge\n    ", count := [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
\\max(i,j),\\min(i,j)]", count := [ 3, 3, 6, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 6, 5 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 51970, 
                                                          root := ~, 
                                                          start := 51942, 
                                                          stop := 51969 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 51980, 
                                                          root := ~, 
                                                          start := 51976, 
                                                          stop := 51979 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 52003, 
                                                          root := ~, 
                                                          start := 51989, 
                                                          stop := 52002 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the mutable d\
igraph ", count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 52109, 
                                                          root := ~, 
                                                          start := 52095, 
                                                          stop := 52108 ), 
                                                      rec( 
                                                          content := " is chan\
ged in-place. ", count := [ 3, 3, 6, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 52135, 
                                                          root := ~, 
                                                          start := 52131, 
                                                          stop := 52134 ), 
                                                      rec( 
                                                          content := "\n\n    \
See ", count := [ 3, 3, 6, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsAntis\
ymmetricDigraph" ), content := 0, count := [ 3, 3, 6, 7 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 52181, 
                                                          root := ~, 
                                                          start := 52145, 
                                                          stop := 52180 ), 
                                                      rec( 
                                                          content := " for mor\
e information.\n    ", count := [ 3, 3, 6, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 2], [1, 3], [4], [3, 1]]);\n<immutable multidigraph wi\
th 4 vertices, 7 edges>\ngap> not IsAntiSymmetricDigraph(D) and IsMultiDigraph\
(D);\ntrue\ngap> OutNeighbours(D);\n[ [ 2, 2 ], [ 1, 3 ], [ 4 ], [ 3, 1 ] ]\ng\
ap> D := MaximalAntiSymmetricSubdigraph(D);\n<immutable antisymmetric digraph \
with 4 vertices, 4 edges>\ngap> IsAntiSymmetricDigraph(D) and not IsMultiDigra\
ph(D);\ntrue\ngap> OutNeighbours(D);\n[ [ 2 ], [ 3 ], [ 4 ], [ 1 ] ]\ngap> D :\
= Digraph(IsMutableDigraph, [[2], [1]]);\n<mutable digraph with 2 vertices, 2 \
edges>\ngap> MaximalAntiSymmetricSubdigraph(D);\n<mutable digraph with 2 verti\
ces, 1 edge>\ngap> D;\n<mutable digraph with 2 vertices, 1 edge>\n", 
                                                                  count := 
                                                                    [ 3, 3, 
                                                                      6, 8 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 6, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 52911, 
                                                          root := ~, 
                                                          start := 52208, 
                                                          stop := 52910 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 6, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 52928, root := ~, 
                                                  start := 51373, 
                                                  stop := 52927 ) ], 
                                          count := [ 3, 3, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 52942, root := ~, 
                                          start := 51198, stop := 52941 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 6, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "UndirectedSpann\
ingForest" ), content := 0, count := [ 3, 3, 7, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 53016, root := ~, 
                                                  start := 52963, 
                                                  stop := 53015 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "UndirectedSpann\
ingForestAttr" ), content := 0, count := [ 3, 3, 7, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 53076, root := ~, 
                                                  start := 53019, 
                                                  stop := 53075 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "UndirectedSpann\
ingTree" ), content := 0, count := [ 3, 3, 7, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 53130, root := ~, 
                                                  start := 53079, 
                                                  stop := 53129 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "UndirectedSpann\
ingTreeAttr" ), content := 0, count := [ 3, 3, 7, 8 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 53188, root := ~, 
                                                  start := 53133, 
                                                  stop := 53187 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
, or ", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 53225, 
                                                          root := ~, 
                                                          start := 53214, 
                                                          stop := 53224 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 7, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 53236, root := ~, 
                                                  start := 53191, 
                                                  stop := 53235 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 53274, 
                                                          root := ~, 
                                                          start := 53260, 
                                                          stop := 53273 ), 
                                                      rec( 
                                                          content := " is a di\
graph with at least one vertex, then\n    ", count := [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "U\
ndirectedSpanningForest", count := [ 3, 3, 7, 9 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 7, 9 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 53354, 
                                                          root := ~, 
                                                          start := 53323, 
                                                          stop := 53353 ), 
                                                      rec( 
                                                          content := " returns\
 an undirected spanning forest of\n    ", count := [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 53414, 
                                                          root := ~, 
                                                          start := 53400, 
                                                          stop := 53413 ), 
                                                      rec( 
                                                          content := ", otherw\
ise this attribute returns ", count := [ 3, 3, 7, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 3, 3, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 53460, 
                                                          root := ~, 
                                                          start := 53449, 
                                                          stop := 53459 ), 
                                                      rec( 
                                                          content := ". See ",
                                                          count := 
                                                            [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsUndir\
ectedSpanningForest" ), content := 0, count := [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 53513, 
                                                          root := ~, 
                                                          start := 53466, 
                                                          stop := 53512 ), 
                                                      rec( 
                                                          content := " for the\
 definition of an undirected\n    spanning forest.", count := [ 3, 3, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 53574, 
                                                          root := ~, 
                                                          start := 53570, 
                                                          stop := 53573 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 53597, 
                                                          root := ~, 
                                                          start := 53583, 
                                                          stop := 53596 ), 
                                                      rec( 
                                                          content := " is a di\
graph with at least one vertex and whose ", count := [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Maximal\
SymmetricSubdigraph" ), content := 0, count := [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 53692, 
                                                          root := ~, 
                                                          start := 53646, 
                                                          stop := 53691 ), 
                                                      rec( 
                                                          content := " is conn\
ected (see ", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsConne\
ctedDigraph" ), content := 0, count := [ 3, 3, 7, 10 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 53750, 
                                                          root := ~, 
                                                          start := 53711, 
                                                          stop := 53749 ), 
                                                      rec( 
                                                          content := "), then \
", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "U\
ndirectedSpanningTree", count := [ 3, 3, 7, 10 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 7, 10 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 53787, 
                                                          root := ~, 
                                                          start := 53758, 
                                                          stop := 53786 ), 
                                                      rec( 
                                                          content := " returns\
\n    an undirected spanning tree of ", count := [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 53845, 
                                                          root := ~, 
                                                          start := 53831, 
                                                          stop := 53844 ), 
                                                      rec( 
                                                          content := ", otherw\
ise this attribute\n    returns ", count := [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 3, 3, 7, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 53895, 
                                                          root := ~, 
                                                          start := 53884, 
                                                          stop := 53894 ), 
                                                      rec( 
                                                          content := ".  See "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsUndir\
ectedSpanningTree" ), content := 0, count := [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 53941, 
                                                          root := ~, 
                                                          start := 53902, 
                                                          stop := 53940 ), 
                                                      rec( 
                                                          content := " for the\
\n    definition of an undirected spanning tree.", count := [ 3, 3, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 7, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 54000, 
                                                          root := ~, 
                                                          start := 53996, 
                                                          stop := 53999 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 54023, 
                                                          root := ~, 
                                                          start := 54009, 
                                                          stop := 54022 ), 
                                                      rec( 
                                                          content := " is immu\
table, then an immutable digraph is returned.\n    Otherwise, the mutable digr\
aph ", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 54126, 
                                                          root := ~, 
                                                          start := 54112, 
                                                          stop := 54125 ), 
                                                      rec( 
                                                          content := " is chan\
ged in-place into an\n    undirected spanning tree of ", count := 
                                                            [ 3, 3, 7, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 7, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 7, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 54201, 
                                                          root := ~, 
                                                          start := 54187, 
                                                          stop := 54200 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 7, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 54206, 
                                                          root := ~, 
                                                          start := 54202, 
                                                          stop := 54205 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that for an immutable digraph that has known undirected spanning tree,\n \
   the attribute ", count := [ 3, 3, 7, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "U\
ndirectedSpanningTree", count := [ 3, 3, 7, 12 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 7, 12 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 54335, 
                                                          root := ~, 
                                                          start := 54306, 
                                                          stop := 54334 ), 
                                                      rec( 
                                                          content := " returns\
 the same digraph as\n    the attribute ", count := [ 3, 3, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "U\
ndirectedSpanningForest", count := [ 3, 3, 7, 12 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 7, 12 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 54413, 
                                                          root := ~, 
                                                          start := 54382, 
                                                          stop := 54412 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 3, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2, 1, 3], [1], [4], [3, 4, 3]]);\n<immutable multidigr\
aph with 4 vertices, 9 edges>\ngap> UndirectedSpanningTree(D);\nfail\ngap> for\
est := UndirectedSpanningForest(D);\n<immutable symmetric digraph with 4 verti\
ces, 4 edges>\ngap> OutNeighbours(forest);\n[ [ 2 ], [ 1 ], [ 4 ], [ 3 ] ]\nga\
p> IsUndirectedSpanningForest(D, forest);\ntrue\ngap> DigraphConnectedComponen\
ts(forest).comps;\n[ [ 1, 2 ], [ 3, 4 ] ]\ngap> DigraphConnectedComponents(Max\
imalSymmetricSubdigraph(D)).comps;\n[ [ 1, 2 ], [ 3, 4 ] ]\ngap> UndirectedSpa\
nningForest(MaximalSymmetricSubdigraph(D))\n> = forest;\ntrue\ngap> D := Compl\
eteDigraph(4);\n<immutable complete digraph with 4 vertices>\ngap> tree := Und\
irectedSpanningTree(D);\n<immutable symmetric digraph with 4 vertices, 6 edges\
>\ngap> IsUndirectedSpanningTree(D, tree);\ntrue\ngap> tree = UndirectedSpanni\
ngForest(D);\ntrue\ngap> UndirectedSpanningForest(EmptyDigraph(0));\nfail\ngap\
> D := PetersenGraph(IsMutableDigraph);\n<mutable digraph with 10 vertices, 30\
 edges>\ngap> UndirectedSpanningTree(D);\n<mutable digraph with 10 vertices, 1\
8 edges>\ngap> D;\n<mutable digraph with 10 vertices, 18 edges>\n", 
                                                                  count := 
                                                                    [ 3, 3, 
                                                                      7, 13 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 7, 13 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 55575, 
                                                          root := ~, 
                                                          start := 54420, 
                                                          stop := 55574 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 7, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 7, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 55592, root := ~, 
                                                  start := 53239, 
                                                  stop := 55591 ) ], 
                                          count := [ 3, 3, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 55606, root := ~, 
                                          start := 52948, stop := 55605 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 7, 14 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, p", 
                                                      Name := "QuotientDigraph\
" ), content := 0, count := [ 3, 3, 8, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 55674, root := ~, 
                                                  start := 55627, 
                                                  stop := 55673 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 55706, root := ~, 
                                                  start := 55677, 
                                                  stop := 55705 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 55744, 
                                                          root := ~, 
                                                          start := 55730, 
                                                          stop := 55743 ), 
                                                      rec( 
                                                          content := " is a di\
graph, and ", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 55771, 
                                                          root := ~, 
                                                          start := 55763, 
                                                          stop := 55770 ), 
                                                      rec( 
                                                          content := " is a pa\
rtition of the vertices\n    of ", count := [ 3, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 55824, 
                                                          root := ~, 
                                                          start := 55810, 
                                                          stop := 55823 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns a digraph constructed by\n    amalgamating all vertices \
of ", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 55926, 
                                                          root := ~, 
                                                          start := 55912, 
                                                          stop := 55925 ), 
                                                      rec( 
                                                          content := " which l\
ie in the same part of\n    ", count := [ 3, 3, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 3, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 55969, 
                                                          root := ~, 
                                                          start := 55961, 
                                                          stop := 55968 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 55979, 
                                                          root := ~, 
                                                          start := 55975, 
                                                          stop := 55978 ), 
                                                      rec( 
                                                          content := "\n\n    \
A partition of the vertices of ", count := [ 3, 3, 8, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56030, 
                                                          root := ~, 
                                                          start := 56016, 
                                                          stop := 56029 ), 
                                                      rec( 
                                                          content := " is a li\
st of non-empty\n    disjoint lists, such that the union of all the sub-lists \
is equal\n    to vertex set of ", count := [ 3, 3, 8, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56159, 
                                                          root := ~, 
                                                          start := 56145, 
                                                          stop := 56158 ), 
                                                      rec( 
                                                          content := ". In par\
ticular, each vertex must appear\n    in precisely one sub-list.\n    ", 
                                                          count := 
                                                            [ 3, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 56239, 
                                                          root := ~, 
                                                          start := 56235, 
                                                          stop := 56238 ), 
                                                      rec( 
                                                          content := "\n\n    \
The vertices of ", count := [ 3, 3, 8, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56275, 
                                                          root := ~, 
                                                          start := 56261, 
                                                          stop := 56274 ), 
                                                      rec( 
                                                          content := " in part\
 ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 56292, 
                                                          root := ~, 
                                                          start := 56284, 
                                                          stop := 56291 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56304, 
                                                          root := ~, 
                                                          start := 56296, 
                                                          stop := 56303 ), 
                                                      rec( 
                                                          content := " will be\
come\n    vertex ", count := [ 3, 3, 8, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 56336, 
                                                          root := ~, 
                                                          start := 56328, 
                                                          stop := 56335 ), 
                                                      rec( 
                                                          content := " in the \
quotient, and there exists some edge in ", count := [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56398, 
                                                          root := ~, 
                                                          start := 56384, 
                                                          stop := 56397 ), 
                                                      rec( 
                                                          content := "\n    wi\
th source in part ", count := [ 3, 3, 8, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 56431, 
                                                          root := ~, 
                                                          start := 56423, 
                                                          stop := 56430 ), 
                                                      rec( 
                                                          content := " and ran\
ge in part ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 56458, 
                                                          root := ~, 
                                                          start := 56450, 
                                                          stop := 56457 ), 
                                                      rec( 
                                                          content := " if and \
only if there\n    is an edge from ", count := [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 56508, 
                                                          root := ~, 
                                                          start := 56500, 
                                                          stop := 56507 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 56520, 
                                                          root := ~, 
                                                          start := 56512, 
                                                          stop := 56519 ), 
                                                      rec( 
                                                          content := " in the \
quotient.\n    In particular, this means that the quotient of a digraph has no\
 multiple edges.\n    which was a change introduced in version 1.0.0 of the ",
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " package\
.\n    ", count := [ 3, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 56708, 
                                                          root := ~, 
                                                          start := 56704, 
                                                          stop := 56707 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56731, 
                                                          root := ~, 
                                                          start := 56717, 
                                                          stop := 56730 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 8, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 56773, 
                                                          root := ~, 
                                                          start := 56743, 
                                                          stop := 56772 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56798, 
                                                          root := ~, 
                                                          start := 56784, 
                                                          stop := 56797 ), 
                                                      rec( 
                                                          content := " is modi\
fied in place. If ", count := [ 3, 3, 8, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 56838, 
                                                          root := ~, 
                                                          start := 56824, 
                                                          stop := 56837 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 8, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 56888, 
                                                          root := ~, 
                                                          start := 56850, 
                                                          stop := 56887 ), 
                                                      rec( 
                                                          content := ", a new \
immutable digraph with the above\n    properties is returned.", 
                                                          count := 
                                                            [ 3, 3, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 56960, 
                                                          root := ~, 
                                                          start := 56956, 
                                                          stop := 56959 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 1], [4], [1], [1, 3, 4]]);\n<immutable digraph with 4 \
vertices, 7 edges>\ngap> DigraphVertices(D);\n[ 1 .. 4 ]\ngap> DigraphEdges(D)\
;\n[ [ 1, 2 ], [ 1, 1 ], [ 2, 4 ], [ 3, 1 ], [ 4, 1 ], [ 4, 3 ], \n  [ 4, 4 ] \
]\ngap> p := [[1], [2, 4], [3]];\n[ [ 1 ], [ 2, 4 ], [ 3 ] ]\ngap> quo := Quot\
ientDigraph(D, p);\n<immutable digraph with 3 vertices, 6 edges>\ngap> Digraph\
Vertices(quo);\n[ 1 .. 3 ]\ngap> DigraphEdges(quo);\n[ [ 1, 1 ], [ 1, 2 ], [ 2\
, 1 ], [ 2, 2 ], [ 2, 3 ], [ 3, 1 ] ]\ngap> QuotientDigraph(EmptyDigraph(0), [\
]);\n<immutable empty digraph with 0 vertices>\n", count := [ 3, 3, 8, 8 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 8, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 57574, 
                                                          root := ~, 
                                                          start := 56966, 
                                                          stop := 57573 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 8, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 57591, root := ~, 
                                                  start := 55709, 
                                                  stop := 57590 ) ], 
                                          count := [ 3, 3, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 57605, root := ~, 
                                          start := 55612, stop := 57604 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 8, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphReverse"\
 ), content := 0, count := [ 3, 3, 9, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 57669, root := ~, 
                                                  start := 57626, 
                                                  stop := 57668 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphReverseA\
ttr" ), content := 0, count := [ 3, 3, 9, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 57719, root := ~, 
                                                  start := 57672, 
                                                  stop := 57718 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 57751, root := ~, 
                                                  start := 57722, 
                                                  stop := 57750 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
 reverse of a digraph is the digraph formed by reversing the orientation\n    \
of each of its edges, i.e. for every edge ", count := [ 3, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i, j]", count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 57907, 
                                                          root := ~, 
                                                          start := 57894, 
                                                          stop := 57906 ), 
                                                      rec( 
                                                          content := " of a di\
graph, the\n    reverse contains the corresponding edge ", 
                                                          count := 
                                                            [ 3, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
j, i]", count := [ 3, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 57983, 
                                                          root := ~, 
                                                          start := 57970, 
                                                          stop := 57982 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 57988, 
                                                          root := ~, 
                                                          start := 57984, 
                                                          stop := 57987 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphReverse", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 58015, 
                                                          root := ~, 
                                                          start := 57994, 
                                                          stop := 58014 ), 
                                                      rec( 
                                                          content := " returns\
 the reverse of the digraph ", count := [ 3, 3, 9, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 58065, 
                                                          root := ~, 
                                                          start := 58051, 
                                                          stop := 58064 ), 
                                                      rec( 
                                                          content := ". If\n  \
  ", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 58088, 
                                                          root := ~, 
                                                          start := 58074, 
                                                          stop := 58087 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned. Otherwise,\n    the mutable d\
igraph ", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 58194, 
                                                          root := ~, 
                                                          start := 58180, 
                                                          stop := 58193 ), 
                                                      rec( 
                                                          content := " is chan\
ged in-place into its reverse.\n    ", count := [ 3, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\n<immutable d\
igraph with 5 vertices, 11 edges>\ngap> DigraphReverse(D);\n<immutable digraph\
 with 5 vertices, 11 edges>\ngap> OutNeighbours(last);\n[ [ 2, 3, 4 ], [ 4, 5 \
], [ 1, 2, 5 ], [ 4 ], [ 2, 5 ] ]\ngap> D := Digraph([[2, 4], [1], [4], [3, 4]\
]);\n<immutable digraph with 4 vertices, 6 edges>\ngap> DigraphEdges(D);\n[ [ \
1, 2 ], [ 1, 4 ], [ 2, 1 ], [ 3, 4 ], [ 4, 3 ], [ 4, 4 ] ]\ngap> DigraphEdges(\
DigraphReverse(D));\n[ [ 1, 2 ], [ 2, 1 ], [ 3, 4 ], [ 4, 1 ], [ 4, 3 ], [ 4, \
4 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 v\
ertices, 3 edges>\ngap> OutNeighbours(D);\n[ [ 2 ], [ 3 ], [ 1 ] ]\ngap> Digra\
phReverse(D);\n<mutable digraph with 3 vertices, 3 edges>\ngap> OutNeighbours(\
D);\n[ [ 3 ], [ 1 ], [ 2 ] ]\n", count := [ 3, 3, 9, 7 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 59058, 
                                                          root := ~, 
                                                          start := 58237, 
                                                          stop := 59057 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 59075, root := ~, 
                                                  start := 57754, 
                                                  stop := 59074 ) ], 
                                          count := [ 3, 3, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 59089, root := ~, 
                                          start := 57611, stop := 59088 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 9, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphDual" ),
                                                  content := 0, 
                                                  count := [ 3, 3, 10, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 59150, root := ~, 
                                                  start := 59110, 
                                                  stop := 59149 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphDualAttr\
" ), content := 0, count := [ 3, 3, 10, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 59197, root := ~, 
                                                  start := 59153, 
                                                  stop := 59196 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 10, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 59229, root := ~, 
                                                  start := 59200, 
                                                  stop := 59228 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
 ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ual", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 59265, 
                                                          root := ~, 
                                                          start := 59254, 
                                                          stop := 59264 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 59283, 
                                                          root := ~, 
                                                          start := 59269, 
                                                          stop := 59282 ), 
                                                      rec( 
                                                          content := " has the\
 same vertices as ", count := [ 3, 3, 10, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 59323, 
                                                          root := ~, 
                                                          start := 59309, 
                                                          stop := 59322 ), 
                                                      rec( 
                                                          content := ",\n    a\
nd there is an edge in the dual from ", count := [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 59375, 
                                                          root := ~, 
                                                          start := 59367, 
                                                          stop := 59374 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 59387, 
                                                          root := ~, 
                                                          start := 59379, 
                                                          stop := 59386 ), 
                                                      rec( 
                                                          content := "\n    wh\
enever there is no edge from ", count := [ 3, 3, 10, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 59431, 
                                                          root := ~, 
                                                          start := 59423, 
                                                          stop := 59430 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 59443, 
                                                          root := ~, 
                                                          start := 59435, 
                                                          stop := 59442 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 59461, 
                                                          root := ~, 
                                                          start := 59447, 
                                                          stop := 59460 ), 
                                                      rec( 
                                                          content := ".\n    T\
he ", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ual", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 59482, 
                                                          root := ~, 
                                                          start := 59471, 
                                                          stop := 59481 ), 
                                                      rec( 
                                                          content := " is some\
times called the ", count := [ 3, 3, 10, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omplement", count := [ 3, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 59524, 
                                                          root := ~, 
                                                          start := 59507, 
                                                          stop := 59523 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 59529, 
                                                          root := ~, 
                                                          start := 59525, 
                                                          stop := 59528 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDual", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 59553, 
                                                          root := ~, 
                                                          start := 59535, 
                                                          stop := 59552 ), 
                                                      rec( 
                                                          content := " returns\
 the dual of the digraph ", count := [ 3, 3, 10, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 59600, 
                                                          root := ~, 
                                                          start := 59586, 
                                                          stop := 59599 ), 
                                                      rec( 
                                                          content := ". If\n  \
  ", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 59623, 
                                                          root := ~, 
                                                          start := 59609, 
                                                          stop := 59622 ), 
                                                      rec( 
                                                          content := " is an i\
mmutable digraph, then a new immutable digraph is\n    returned. Otherwise, th\
e mutable digraph ", count := [ 3, 3, 10, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 10, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 59740, 
                                                          root := ~, 
                                                          start := 59726, 
                                                          stop := 59739 ), 
                                                      rec( 
                                                          content := " is chan\
ged in-place\n    into its dual.\n    ", count := [ 3, 3, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 3], [], [4, 6], [5], [],\n> [7, 8, 9], [], [], []]);\n\
<immutable digraph with 9 vertices, 8 edges>\ngap> DigraphDual(D);\n<immutable\
 digraph with 9 vertices, 73 edges>\ngap> D := CycleDigraph(IsMutableDigraph, \
3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> DigraphDual(D);\n<mutabl\
e digraph with 3 vertices, 6 edges>\ngap> D;\n<mutable digraph with 3 vertices\
, 6 edges>\n", count := [ 3, 3, 10, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 10, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 60206, 
                                                          root := ~, 
                                                          start := 59784, 
                                                          stop := 60205 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 10, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 10, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 60223, root := ~, 
                                                  start := 59232, 
                                                  stop := 60222 ) ], 
                                          count := [ 3, 3, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 60237, root := ~, 
                                          start := 59095, stop := 60236 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 10, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphSymmetri\
cClosure" ), content := 0, count := [ 3, 3, 11, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 60310, root := ~, 
                                                  start := 60258, 
                                                  stop := 60309 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphSymmetri\
cClosureAttr" ), content := 0, count := [ 3, 3, 11, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 60369, root := ~, 
                                                  start := 60313, 
                                                  stop := 60368 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 60401, root := ~, 
                                                  start := 60372, 
                                                  stop := 60400 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 60439, 
                                                          root := ~, 
                                                          start := 60425, 
                                                          stop := 60438 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then this attribute gives the minimal\n    symmetric digraph which has \
the same vertices and contains all the edges of\n    ", count := 
                                                            [ 3, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 60590, 
                                                          root := ~, 
                                                          start := 60576, 
                                                          stop := 60589 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 60595, 
                                                          root := ~, 
                                                          start := 60591, 
                                                          stop := 60594 ), 
                                                      rec( 
                                                          content := "\n    \n\
    A digraph is ", count := [ 3, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ymmetric", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 60634, 
                                                          root := ~, 
                                                          start := 60618, 
                                                          stop := 60633 ), 
                                                      rec( 
                                                          content := " if its \
adjacency matrix \n    ", count := [ 3, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Adjacen\
cyMatrix" ), content := 0, count := [ 3, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 60693, 
                                                          root := ~, 
                                                          start := 60664, 
                                                          stop := 60692 ), 
                                                      rec( 
                                                          content := " is symm\
etric. For a digraph with multiple\n    edges this means that there are the sa\
me number of edges from a vertex\n    ", count := [ 3, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 60823, 
                                                          root := ~, 
                                                          start := 60815, 
                                                          stop := 60822 ), 
                                                      rec( 
                                                          content := " to a ve\
rtex ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 60844, 
                                                          root := ~, 
                                                          start := 60836, 
                                                          stop := 60843 ), 
                                                      rec( 
                                                          content := " as ther\
e are from ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 60871, 
                                                          root := ~, 
                                                          start := 60863, 
                                                          stop := 60870 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 60883, 
                                                          root := ~, 
                                                          start := 60875, 
                                                          stop := 60882 ), 
                                                      rec( 
                                                          content := "; \n    \
see ", count := [ 3, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsSymme\
tricDigraph" ), content := 0, count := [ 3, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 60926, 
                                                          root := ~, 
                                                          start := 60894, 
                                                          stop := 60925 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 60931, 
                                                          root := ~, 
                                                          start := 60927, 
                                                          stop := 60930 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 60954, 
                                                          root := ~, 
                                                          start := 60940, 
                                                          stop := 60953 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the mutable d\
igraph ", count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 61060, 
                                                          root := ~, 
                                                          start := 61046, 
                                                          stop := 61059 ), 
                                                      rec( 
                                                          content := " is chan\
ged in-place into its\n    symmetric closure.\n", count := [ 3, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2, 3], [2, 4], [1], [3, 4]]);\n<immutable digraph with\
 4 vertices, 8 edges>\ngap> D := DigraphSymmetricClosure(D);\n<immutable symme\
tric digraph with 4 vertices, 11 edges>\ngap> IsSymmetricDigraph(D);\ntrue\nga\
p> List(OutNeighbours(D), AsSet);\n[ [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 4 ], [ 2, \
3, 4 ] ]\ngap> D := Digraph([[2, 2], [1]]);\n<immutable multidigraph with 2 ve\
rtices, 3 edges>\ngap> D := DigraphSymmetricClosure(D);\n<immutable symmetric \
multidigraph with 2 vertices, 4 edges>\ngap> OutNeighbours(D);\n[ [ 2, 2 ], [ \
1, 1 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with \
3 vertices, 3 edges>\ngap> DigraphSymmetricClosure(D);\n<mutable digraph with \
3 vertices, 6 edges>\ngap> D;\n<mutable digraph with 3 vertices, 6 edges>\n", 
                                                                  count := 
                                                                    [ 3, 3, 
                                                                      11, 8 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 11, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 61901, 
                                                          root := ~, 
                                                          start := 61113, 
                                                          stop := 61900 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 11, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 61918, root := ~, 
                                                  start := 60404, 
                                                  stop := 61917 ) ], 
                                          count := [ 3, 3, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 61932, root := ~, 
                                          start := 60243, stop := 61931 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 11, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphTransiti\
veClosure" ), content := 0, count := [ 3, 3, 12, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 62006, root := ~, 
                                                  start := 61953, 
                                                  stop := 62005 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphTransiti\
veClosureAttr" ), content := 0, count := [ 3, 3, 12, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 62066, root := ~, 
                                                  start := 62009, 
                                                  stop := 62065 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphReflexiv\
eTransitiveClosure" ), content := 0, count := [ 3, 3, 12, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 62131, root := ~, 
                                                  start := 62069, 
                                                  stop := 62130 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphReflexiv\
eTransitiveClosureAttr" ), content := 0, count := [ 3, 3, 12, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 62200, root := ~, 
                                                  start := 62134, 
                                                  stop := 62199 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 12, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 62232, root := ~, 
                                                  start := 62203, 
                                                  stop := 62231 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 62270, 
                                                          root := ~, 
                                                          start := 62256, 
                                                          stop := 62269 ), 
                                                      rec( 
                                                          content := " is a di\
graph with no multiple edges, then these\n    attributes return the (reflexive\
) transitive closure of ", count := [ 3, 3, 12, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 12, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 62393, 
                                                          root := ~, 
                                                          start := 62379, 
                                                          stop := 62392 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 12, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 62398, 
                                                          root := ~, 
                                                          start := 62394, 
                                                          stop := 62397 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph is ", count := [ 3, 3, 12, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
eflexive", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 62433, 
                                                          root := ~, 
                                                          start := 62417, 
                                                          stop := 62432 ), 
                                                      rec( 
                                                          content := " if it h\
as a loop at every vertex, and it is\n    ", count := [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
ransitive", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 62499, 
                                                          root := ~, 
                                                          start := 62482, 
                                                          stop := 62498 ), 
                                                      rec( 
                                                          content := " if when\
ever ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i,j]", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 62524, 
                                                          root := ~, 
                                                          start := 62512, 
                                                          stop := 62523 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
j,k]", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 62541, 
                                                          root := ~, 
                                                          start := 62529, 
                                                          stop := 62540 ), 
                                                      rec( 
                                                          content := " are edg\
es of\n    ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 62573, 
                                                          root := ~, 
                                                          start := 62559, 
                                                          stop := 62572 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i,k]", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 62587, 
                                                          root := ~, 
                                                          start := 62575, 
                                                          stop := 62586 ), 
                                                      rec( 
                                                          content := " is also\
 an edge.  The ", count := [ 3, 3, 12, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "(\
reflexive)\n      transitive closure", count := [ 3, 3, 12, 10 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 62653, 
                                                          root := ~, 
                                                          start := 62610, 
                                                          stop := 62652 ), 
                                                      rec( 
                                                          content := " of a di\
graph ", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 62681, 
                                                          root := ~, 
                                                          start := 62667, 
                                                          stop := 62680 ), 
                                                      rec( 
                                                          content := " is the \
least\n    (reflexive and) transitive digraph containing ", 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 12, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 62759, 
                                                          root := ~, 
                                                          start := 62745, 
                                                          stop := 62758 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 12, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 12, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 62764, 
                                                          root := ~, 
                                                          start := 62760, 
                                                          stop := 62763 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 62787, 
                                                          root := ~, 
                                                          start := 62773, 
                                                          stop := 62786 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the mutable d\
igraph ", count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 12, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 62893, 
                                                          root := ~, 
                                                          start := 62879, 
                                                          stop := 62892 ), 
                                                      rec( 
                                                          content := " is chan\
ged in-place into its\n    (reflexive) transitive closure.", 
                                                          count := 
                                                            [ 3, 3, 12, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 12, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 62962, 
                                                          root := ~, 
                                                          start := 62958, 
                                                          stop := 62961 ), 
                                                      rec( 
                                                          content := "\n\n    \
Let ", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 12, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 62980, 
                                                          root := ~, 
                                                          start := 62972, 
                                                          stop := 62979 ), 
                                                      rec( 
                                                          content := " be the \
number of vertices of ", count := [ 3, 3, 12, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 63024, 
                                                          root := ~, 
                                                          start := 63010, 
                                                          stop := 63023 ), 
                                                      rec( 
                                                          content := ", and le\
t\n    ", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 12, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 63046, 
                                                          root := ~, 
                                                          start := 63038, 
                                                          stop := 63045 ), 
                                                      rec( 
                                                          content := " be the \
number of edges.  For an arbitrary digraph, these\n    attributes will use a v\
ersion of the Floyd-Warshall algorithm, with\n    complexity ", 
                                                          count := 
                                                            [ 3, 3, 12, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(n^3)", count := [ 3, 3, 12, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 12, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 63204, 
                                                          root := ~, 
                                                          start := 63191, 
                                                          stop := 63203 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 However, for a topologically sortable digraph [see ", count := 
                                                            [ 3, 3, 12, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
TopologicalSort" ), content := 0, count := [ 3, 3, 12, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 63304, 
                                                          root := ~, 
                                                          start := 63262, 
                                                          stop := 63303 ), 
                                                      rec( 
                                                          content := "], these\
 attributes will use methods\n    with complexity ", count := [ 3, 3, 12, 12 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m + n + m \\cdot n)", count := [ 3, 3, 12, 12 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 12, 12 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 63388, 
                                                          root := ~, 
                                                          start := 63361, 
                                                          stop := 63387 ), 
                                                      rec( 
                                                          content := " when th\
is is faster.", count := [ 3, 3, 12, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 12, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 63413, 
                                                          root := ~, 
                                                          start := 63409, 
                                                          stop := 63412 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 12, 13 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDiSparse6String(\".H`eOWR`Ul^\");\n<immutable digraph wi\
th 9 vertices, 8 edges>\ngap> IsReflexiveDigraph(D) or IsTransitiveDigraph(D);\
\nfalse\ngap> OutNeighbours(D);\n[ [ 4, 6 ], [ 1, 3 ], [  ], [ 5 ], [  ], [ 7,\
 8, 9 ], [  ], [  ], \n  [  ] ]\ngap> T := DigraphTransitiveClosure(D);\n<immu\
table transitive digraph with 9 vertices, 18 edges>\ngap> OutNeighbours(T);\n[\
 [ 4, 6, 5, 7, 8, 9 ], [ 1, 3, 4, 5, 6, 7, 8, 9 ], [  ], [ 5 ], \n  [  ], [ 7,\
 8, 9 ], [  ], [  ], [  ] ]\ngap> RT := DigraphReflexiveTransitiveClosure(D);\
\n<immutable preorder digraph with 9 vertices, 27 edges>\ngap> OutNeighbours(R\
T);\n[ [ 4, 6, 5, 7, 8, 9, 1 ], [ 1, 3, 4, 5, 6, 7, 8, 9, 2 ], [ 3 ], \n  [ 5,\
 4 ], [ 5 ], [ 7, 8, 9, 6 ], [ 7 ], [ 8 ], [ 9 ] ]\ngap> D := CycleDigraph(IsM\
utableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> DigraphRe\
flexiveTransitiveClosure(D);\n<mutable digraph with 3 vertices, 9 edges>\ngap>\
 D;\n<mutable digraph with 3 vertices, 9 edges>\n", count := [ 3, 3, 12, 14 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 12, 14 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 64409, 
                                                          root := ~, 
                                                          start := 63419, 
                                                          stop := 64408 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 12, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 12, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 64426, root := ~, 
                                                  start := 62235, 
                                                  stop := 64425 ) ], 
                                          count := [ 3, 3, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 64440, root := ~, 
                                          start := 61938, stop := 64439 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 12, 15 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphTransiti\
veReduction" ), content := 0, count := [ 3, 3, 13, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 64516, root := ~, 
                                                  start := 64461, 
                                                  stop := 64515 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphTransiti\
veReductionAttr" ), content := 0, count := [ 3, 3, 13, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 64578, root := ~, 
                                                  start := 64519, 
                                                  stop := 64577 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphReflexiv\
eTransitiveReduction" ), content := 0, count := [ 3, 3, 13, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 64645, root := ~, 
                                                  start := 64581, 
                                                  stop := 64644 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphReflexiv\
eTransitiveReductionAttr" ), content := 0, count := [ 3, 3, 13, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 64716, root := ~, 
                                                  start := 64648, 
                                                  stop := 64715 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 13, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 64748, root := ~, 
                                                  start := 64719, 
                                                  stop := 64747 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 13, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 64786, 
                                                          root := ~, 
                                                          start := 64772, 
                                                          stop := 64785 ), 
                                                      rec( 
                                                          content := " is a to\
pologically sortable digraph\n    [see ", count := [ 3, 3, 13, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
TopologicalSort" ), content := 0, count := [ 3, 3, 13, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 64868, 
                                                          root := ~, 
                                                          start := 64832, 
                                                          stop := 64867 ), 
                                                      rec( 
                                                          content := "]\n    w\
ith no multiple edges, then these  operations return the\n    (reflexive) tran\
sitive reduction of ", count := [ 3, 3, 13, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 13, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 64986, 
                                                          root := ~, 
                                                          start := 64972, 
                                                          stop := 64985 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 13, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 13, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 64991, 
                                                          root := ~, 
                                                          start := 64987, 
                                                          stop := 64990 ), 
                                                      rec( 
                                                          content := "\n\n    \
The (reflexive) transitive reduction of such a digraph is the unique\n    leas\
t subgraph such that the (reflexive) transitive closure of the\n    subgraph i\
s equal to the (reflexive) transitive closure of ", count := [ 3, 3, 13, 10 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 13, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 65214, 
                                                          root := ~, 
                                                          start := 65200, 
                                                          stop := 65213 ), 
                                                      rec( 
                                                          content := "\n    [s\
ee ", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
ReflexiveTransitiveClosure" ), content := 0, count := [ 3, 3, 13, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 65271, 
                                                          root := ~, 
                                                          start := 65224, 
                                                          stop := 65270 ), 
                                                      rec( 
                                                          content := "].\n    \
In order words, it is the least subgraph of ", count := [ 3, 3, 13, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 13, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 65336, 
                                                          root := ~, 
                                                          start := 65322, 
                                                          stop := 65335 ), 
                                                      rec( 
                                                          content := " which\n\
    retains the same reachability as ", count := [ 3, 3, 13, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 13, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 13, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 65394, 
                                                          root := ~, 
                                                          start := 65380, 
                                                          stop := 65393 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 13, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 13, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 65399, 
                                                          root := ~, 
                                                          start := 65395, 
                                                          stop := 65398 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 13, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 65422, 
                                                          root := ~, 
                                                          start := 65408, 
                                                          stop := 65421 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the mutable d\
igraph ", count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 13, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 65528, 
                                                          root := ~, 
                                                          start := 65514, 
                                                          stop := 65527 ), 
                                                      rec( 
                                                          content := " is chan\
ged in-place into its\n    (reflexive) transitive reduction.", 
                                                          count := 
                                                            [ 3, 3, 13, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 13, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 65599, 
                                                          root := ~, 
                                                          start := 65595, 
                                                          stop := 65598 ), 
                                                      rec( 
                                                          content := "\n\n    \
Let ", count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 13, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 65617, 
                                                          root := ~, 
                                                          start := 65609, 
                                                          stop := 65616 ), 
                                                      rec( 
                                                          content := " be the \
number of vertices of an arbitrary digraph, and let\n        ", 
                                                          count := 
                                                            [ 3, 3, 13, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 3, 13, 12 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 13, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 65693, 
                                                          root := ~, 
                                                          start := 65685, 
                                                          stop := 65692 ), 
                                                      rec( 
                                                          content := " be the \
number of edges.\n    Then these operations\n    use methods with complexity "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 13, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m + n + m \\cdot n)", count := [ 3, 3, 13, 12 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 13, 12 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 65803, 
                                                          root := ~, 
                                                          start := 65776, 
                                                          stop := 65802 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 13, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 13, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 65813, 
                                                          root := ~, 
                                                          start := 65809, 
                                                          stop := 65812 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 3, 3, 13, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2, 3], [3], [3]]);;\ngap> DigraphHasLoops(D);\ntrue\ng\
ap> D1 := DigraphReflexiveTransitiveReduction(D);\n<immutable digraph with 3 v\
ertices, 2 edges>\ngap> DigraphHasLoops(D1);\nfalse\ngap> OutNeighbours(D1);\n\
[ [ 2 ], [ 3 ], [  ] ]\ngap> D2 := DigraphTransitiveReduction(D);\n<immutable \
digraph with 3 vertices, 4 edges>\ngap> DigraphHasLoops(D2);\ntrue\ngap> OutNe\
ighbours(D2);\n[ [ 2, 1 ], [ 3 ], [ 3 ] ]\ngap> DigraphReflexiveTransitiveClos\
ure(D)\n>  = DigraphReflexiveTransitiveClosure(D1);\ntrue\ngap> DigraphTransit\
iveClosure(D)\n>  = DigraphTransitiveClosure(D2);\ntrue\ngap> D := Digraph(IsM\
utableDigraph, [[1], [1], [1, 2, 3]]);\n<mutable digraph with 3 vertices, 5 ed\
ges>\ngap> DigraphReflexiveTransitiveReduction(D);\n<mutable digraph with 3 ve\
rtices, 2 edges>\ngap> D;\n<mutable digraph with 3 vertices, 2 edges>\n", 
                                                                  count := 
                                                                    [ 3, 3, 
                                                                      13, 14 ]
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 13, 14 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 66673, 
                                                          root := ~, 
                                                          start := 65818, 
                                                          stop := 66672 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 13, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 13, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 66690, root := ~, 
                                                  start := 64751, 
                                                  stop := 66689 ) ], 
                                          count := [ 3, 3, 13, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 66704, root := ~, 
                                          start := 64446, stop := 66703 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 13, 15 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, label \
]", Name := "DigraphAddVertex" ), content := 0, count := [ 3, 3, 14, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 66780, root := ~, 
                                                  start := 66725, 
                                                  stop := 66779 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 66812, root := ~, 
                                                  start := 66783, 
                                                  stop := 66811 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
 operation returns a digraph constructed from ", count := [ 3, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 66896, 
                                                          root := ~, 
                                                          start := 66882, 
                                                          stop := 66895 ), 
                                                      rec( 
                                                          content := " by addi\
ng a\n    single new vertex, and no new edges. ", count := [ 3, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 66954, 
                                                          root := ~, 
                                                          start := 66950, 
                                                          stop := 66953 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional second argument ", count := [ 3, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
abel", count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 67004, 
                                                          root := ~, 
                                                          start := 66992, 
                                                          stop := 67003 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 3, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " object,\
\n    then the new vertex will be labelled ", count := [ 3, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
abel", count := [ 3, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 67077, 
                                                          root := ~, 
                                                          start := 67065, 
                                                          stop := 67076 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 67087, 
                                                          root := ~, 
                                                          start := 67083, 
                                                          stop := 67086 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 67110, 
                                                          root := ~, 
                                                          start := 67096, 
                                                          stop := 67109 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 14, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 67152, 
                                                          root := ~, 
                                                          start := 67122, 
                                                          stop := 67151 ), 
                                                      rec( 
                                                          content := ", then t\
he\n    vertex is added directly to ", count := [ 3, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 67209, 
                                                          root := ~, 
                                                          start := 67195, 
                                                          stop := 67208 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 3, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 67228, 
                                                          root := ~, 
                                                          start := 67214, 
                                                          stop := 67227 ), 
                                                      rec( 
                                                          content := " belongs\
 to\n    ", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 14, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 67276, 
                                                          root := ~, 
                                                          start := 67244, 
                                                          stop := 67275 ), 
                                                      rec( 
                                                          content := ", an imm\
utable copy of ", count := [ 3, 3, 14, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 67313, 
                                                          root := ~, 
                                                          start := 67299, 
                                                          stop := 67312 ), 
                                                      rec( 
                                                          content := " with\n \
   the additional vertex is returned.", count := [ 3, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 67361, 
                                                          root := ~, 
                                                          start := 67357, 
                                                          stop := 67360 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(3);\n<immutable complete digraph with 3 vertices>\n\
gap> new := DigraphAddVertex(D);\n<immutable digraph with 4 vertices, 6 edges>\
\ngap> D = new;\nfalse\ngap> DigraphVertices(new);\n[ 1 .. 4 ]\ngap> new := Di\
graphAddVertex(D, Group([(1, 2)]));\n<immutable digraph with 4 vertices, 6 edg\
es>\ngap> DigraphVertexLabels(new);\n[ 1, 2, 3, Group([ (1,2) ]) ]\ngap> D := \
CompleteBipartiteDigraph(IsMutableDigraph, 2, 3);\n<mutable digraph with 5 ver\
tices, 12 edges>\ngap> new := DigraphAddVertex(D);\n<mutable digraph with 6 ve\
rtices, 12 edges>\ngap> D = new;\ntrue\n", count := [ 3, 3, 14, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 14, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 67966, 
                                                          root := ~, 
                                                          start := 67367, 
                                                          stop := 67965 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 14, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 67983, root := ~, 
                                                  start := 66815, 
                                                  stop := 67982 ) ], 
                                          count := [ 3, 3, 14, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 67997, root := ~, 
                                          start := 66710, stop := 67996 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 14, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, m", 
                                                      Label := "for a digraph \
and an integer", Name := "DigraphAddVertices" ), content := 0, 
                                                  count := [ 3, 3, 15, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 68109, root := ~, 
                                                  start := 68018, 
                                                  stop := 68108 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, labels"
                                                        , 
                                                      Label := "for a digraph \
and a list of labels", Name := "DigraphAddVertices" ), content := 0, 
                                                  count := [ 3, 3, 15, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 68214, root := ~, 
                                                  start := 68112, 
                                                  stop := 68213 ), 
                                              rec( 
                                                  content := " The 3-argument \
version is deliberately undocumented. It is redundant,\n       but it is inclu\
ded for backwards compatibility. ", count := [ 3, 3, 15, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "XMLCOMMENT", 
                                                  root := ~ ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 15, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 68382, root := ~, 
                                                  start := 68353, 
                                                  stop := 68381 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    For\
 a non-negative integer ", count := [ 3, 3, 15, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 68438, 
                                                          root := ~, 
                                                          start := 68430, 
                                                          stop := 68437 ), 
                                                      rec( 
                                                          content := ", this o\
peration returns a digraph\n    constructed from ", count := [ 3, 3, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 68508, 
                                                          root := ~, 
                                                          start := 68494, 
                                                          stop := 68507 ), 
                                                      rec( 
                                                          content := " by addi\
ng ", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 68527, 
                                                          root := ~, 
                                                          start := 68519, 
                                                          stop := 68526 ), 
                                                      rec( 
                                                          content := " new ver\
tices.\n    ", count := [ 3, 3, 15, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 68550, 
                                                          root := ~, 
                                                          start := 68546, 
                                                          stop := 68549 ), 
                                                      rec( 
                                                          content := "\n\n    \
Otherwise, if ", count := [ 3, 3, 15, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
abels", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 68583, 
                                                          root := ~, 
                                                          start := 68570, 
                                                          stop := 68582 ), 
                                                      rec( 
                                                          content := " is a li\
st\n    consisting of ", count := [ 3, 3, 15, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 68620, 
                                                          root := ~, 
                                                          start := 68612, 
                                                          stop := 68619 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " objects\
, then this operation returns a\n    digraph constructed from ", 
                                                          count := 
                                                            [ 3, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 68709, 
                                                          root := ~, 
                                                          start := 68695, 
                                                          stop := 68708 ), 
                                                      rec( 
                                                          content := " by addi\
ng ", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 68728, 
                                                          root := ~, 
                                                          start := 68720, 
                                                          stop := 68727 ), 
                                                      rec( 
                                                          content := " new ver\
tices,\n    which are labelled according to this list.\n    ", 
                                                          count := 
                                                            [ 3, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 68798, 
                                                          root := ~, 
                                                          start := 68794, 
                                                          stop := 68797 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 68821, 
                                                          root := ~, 
                                                          start := 68807, 
                                                          stop := 68820 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 15, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 68863, 
                                                          root := ~, 
                                                          start := 68833, 
                                                          stop := 68862 ), 
                                                      rec( 
                                                          content := ", then t\
he\n    vertices are added directly to ", count := [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 68923, 
                                                          root := ~, 
                                                          start := 68909, 
                                                          stop := 68922 ), 
                                                      rec( 
                                                          content := ", which \
is changed in-place.\n    If ", count := [ 3, 3, 15, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 68973, 
                                                          root := ~, 
                                                          start := 68959, 
                                                          stop := 68972 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 15, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 69017, 
                                                          root := ~, 
                                                          start := 68985, 
                                                          stop := 69016 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 69042, 
                                                          root := ~, 
                                                          start := 69028, 
                                                          stop := 69041 ), 
                                                      rec( 
                                                          content := " itself \
is returned if no vertices are added\n    (i.e. ", count := [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "m", count := [ 3, 3, 15, 7 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 15, 7 ], 
                                                                  mathmode := \
"Text", name := "A", next := 69108, root := ~, start := 69100, stop := 69107 )
                                                                , 
                                                              rec( 
                                                                  content := "\
=0", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 69114, 
                                                          root := ~, 
                                                          start := 69097, 
                                                          stop := 69113 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
abels", count := [ 3, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 69131, 
                                                          root := ~, 
                                                          start := 69118, 
                                                          stop := 69130 ), 
                                                      rec( 
                                                          content := " is empt\
y), otherwise\n    the result is a new immutable digraph.\n    ", 
                                                          count := 
                                                            [ 3, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 69204, 
                                                          root := ~, 
                                                          start := 69200, 
                                                          stop := 69203 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(3);\n<immutable complete digraph with 3 vertices>\n\
gap> new := DigraphAddVertices(D, 3);\n<immutable digraph with 6 vertices, 6 e\
dges>\ngap> DigraphVertices(new);\n[ 1 .. 6 ]\ngap> new := DigraphAddVertices(\
D, [Group([(1, 2)]), \"d\"]);\n<immutable digraph with 5 vertices, 6 edges>\ng\
ap> DigraphVertexLabels(new);\n[ 1, 2, 3, Group([ (1,2) ]), \"d\" ]\ngap> Digr\
aphAddVertices(D, 0) = D;\ntrue\ngap> D := CompleteBipartiteDigraph(IsMutableD\
igraph, 2, 3);\n<mutable digraph with 5 vertices, 12 edges>\ngap> new := Digra\
phAddVertices(D, 4);\n<mutable digraph with 9 vertices, 12 edges>\ngap> D = ne\
w;\ntrue\n", count := [ 3, 3, 15, 9 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 15, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 69853, 
                                                          root := ~, 
                                                          start := 69210, 
                                                          stop := 69852 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 15, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 15, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 69870, root := ~, 
                                                  start := 68385, 
                                                  stop := 69869 ) ], 
                                          count := [ 3, 3, 15, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 69884, root := ~, 
                                          start := 68003, stop := 69883 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 15, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edge", 
                                                      Label := "for a digraph \
and an edge", Name := "DigraphAddEdge" ), content := 0, 
                                                  count := [ 3, 3, 16, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 69992, root := ~, 
                                                  start := 69905, 
                                                  stop := 69991 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, src, ra\
n", Label := "for a digraph, source, and range", Name := "DigraphAddEdge" ), 
                                                  content := 0, 
                                                  count := [ 3, 3, 16, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 70093, root := ~, 
                                                  start := 69995, 
                                                  stop := 70092 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 16, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 70125, root := ~, 
                                                  start := 70096, 
                                                  stop := 70124 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70160, 
                                                          root := ~, 
                                                          start := 70149, 
                                                          stop := 70159 ), 
                                                      rec( 
                                                          content := " is a pa\
ir of vertices of ", count := [ 3, 3, 16, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70200, 
                                                          root := ~, 
                                                          start := 70186, 
                                                          stop := 70199 ), 
                                                      rec( content := ", or ",
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70215, 
                                                          root := ~, 
                                                          start := 70205, 
                                                          stop := 70214 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70234, 
                                                          root := ~, 
                                                          start := 70224, 
                                                          stop := 70233 ), 
                                                      rec( 
                                                          content := " are ver\
tices of ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70265, 
                                                          root := ~, 
                                                          start := 70251, 
                                                          stop := 70264 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen this operation returns a digraph constructed from ", count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70340, 
                                                          root := ~, 
                                                          start := 70326, 
                                                          stop := 70339 ), 
                                                      rec( 
                                                          content := "\n    by\
 adding a new edge with source ", count := [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70389, 
                                                          root := ~, 
                                                          start := 70378, 
                                                          stop := 70388 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1]", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 70399, 
                                                          root := ~, 
                                                          start := 70389, 
                                                          stop := 70398 ), 
                                                      rec( content := " [", 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70411, 
                                                          root := ~, 
                                                          start := 70401, 
                                                          stop := 70410 ), 
                                                      rec( 
                                                          content := "] and ra\
nge\n    ", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70438, 
                                                          root := ~, 
                                                          start := 70427, 
                                                          stop := 70437 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
2]", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 70448, 
                                                          root := ~, 
                                                          start := 70438, 
                                                          stop := 70447 ), 
                                                      rec( content := " [", 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70460, 
                                                          root := ~, 
                                                          start := 70450, 
                                                          stop := 70459 ), 
                                                      rec( 
                                                          content := "].\n    \
", count := [ 3, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 70471, 
                                                          root := ~, 
                                                          start := 70467, 
                                                          stop := 70470 ), 
                                                      rec( 
                                                          content := "\n    \n\
    If ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70498, 
                                                          root := ~, 
                                                          start := 70484, 
                                                          stop := 70497 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 16, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 70540, 
                                                          root := ~, 
                                                          start := 70510, 
                                                          stop := 70539 ), 
                                                      rec( 
                                                          content := ", then t\
he edge\n    is added directly to ", count := [ 3, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70595, 
                                                          root := ~, 
                                                          start := 70581, 
                                                          stop := 70594 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 3, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70614, 
                                                          root := ~, 
                                                          start := 70600, 
                                                          stop := 70613 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 16, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 70664, 
                                                          root := ~, 
                                                          start := 70626, 
                                                          stop := 70663 ), 
                                                      rec( 
                                                          content := ", then a\
n immutable copy of ", count := [ 3, 3, 16, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 70706, 
                                                          root := ~, 
                                                          start := 70692, 
                                                          stop := 70705 ), 
                                                      rec( 
                                                          content := " with th\
e\n    additional edge is returned.  ", count := [ 3, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 16, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 70754, 
                                                          root := ~, 
                                                          start := 70750, 
                                                          stop := 70753 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D1 := Digraph([[2], [3], []]);\n<immutable digraph with 3 vertices, 2 ed\
ges>\ngap> DigraphEdges(D1);\n[ [ 1, 2 ], [ 2, 3 ] ]\ngap> D2 := DigraphAddEdg\
e(D1, [3, 1]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> DigraphEdge\
s(D2);\n[ [ 1, 2 ], [ 2, 3 ], [ 3, 1 ] ]\ngap> D3 := DigraphAddEdge(D2, [2, 3]\
);\n<immutable multidigraph with 3 vertices, 4 edges>\ngap> DigraphEdges(D3);\
\n[ [ 1, 2 ], [ 2, 3 ], [ 2, 3 ], [ 3, 1 ] ]\ngap> D := CycleDigraph(IsMutable\
Digraph, 4);\n<mutable digraph with 4 vertices, 4 edges>\ngap> new := DigraphA\
ddEdge(D, [1, 3]);\n<mutable digraph with 4 vertices, 5 edges>\ngap> DigraphEd\
ges(new);\n[ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ] ]\ngap> D = new;\
\ntrue\n", count := [ 3, 3, 16, 8 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 16, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 71480, 
                                                          root := ~, 
                                                          start := 70760, 
                                                          stop := 71479 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 16, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 71497, root := ~, 
                                                  start := 70128, 
                                                  stop := 71496 ) ], 
                                          count := [ 3, 3, 16, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 71511, root := ~, 
                                          start := 69890, stop := 71510 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 16, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edge", 
                                                      Name := "DigraphAddEdgeO\
rbit" ), content := 0, count := [ 3, 3, 17, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 71586, root := ~, 
                                                  start := 71532, 
                                                  stop := 71585 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A n\
ew digraph.\n  ", count := [ 3, 3, 17, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 71630, root := ~, 
                                                  start := 71589, 
                                                  stop := 71629 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns a new digraph with the same vertices and edges as\n    ", 
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 71742, 
                                                          root := ~, 
                                                          start := 71728, 
                                                          stop := 71741 ), 
                                                      rec( 
                                                          content := " and wit\
h additional edges consisting of the orbit of the\n    edge ", 
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 71820, 
                                                          root := ~, 
                                                          start := 71809, 
                                                          stop := 71819 ), 
                                                      rec( 
                                                          content := " under t\
he action of the ", count := [ 3, 3, 17, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Group" ), content := 0, count := [ 3, 3, 17, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 71871, 
                                                          root := ~, 
                                                          start := 71845, 
                                                          stop := 71870 ), 
                                                      rec( 
                                                          content := " of\n   \
 ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 71893, 
                                                          root := ~, 
                                                          start := 71879, 
                                                          stop := 71892 ), 
                                                      rec( 
                                                          content := ".  If ",
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 71910, 
                                                          root := ~, 
                                                          start := 71899, 
                                                          stop := 71909 ), 
                                                      rec( 
                                                          content := " is alre\
ady an edge in ", count := [ 3, 3, 17, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 71947, 
                                                          root := ~, 
                                                          start := 71933, 
                                                          stop := 71946 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 71972, 
                                                          root := ~, 
                                                          start := 71958, 
                                                          stop := 71971 ), 
                                                      rec( 
                                                          content := " is retu\
rned unchanged. The argument ", count := [ 3, 3, 17, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 72023, 
                                                          root := ~, 
                                                          start := 72009, 
                                                          stop := 72022 ), 
                                                      rec( 
                                                          content := " must be\
\n    an immutable digraph.\n    ", count := [ 3, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 72066, 
                                                          root := ~, 
                                                          start := 72062, 
                                                          stop := 72065 ), 
                                                      rec( 
                                                          content := "\n\n    \
An edge is simply a pair of vertices of ", count := [ 3, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 72126, 
                                                          root := ~, 
                                                          start := 72112, 
                                                          stop := 72125 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := CayleyDigraph(DihedralGroup(8));\n<immutable digraph with 8 verti\
ces, 24 edges>\ngap> gr2 := DigraphAddEdgeOrbit(gr1, [1, 8]);\n<immutable digr\
aph with 8 vertices, 32 edges>\ngap> DigraphEdges(gr1);\n[ [ 1, 2 ], [ 1, 3 ],\
 [ 1, 4 ], [ 2, 1 ], [ 2, 5 ], [ 2, 6 ], \n  [ 3, 8 ], [ 3, 4 ], [ 3, 7 ], [ 4\
, 6 ], [ 4, 7 ], [ 4, 1 ], \n  [ 5, 7 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 6, 8 \
], [ 6, 2 ], \n  [ 7, 5 ], [ 7, 1 ], [ 7, 3 ], [ 8, 3 ], [ 8, 2 ], [ 8, 5 ] ]\
\ngap> DigraphEdges(gr2);\n[ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 8 ], [ 2, 1 ],\
 [ 2, 5 ], \n  [ 2, 6 ], [ 2, 7 ], [ 3, 8 ], [ 3, 4 ], [ 3, 7 ], [ 3, 6 ], \n \
 [ 4, 6 ], [ 4, 7 ], [ 4, 1 ], [ 4, 5 ], [ 5, 7 ], [ 5, 6 ], \n  [ 5, 8 ], [ 5\
, 4 ], [ 6, 4 ], [ 6, 8 ], [ 6, 2 ], [ 6, 3 ], \n  [ 7, 5 ], [ 7, 1 ], [ 7, 3 \
], [ 7, 2 ], [ 8, 3 ], [ 8, 2 ], \n  [ 8, 5 ], [ 8, 1 ] ]\ngap> gr3 := Digraph\
RemoveEdgeOrbit(gr2, [1, 8]);\n<immutable digraph with 8 vertices, 24 edges>\n\
gap> gr3 = gr1;\ntrue\n", count := [ 3, 3, 17, 5 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 73102, 
                                                          root := ~, 
                                                          start := 72133, 
                                                          stop := 73101 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 73119, root := ~, 
                                                  start := 71633, 
                                                  stop := 73118 ) ], 
                                          count := [ 3, 3, 17, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 73133, root := ~, 
                                          start := 71517, stop := 73132 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 17, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edges",
                                                      Name := "DigraphAddEdges\
" ), content := 0, count := [ 3, 3, 18, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 73205, root := ~, 
                                                  start := 73154, 
                                                  stop := 73204 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 73237, root := ~, 
                                                  start := 73208, 
                                                  stop := 73236 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 73273, 
                                                          root := ~, 
                                                          start := 73261, 
                                                          stop := 73272 ), 
                                                      rec( 
                                                          content := " is a (p\
ossibly empty) list of pairs of vertices of\n    ", count := [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 73343, 
                                                          root := ~, 
                                                          start := 73329, 
                                                          stop := 73342 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns a digraph constructed from\n    ", count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 73418, 
                                                          root := ~, 
                                                          start := 73404, 
                                                          stop := 73417 ), 
                                                      rec( 
                                                          content := " by addi\
ng the edges specified by ", count := [ 3, 3, 18, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 73464, 
                                                          root := ~, 
                                                          start := 73452, 
                                                          stop := 73463 ), 
                                                      rec( 
                                                          content := ".  More\\
n    precisely, for every ", count := [ 3, 3, 18, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 73508, 
                                                          root := ~, 
                                                          start := 73497, 
                                                          stop := 73507 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 73524, 
                                                          root := ~, 
                                                          start := 73512, 
                                                          stop := 73523 ), 
                                                      rec( 
                                                          content := ", a new \
edge\n    will be added with source ", count := [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge[1]", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 73581, 
                                                          root := ~, 
                                                          start := 73567, 
                                                          stop := 73580 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges[2]", count := [ 3, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 73607, 
                                                          root := ~, 
                                                          start := 73592, 
                                                          stop := 73606 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 73617, 
                                                          root := ~, 
                                                          start := 73613, 
                                                          stop := 73616 ), 
                                                      rec( 
                                                          content := "\n\n    \
If an edge is included in ", count := [ 3, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 73661, 
                                                          root := ~, 
                                                          start := 73649, 
                                                          stop := 73660 ), 
                                                      rec( 
                                                          content := " with mu\
ltiplicity ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 73688, 
                                                          root := ~, 
                                                          start := 73680, 
                                                          stop := 73687 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen it will be added ", count := [ 3, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 73724, 
                                                          root := ~, 
                                                          start := 73716, 
                                                          stop := 73723 ), 
                                                      rec( 
                                                          content := " times.\\
n\n    If ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 73754, 
                                                          root := ~, 
                                                          start := 73740, 
                                                          stop := 73753 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 73796, 
                                                          root := ~, 
                                                          start := 73766, 
                                                          stop := 73795 ), 
                                                      rec( 
                                                          content := ", then t\
he edges\n    are added directly to ", count := [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 73853, 
                                                          root := ~, 
                                                          start := 73839, 
                                                          stop := 73852 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 73872, 
                                                          root := ~, 
                                                          start := 73858, 
                                                          stop := 73871 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 73922, 
                                                          root := ~, 
                                                          start := 73884, 
                                                          stop := 73921 ), 
                                                      rec( 
                                                          content := ", then t\
he result is returned as an immutable\n    digraph.\n    ", 
                                                          count := 
                                                            [ 3, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 73989, 
                                                          root := ~, 
                                                          start := 73985, 
                                                          stop := 73988 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> func := function(n)\n>  local source, range, i;\n>  source := [];\n>  ra\
nge  := [];\n>  for i in [1 .. n - 2] do\n>    Add(source, i);\n>    Add(range\
, i + 1);\n>  od;\n>  return Digraph(n, source, range);\n> end;;\ngap> D := fu\
nc(1024);\n<immutable digraph with 1024 vertices, 1022 edges>\ngap> new := Dig\
raphAddEdges(D,\n> [[1023, 1024], [1, 1024], [1023, 1024], [1024, 1]]);\n<immu\
table multidigraph with 1024 vertices, 1026 edges>\ngap> D = new;\nfalse\ngap>\
 D2 := DigraphMutableCopy(func(1024));\n<mutable digraph with 1024 vertices, 1\
022 edges>\ngap> new := DigraphAddEdges(D2,\n> [[1023, 1024], [1, 1024], [1023\
, 1024], [1024, 1]]);\n<mutable multidigraph with 1024 vertices, 1026 edges>\n\
gap> D2 = new;\ntrue\n", count := [ 3, 3, 18, 6 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 18, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 74726, 
                                                          root := ~, 
                                                          start := 73995, 
                                                          stop := 74725 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 18, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 74743, root := ~, 
                                                  start := 73240, 
                                                  stop := 74742 ) ], 
                                          count := [ 3, 3, 18, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 74757, root := ~, 
                                          start := 73139, stop := 74756 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 18, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, v", 
                                                      Name := "DigraphRemoveVe\
rtex" ), content := 0, count := [ 3, 3, 19, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 74829, root := ~, 
                                                  start := 74778, 
                                                  stop := 74828 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 19, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 74861, root := ~, 
                                                  start := 74832, 
                                                  stop := 74860 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 74893, 
                                                          root := ~, 
                                                          start := 74885, 
                                                          stop := 74892 ), 
                                                      rec( 
                                                          content := " is a ve\
rtex of ", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 74923, 
                                                          root := ~, 
                                                          start := 74909, 
                                                          stop := 74922 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns a\n    digraph constructed from ", count := 
                                                            [ 3, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 74998, 
                                                          root := ~, 
                                                          start := 74984, 
                                                          stop := 74997 ), 
                                                      rec( 
                                                          content := " by remo\
ving vertex ", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 75026, 
                                                          root := ~, 
                                                          start := 75018, 
                                                          stop := 75025 ), 
                                                      rec( 
                                                          content := ",\n    a\
long with any edge whose source or range vertex is ", count := [ 3, 3, 19, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 75092, 
                                                          root := ~, 
                                                          start := 75084, 
                                                          stop := 75091 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 75097, 
                                                          root := ~, 
                                                          start := 75093, 
                                                          stop := 75096 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 75120, 
                                                          root := ~, 
                                                          start := 75106, 
                                                          stop := 75119 ), 
                                                      rec( content := " has ",
                                                          count := 
                                                            [ 3, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 75133, 
                                                          root := ~, 
                                                          start := 75125, 
                                                          stop := 75132 ), 
                                                      rec( 
                                                          content := " vertice\
s, then the vertices of the returned\n    digraph are ", count := 
                                                            [ 3, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1..n-1]", count := [ 3, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 75209, 
                                                          root := ~, 
                                                          start := 75194, 
                                                          stop := 75208 ), 
                                                      rec( 
                                                          content := ", but th\
e original labels can be\n    accessed via ", count := [ 3, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 3, 3, 19, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 75292, 
                                                          root := ~, 
                                                          start := 75259, 
                                                          stop := 75291 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 19, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 75298, 
                                                          root := ~, 
                                                          start := 75294, 
                                                          stop := 75297 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 19, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 75321, 
                                                          root := ~, 
                                                          start := 75307, 
                                                          stop := 75320 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 19, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 75363, 
                                                          root := ~, 
                                                          start := 75333, 
                                                          stop := 75362 ), 
                                                      rec( 
                                                          content := ", then t\
he\n    vertex is removed directly from ", count := [ 3, 3, 19, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 19, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 75424, 
                                                          root := ~, 
                                                          start := 75410, 
                                                          stop := 75423 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 3, 3, 19, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 19, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 75443, 
                                                          root := ~, 
                                                          start := 75429, 
                                                          stop := 75442 ), 
                                                      rec( 
                                                          content := " belongs\
\n    to ", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 19, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 75491, 
                                                          root := ~, 
                                                          start := 75459, 
                                                          stop := 75490 ), 
                                                      rec( 
                                                          content := ", an imm\
utable copy of ", count := [ 3, 3, 19, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 19, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 19, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 75528, 
                                                          root := ~, 
                                                          start := 75514, 
                                                          stop := 75527 ), 
                                                      rec( 
                                                          content := "\n    wi\
thout the vertex is returned.", count := [ 3, 3, 19, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 19, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 75568, 
                                                          root := ~, 
                                                          start := 75564, 
                                                          stop := 75567 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 19, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\"a\", \"b\", \"c\"],\n>                  [\"a\", \"a\", \
\"b\", \"c\", \"c\"],\n>                  [\"b\", \"c\", \"a\", \"a\", \"c\"])\
;\n<immutable digraph with 3 vertices, 5 edges>\ngap> DigraphVertexLabels(D);\
\n[ \"a\", \"b\", \"c\" ]\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 3 ], [ 2, 1\
 ], [ 3, 1 ], [ 3, 3 ] ]\ngap> new := DigraphRemoveVertex(D, 2);\n<immutable d\
igraph with 2 vertices, 3 edges>\ngap> DigraphVertexLabels(new);\n[ \"a\", \"c\
\" ]\ngap> D := CycleDigraph(IsMutableDigraph, 5);\n<mutable digraph with 5 ve\
rtices, 5 edges>\ngap> new := DigraphRemoveVertex(D, 1);\n<mutable digraph wit\
h 4 vertices, 3 edges>\ngap> DigraphVertexLabels(D);\n[ 2, 3, 4, 5 ]\ngap> D =\
 new;\ntrue\n", count := [ 3, 3, 19, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 19, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 76262, 
                                                          root := ~, 
                                                          start := 75574, 
                                                          stop := 76261 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 19, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 19, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 76279, root := ~, 
                                                  start := 74864, 
                                                  stop := 76278 ) ], 
                                          count := [ 3, 3, 19, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 76293, root := ~, 
                                          start := 74763, stop := 76292 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 19, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, verts",
                                                      Name := "DigraphRemoveVe\
rtices" ), content := 0, count := [ 3, 3, 20, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 76371, root := ~, 
                                                  start := 76314, 
                                                  stop := 76370 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 20, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 76403, root := ~, 
                                                  start := 76374, 
                                                  stop := 76402 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
erts", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 76439, 
                                                          root := ~, 
                                                          start := 76427, 
                                                          stop := 76438 ), 
                                                      rec( 
                                                          content := " is a (p\
ossibly empty) duplicate-free list of vertices of\n    ", count := 
                                                            [ 3, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 76515, 
                                                          root := ~, 
                                                          start := 76501, 
                                                          stop := 76514 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns a digraph constructed from\n    ", count := 
                                                            [ 3, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 76590, 
                                                          root := ~, 
                                                          start := 76576, 
                                                          stop := 76589 ), 
                                                      rec( 
                                                          content := " by remo\
ving every vertex in ", count := [ 3, 3, 20, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
erts", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 76631, 
                                                          root := ~, 
                                                          start := 76619, 
                                                          stop := 76630 ), 
                                                      rec( 
                                                          content := ", along \
with any edge\n    whose source or range vertex is in ", count := 
                                                            [ 3, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
erts", count := [ 3, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 76704, 
                                                          root := ~, 
                                                          start := 76692, 
                                                          stop := 76703 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 76709, 
                                                          root := ~, 
                                                          start := 76705, 
                                                          stop := 76708 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 76732, 
                                                          root := ~, 
                                                          start := 76718, 
                                                          stop := 76731 ), 
                                                      rec( content := " has ",
                                                          count := 
                                                            [ 3, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 76745, 
                                                          root := ~, 
                                                          start := 76737, 
                                                          stop := 76744 ), 
                                                      rec( 
                                                          content := " vertice\
s, then the vertices of the new\n    digraph are ", count := [ 3, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. n-Length(", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "vert\
s", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 3, 3, 
                                                                      20, 4 ],
                                                                  mathmode := \
"Text", name := "A", next := 76831, root := ~, start := 76819, stop := 76830 )
                                                                , 
                                                              rec( 
                                                                  content := "\
)]", count := [ 3, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 76837, 
                                                          root := ~, 
                                                          start := 76801, 
                                                          stop := 76836 ), 
                                                      rec( 
                                                          content := ", but th\
e\n    original labels can be accessed via ", count := [ 3, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 3, 3, 20, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 76920, 
                                                          root := ~, 
                                                          start := 76887, 
                                                          stop := 76919 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 20, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 76926, 
                                                          root := ~, 
                                                          start := 76922, 
                                                          stop := 76925 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 76949, 
                                                          root := ~, 
                                                          start := 76935, 
                                                          stop := 76948 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 20, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 76991, 
                                                          root := ~, 
                                                          start := 76961, 
                                                          stop := 76990 ), 
                                                      rec( 
                                                          content := ", then t\
he\n    vertices are removed directly from ", count := [ 3, 3, 20, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 77055, 
                                                          root := ~, 
                                                          start := 77041, 
                                                          stop := 77054 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 3, 3, 20, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 77074, 
                                                          root := ~, 
                                                          start := 77060, 
                                                          stop := 77073 ), 
                                                      rec( 
                                                          content := " belongs\
\n    to ", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 20, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 77122, 
                                                          root := ~, 
                                                          start := 77090, 
                                                          stop := 77121 ), 
                                                      rec( 
                                                          content := ", an imm\
utable copy of ", count := [ 3, 3, 20, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 20, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 77159, 
                                                          root := ~, 
                                                          start := 77145, 
                                                          stop := 77158 ), 
                                                      rec( 
                                                          content := "\n    wi\
thout the vertices is returned.", count := [ 3, 3, 20, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 20, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 77201, 
                                                          root := ~, 
                                                          start := 77197, 
                                                          stop := 77200 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 20, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\n<immutable d\
igraph with 5 vertices, 11 edges>\ngap> SetDigraphVertexLabels(D, [\"a\", \"b\
\", \"c\", \"d\", \"e\"]);\ngap> new := DigraphRemoveVertices(D, [2, 4]);\n<im\
mutable digraph with 3 vertices, 4 edges>\ngap> DigraphVertexLabels(new);\n[ \
\"a\", \"c\", \"e\" ]\ngap> D := CycleDigraph(IsMutableDigraph, 5);\n<mutable \
digraph with 5 vertices, 5 edges>\ngap> new := DigraphRemoveVertices(D, [1, 3]\
);\n<mutable digraph with 3 vertices, 1 edge>\ngap> DigraphVertexLabels(D);\n[\
 2, 4, 5 ]\ngap> D = new;\ntrue\n", count := [ 3, 3, 20, 7 ], name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 20, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 77784, 
                                                          root := ~, 
                                                          start := 77207, 
                                                          stop := 77783 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 20, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 20, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 77801, root := ~, 
                                                  start := 76406, 
                                                  stop := 77800 ) ], 
                                          count := [ 3, 3, 20, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 77815, root := ~, 
                                          start := 76299, stop := 77814 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 20, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edge", 
                                                      Label := "for a digraph \
and an edge", Name := "DigraphRemoveEdge" ), content := 0, 
                                                  count := [ 3, 3, 21, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 77926, root := ~, 
                                                  start := 77836, 
                                                  stop := 77925 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, src, ra\
n", Label := "for a digraph, source, and range", Name := "DigraphRemoveEdge" )
                                                    , content := 0, 
                                                  count := [ 3, 3, 21, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 78030, root := ~, 
                                                  start := 77929, 
                                                  stop := 78029 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 21, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 78062, root := ~, 
                                                  start := 78033, 
                                                  stop := 78061 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78100, 
                                                          root := ~, 
                                                          start := 78086, 
                                                          stop := 78099 ), 
                                                      rec( 
                                                          content := " is a di\
graph with no multiple edges and ", count := [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78152, 
                                                          root := ~, 
                                                          start := 78141, 
                                                          stop := 78151 ), 
                                                      rec( 
                                                          content := " is a\n \
   pair of vertices of ", count := [ 3, 3, 21, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78196, 
                                                          root := ~, 
                                                          start := 78182, 
                                                          stop := 78195 ), 
                                                      rec( content := ", or ",
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78211, 
                                                          root := ~, 
                                                          start := 78201, 
                                                          stop := 78210 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78226, 
                                                          root := ~, 
                                                          start := 78216, 
                                                          stop := 78225 ), 
                                                      rec( 
                                                          content := " are\n  \
  vertices of ", count := [ 3, 3, 21, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78261, 
                                                          root := ~, 
                                                          start := 78247, 
                                                          stop := 78260 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns a digraph\n    constructed from ", count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78336, 
                                                          root := ~, 
                                                          start := 78322, 
                                                          stop := 78335 ), 
                                                      rec( 
                                                          content := " by remo\
ving the edge specified by\n    ", count := [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78386, 
                                                          root := ~, 
                                                          start := 78375, 
                                                          stop := 78385 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
src, ran]", count := [ 3, 3, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78407, 
                                                          root := ~, 
                                                          start := 78390, 
                                                          stop := 78406 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 78413, 
                                                          root := ~, 
                                                          start := 78409, 
                                                          stop := 78412 ), 
                                                      rec( 
                                                          content := "  \n\n  \
  If ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78438, 
                                                          root := ~, 
                                                          start := 78424, 
                                                          stop := 78437 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 21, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 78486, 
                                                          root := ~, 
                                                          start := 78450, 
                                                          stop := 78485 ), 
                                                      rec( 
                                                          content := ", then t\
he edge is removed directly from\n    ", count := [ 3, 3, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78545, 
                                                          root := ~, 
                                                          start := 78531, 
                                                          stop := 78544 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 3, 3, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78564, 
                                                          root := ~, 
                                                          start := 78550, 
                                                          stop := 78563 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 21, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 78614, 
                                                          root := ~, 
                                                          start := 78576, 
                                                          stop := 78613 ), 
                                                      rec( 
                                                          content := ", an imm\
utable copy of ", count := [ 3, 3, 21, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78651, 
                                                          root := ~, 
                                                          start := 78637, 
                                                          stop := 78650 ), 
                                                      rec( 
                                                          content := " without\
\n    the edge is returned.\n    ", count := [ 3, 3, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 78694, 
                                                          root := ~, 
                                                          start := 78690, 
                                                          stop := 78693 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that if ", count := [ 3, 3, 21, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78727, 
                                                          root := ~, 
                                                          start := 78713, 
                                                          stop := 78726 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 21, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 78771, 
                                                          root := ~, 
                                                          start := 78739, 
                                                          stop := 78770 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen a new copy of ", count := [ 3, 3, 21, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78810, 
                                                          root := ~, 
                                                          start := 78796, 
                                                          stop := 78809 ), 
                                                      rec( 
                                                          content := " will be\
 returned even if ", count := [ 3, 3, 21, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78847, 
                                                          root := ~, 
                                                          start := 78836, 
                                                          stop := 78846 ), 
                                                      rec( 
                                                          content := " or \n  \
  ", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
src, ran]", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78873, 
                                                          root := ~, 
                                                          start := 78856, 
                                                          stop := 78872 ), 
                                                      rec( 
                                                          content := " does no\
t define an edge of ", count := [ 3, 3, 21, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 21, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 78915, 
                                                          root := ~, 
                                                          start := 78901, 
                                                          stop := 78914 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 21, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 78920, 
                                                          root := ~, 
                                                          start := 78916, 
                                                          stop := 78919 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(250000);\n<immutable cycle digraph with 250000 vertice\
s>\ngap> D := DigraphRemoveEdge(D, [250000, 1]);\n<immutable digraph with 2500\
00 vertices, 249999 edges>\ngap> new := DigraphRemoveEdge(D, [25000, 2]);;\nga\
p> new = D;\ntrue\ngap> IsIdenticalObj(new, D);\nfalse\ngap> D := DigraphMutab\
leCopy(D);;\ngap> new := DigraphRemoveEdge(D, 2500, 2);;\ngap> IsIdenticalObj(\
new, D);\ntrue\n", count := [ 3, 3, 21, 9 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 21, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 79350, 
                                                          root := ~, 
                                                          start := 78926, 
                                                          stop := 79349 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 21, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 21, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 79367, root := ~, 
                                                  start := 78065, 
                                                  stop := 79366 ) ], 
                                          count := [ 3, 3, 21, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 79381, root := ~, 
                                          start := 77821, stop := 79380 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 21, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edge", 
                                                      Name := "DigraphRemoveEd\
geOrbit" ), content := 0, count := [ 3, 3, 22, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 79459, root := ~, 
                                                  start := 79402, 
                                                  stop := 79458 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A n\
ew digraph.\n  ", count := [ 3, 3, 22, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 22, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 79503, root := ~, 
                                                  start := 79462, 
                                                  stop := 79502 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns a new digraph with the same vertices as\n    ", 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 79605, 
                                                          root := ~, 
                                                          start := 79591, 
                                                          stop := 79604 ), 
                                                      rec( 
                                                          content := " and wit\
h the orbit of the edge ", count := [ 3, 3, 22, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 79648, 
                                                          root := ~, 
                                                          start := 79637, 
                                                          stop := 79647 ), 
                                                      rec( 
                                                          content := " (under \
the action\n    of the ", count := [ 3, 3, 22, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Group" ), content := 0, count := [ 3, 3, 22, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 79704, 
                                                          root := ~, 
                                                          start := 79678, 
                                                          stop := 79703 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 79722, 
                                                          root := ~, 
                                                          start := 79708, 
                                                          stop := 79721 ), 
                                                      rec( 
                                                          content := ") remove\
d.\n    If ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 79751, 
                                                          root := ~, 
                                                          start := 79740, 
                                                          stop := 79750 ), 
                                                      rec( 
                                                          content := " is not \
an edge in ", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 79784, 
                                                          root := ~, 
                                                          start := 79770, 
                                                          stop := 79783 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 79805, 
                                                          root := ~, 
                                                          start := 79791, 
                                                          stop := 79804 ), 
                                                      rec( 
                                                          content := " is\n   \
 returned unchanged. The argument ", count := [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 79860, 
                                                          root := ~, 
                                                          start := 79846, 
                                                          stop := 79859 ), 
                                                      rec( 
                                                          content := " must be\
 an immutable\n    digraph.\n    ", count := [ 3, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 79903, 
                                                          root := ~, 
                                                          start := 79899, 
                                                          stop := 79902 ), 
                                                      rec( 
                                                          content := "\n\n    \
An edge is simply a pair of vertices of ", count := [ 3, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 79963, 
                                                          root := ~, 
                                                          start := 79949, 
                                                          stop := 79962 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := CayleyDigraph(DihedralGroup(8));\n<immutable digraph with 8 verti\
ces, 24 edges>\ngap> gr2 := DigraphAddEdgeOrbit(gr1, [1, 8]);\n<immutable digr\
aph with 8 vertices, 32 edges>\ngap> DigraphEdges(gr1);\n[ [ 1, 2 ], [ 1, 3 ],\
 [ 1, 4 ], [ 2, 1 ], [ 2, 5 ], [ 2, 6 ], \n  [ 3, 8 ], [ 3, 4 ], [ 3, 7 ], [ 4\
, 6 ], [ 4, 7 ], [ 4, 1 ], \n  [ 5, 7 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 6, 8 \
], [ 6, 2 ], \n  [ 7, 5 ], [ 7, 1 ], [ 7, 3 ], [ 8, 3 ], [ 8, 2 ], [ 8, 5 ] ]\
\ngap> DigraphEdges(gr2);\n[ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 8 ], [ 2, 1 ],\
 [ 2, 5 ], \n  [ 2, 6 ], [ 2, 7 ], [ 3, 8 ], [ 3, 4 ], [ 3, 7 ], [ 3, 6 ], \n \
 [ 4, 6 ], [ 4, 7 ], [ 4, 1 ], [ 4, 5 ], [ 5, 7 ], [ 5, 6 ], \n  [ 5, 8 ], [ 5\
, 4 ], [ 6, 4 ], [ 6, 8 ], [ 6, 2 ], [ 6, 3 ], \n  [ 7, 5 ], [ 7, 1 ], [ 7, 3 \
], [ 7, 2 ], [ 8, 3 ], [ 8, 2 ], \n  [ 8, 5 ], [ 8, 1 ] ]\ngap> gr3 := Digraph\
RemoveEdgeOrbit(gr2, [1, 8]);\n<immutable digraph with 8 vertices, 24 edges>\n\
gap> gr3 = gr1;\ntrue\n", count := [ 3, 3, 22, 5 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 22, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 80938, 
                                                          root := ~, 
                                                          start := 79969, 
                                                          stop := 80937 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 22, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 22, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 80955, root := ~, 
                                                  start := 79506, 
                                                  stop := 80954 ) ], 
                                          count := [ 3, 3, 22, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 80969, root := ~, 
                                          start := 79387, stop := 80968 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 22, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edges",
                                                      Name := "DigraphRemoveEd\
ges" ), content := 0, count := [ 3, 3, 23, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 81044, root := ~, 
                                                  start := 80990, 
                                                  stop := 81043 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 23, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 81076, root := ~, 
                                                  start := 81047, 
                                                  stop := 81075 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
one of the following holds:\n    ", count := [ 3, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 3, 3, 23, 5 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "digraph", count := [ 3, 3, 23, 5 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 5 ], mathmode := "Te\
xt", name := "A", next := 81174, root := ~, start := 81160, stop := 81173 ), 
                                                                      rec( 
                                                                          cont\
ent := " is a digraph with no multiple edges, and\n        ", count := [ 3, 3,\
 23, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( content := "edges", count := [ 3, 3, 23, 5 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 5 ], 
                                                                          math\
mode := "Text", name := "A", next := 81236, root := ~, start := 81224, stop :=\
 81235 ), rec( content := " is a list of pairs of vertices of ", count := [ 3,\
 3, 23, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\
s := rec(  ), content := [ rec( content := "digraph", count := [ 3, 3, 23, 5 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 5 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 81285, root := ~, start := 81271, stop :=\
 81284 ), rec( content := ", or\n      ", count := [ 3, 3, 23, 5 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 5 ], 
                                                                  name := "Ite\
m", next := 81303, root := ~, start := 81145, stop := 81302 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := " ", count := [ 3, 3, 23, 7 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conten\
t := [ rec( content := "digraph", count := [ 3, 3, 23, 7 ], mathmode := "Text"\
, name := "PCDATA", root := ~ ) ], count := [ 3, 3, 23, 7 ], mathmode := "Text\
", name := "A", next := 81331, root := ~, start := 81317, stop := 81330 ), 
                                                                      rec( 
                                                                          cont\
ent := " is a digraph and ", count := [ 3, 3, 23, 7 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "edges", count := [ 3, 3, 23, 7 ], mathmode := "Text", name := "PCDATA",\
 root := ~ ) ], count := [ 3, 3, 23, 7 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 81361, root := ~, start := 81349, stop := 81360 ), rec( content := " is an\
 empty list ", count := [ 3, 3, 23, 7 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ) ], count := [ 3, 3, 23, 7 ], name := "Item", next := 81386, 
                                                                  root := ~, 
                                                                  start := 813\
10, stop := 81385 ) ], count := [ 3, 3, 23, 4 ], mathmode := "Text", 
                                                          name := "List", 
                                                          next := 81398, 
                                                          root := ~, 
                                                          start := 81132, 
                                                          stop := 81397 ), 
                                                      rec( 
                                                          content := "\n\n    \
then this operation returns a digraph constructed from ", count := 
                                                            [ 3, 3, 23, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 81473, 
                                                          root := ~, 
                                                          start := 81459, 
                                                          stop := 81472 ), 
                                                      rec( 
                                                          content := "\n    by\
 removing all of the edges specified by ", count := [ 3, 3, 23, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 81532, 
                                                          root := ~, 
                                                          start := 81520, 
                                                          stop := 81531 ), 
                                                      rec( 
                                                          content := "\n    (s\
ee ", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and an edge", Oper := "DigraphRemoveEdge" ), content := 0, 
                                                          count := 
                                                            [ 3, 3, 23, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 81607, 
                                                          root := ~, 
                                                          start := 81542, 
                                                          stop := 81606 ), 
                                                      rec( 
                                                          content := ").\n    \
", count := [ 3, 3, 23, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 23, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 81618, 
                                                          root := ~, 
                                                          start := 81614, 
                                                          stop := 81617 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 81641, 
                                                          root := ~, 
                                                          start := 81627, 
                                                          stop := 81640 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 23, 10 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 81683, 
                                                          root := ~, 
                                                          start := 81653, 
                                                          stop := 81682 ), 
                                                      rec( 
                                                          content := ", then t\
he edge\n    is removed directly from ", count := [ 3, 3, 23, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 81742, 
                                                          root := ~, 
                                                          start := 81728, 
                                                          stop := 81741 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 3, 3, 23, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 81761, 
                                                          root := ~, 
                                                          start := 81747, 
                                                          stop := 81760 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 23, 10 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 81811, 
                                                          root := ~, 
                                                          start := 81773, 
                                                          stop := 81810 ), 
                                                      rec( 
                                                          content := ", the ed\
ge is removed from an immutable copy of\n    ", count := [ 3, 3, 23, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 23, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 81877, 
                                                          root := ~, 
                                                          start := 81863, 
                                                          stop := 81876 ), 
                                                      rec( 
                                                          content := " and thi\
s new digraph is returned.", count := [ 3, 3, 23, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 23, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 81915, 
                                                          root := ~, 
                                                          start := 81911, 
                                                          stop := 81914 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that if ", count := [ 3, 3, 23, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 81946, 
                                                          root := ~, 
                                                          start := 81934, 
                                                          stop := 81945 ), 
                                                      rec( 
                                                          content := " is empt\
y, then this operation\n    will always return ", count := [ 3, 3, 23, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 82014, 
                                                          root := ~, 
                                                          start := 82000, 
                                                          stop := 82013 ), 
                                                      rec( 
                                                          content := " rather \
than a copy. Also, if any element\n    of ", count := [ 3, 3, 23, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 82075, 
                                                          root := ~, 
                                                          start := 82063, 
                                                          stop := 82074 ), 
                                                      rec( 
                                                          content := " is inva\
lid (i.e. does not define an edge of ", count := [ 3, 3, 23, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 23, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 82134, 
                                                          root := ~, 
                                                          start := 82120, 
                                                          stop := 82133 ), 
                                                      rec( 
                                                          content := ")\n    t\
hen that element will simply be ignored.\n\n    ", count := [ 3, 3, 23, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(250000);\n<immutable cycle digraph with 250000 vertice\
s>\ngap> D := DigraphRemoveEdges(D, [[250000, 1]]);\n<immutable digraph with 2\
50000 vertices, 249999 edges>\ngap> D := DigraphMutableCopy(D);\n<mutable digr\
aph with 250000 vertices, 249999 edges>\ngap> new := DigraphRemoveEdges(D, [[1\
, 2], [2, 3], [3, 100]]);\n<mutable digraph with 250000 vertices, 249997 edges\
>\ngap> new = D;\ntrue\n", count := [ 3, 3, 23, 12 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 23, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 82622, 
                                                          root := ~, 
                                                          start := 82187, 
                                                          stop := 82621 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 23, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 23, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 82639, root := ~, 
                                                  start := 81079, 
                                                  stop := 82638 ) ], 
                                          count := [ 3, 3, 23, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 82653, root := ~, 
                                          start := 80975, stop := 82652 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 23, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphRemoveLo\
ops" ), content := 0, count := [ 3, 3, 24, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 82721, root := ~, 
                                                  start := 82674, 
                                                  stop := 82720 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphRemoveLo\
opsAttr" ), content := 0, count := [ 3, 3, 24, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 82775, root := ~, 
                                                  start := 82724, 
                                                  stop := 82774 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 24, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 82807, root := ~, 
                                                  start := 82778, 
                                                  stop := 82806 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 82845, 
                                                          root := ~, 
                                                          start := 82831, 
                                                          stop := 82844 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then this operation returns a\n    digraph  constructed from ", 
                                                          count := 
                                                            [ 3, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 82934, 
                                                          root := ~, 
                                                          start := 82920, 
                                                          stop := 82933 ), 
                                                      rec( 
                                                          content := " by remo\
ving every loop. A loop\n    is an edge with equal source and range.", 
                                                          count := 
                                                            [ 3, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 83013, 
                                                          root := ~, 
                                                          start := 83009, 
                                                          stop := 83012 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 83036, 
                                                          root := ~, 
                                                          start := 83022, 
                                                          stop := 83035 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the loops are\
 removed from the mutable digraph ", count := [ 3, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 83169, 
                                                          root := ~, 
                                                          start := 83155, 
                                                          stop := 83168 ), 
                                                      rec( 
                                                          content := "\n    in\
-place.\n    ", count := [ 3, 3, 24, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2, 4], [1, 4], [3, 4], [1, 4, 5], [1, 5]]);\n<immutabl\
e digraph with 5 vertices, 12 edges>\ngap> DigraphRemoveLoops(D);\n<immutable \
digraph with 5 vertices, 8 edges>\ngap> D := Digraph(IsMutableDigraph, [[1, 2]\
, [1]]);\n<mutable digraph with 2 vertices, 3 edges>\ngap> DigraphRemoveLoops(\
D);\n<mutable digraph with 2 vertices, 2 edges>\ngap> D;\n<mutable digraph wit\
h 2 vertices, 2 edges>\n", count := [ 3, 3, 24, 7 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 24, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 83623, 
                                                          root := ~, 
                                                          start := 83188, 
                                                          stop := 83622 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 24, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 24, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 83640, root := ~, 
                                                  start := 82810, 
                                                  stop := 83639 ) ], 
                                          count := [ 3, 3, 24, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 83654, root := ~, 
                                          start := 82659, stop := 83653 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 24, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphRemoveAl\
lMultipleEdges" ), content := 0, count := [ 3, 3, 25, 2 ], mathmode := "Text",
                                                  name := "Oper", 
                                                  next := 83733, root := ~, 
                                                  start := 83675, 
                                                  stop := 83732 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphRemoveAl\
lMultipleEdgesAttr" ), content := 0, count := [ 3, 3, 25, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 83798, root := ~, 
                                                  start := 83736, 
                                                  stop := 83797 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 25, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 83830, root := ~, 
                                                  start := 83801, 
                                                  stop := 83829 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 83868, 
                                                          root := ~, 
                                                          start := 83854, 
                                                          stop := 83867 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then this operation returns a\n    digraph  constructed from ", 
                                                          count := 
                                                            [ 3, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 83957, 
                                                          root := ~, 
                                                          start := 83943, 
                                                          stop := 83956 ), 
                                                      rec( 
                                                          content := " by remo\
ving all multiple edges.\n    The result is the largest subdigraph of ", 
                                                          count := 
                                                            [ 3, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 84048, 
                                                          root := ~, 
                                                          start := 84034, 
                                                          stop := 84047 ), 
                                                      rec( 
                                                          content := " which d\
oes not\n    contain multiple edges.", count := [ 3, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 25, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 84095, 
                                                          root := ~, 
                                                          start := 84091, 
                                                          stop := 84094 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 25, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 84118, 
                                                          root := ~, 
                                                          start := 84104, 
                                                          stop := 84117 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the multiple \
edges of the mutable digraph ", count := [ 3, 3, 25, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 25, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 25, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 84246, 
                                                          root := ~, 
                                                          start := 84232, 
                                                          stop := 84245 ), 
                                                      rec( 
                                                          content := " are\n  \
  removed in-place.\n    ", count := [ 3, 3, 25, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D1 := Digraph([[1, 2, 3, 2], [1, 1, 3], [2, 2, 2]]);\n<immutable multidi\
graph with 3 vertices, 10 edges>\ngap> D2 := DigraphRemoveAllMultipleEdges(D1)\
;\n<immutable digraph with 3 vertices, 6 edges>\ngap> OutNeighbours(D2);\n[ [ \
1, 2, 3 ], [ 1, 3 ], [ 2 ] ]\ngap> D := Digraph(IsMutableDigraph, [[2, 2], [1]\
]);\n<mutable multidigraph with 2 vertices, 3 edges>\ngap> DigraphRemoveAllMul\
tipleEdges(D);\n<mutable digraph with 2 vertices, 2 edges>\ngap> D;\n<mutable \
digraph with 2 vertices, 2 edges>\n", count := [ 3, 3, 25, 7 ], name := "PCDAT\
A", root := ~ ) ], count := [ 3, 3, 25, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 84799, 
                                                          root := ~, 
                                                          start := 84277, 
                                                          stop := 84798 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 25, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 25, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 84816, root := ~, 
                                                  start := 83833, 
                                                  stop := 84815 ) ], 
                                          count := [ 3, 3, 25, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 84830, root := ~, 
                                          start := 83660, stop := 84829 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 25, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edges",
                                                      Label := "for a digraph \
and a list of edges", Name := "DigraphReverseEdges" ), content := 0, 
                                                  count := [ 3, 3, 26, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 84952, root := ~, 
                                                  start := 84851, 
                                                  stop := 84951 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edge", 
                                                      Label := "for a digraph \
and an edge", Name := "DigraphReverseEdge" ), content := 0, 
                                                  count := [ 3, 3, 26, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 85046, root := ~, 
                                                  start := 84955, 
                                                  stop := 85045 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, src, ra\
n", Label := "for a digraph, source, and range", Name := "DigraphReverseEdge" 
                                                     ), content := 0, 
                                                  count := [ 3, 3, 26, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 85151, root := ~, 
                                                  start := 85049, 
                                                  stop := 85150 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 26, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 85183, root := ~, 
                                                  start := 85154, 
                                                  stop := 85182 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 85221, 
                                                          root := ~, 
                                                          start := 85207, 
                                                          stop := 85220 ), 
                                                      rec( 
                                                          content := " is a di\
graph without multiple edges, and ", count := [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 85275, 
                                                          root := ~, 
                                                          start := 85263, 
                                                          stop := 85274 ), 
                                                      rec( 
                                                          content := " is a\n \
   list of pairs of vertices of ", count := [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 85328, 
                                                          root := ~, 
                                                          start := 85314, 
                                                          stop := 85327 ), 
                                                      rec( 
                                                          content := " (the en\
tries of each pair\n    corresponding to the source and the range of an edge, \
respectively),\n    then ", count := [ 3, 3, 26, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphReverseEdges", count := [ 3, 3, 26, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 85463, 
                                                          root := ~, 
                                                          start := 85437, 
                                                          stop := 85462 ), 
                                                      rec( 
                                                          content := " returns\
 a digraph constructed from\n    ", count := [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 85517, 
                                                          root := ~, 
                                                          start := 85503, 
                                                          stop := 85516 ), 
                                                      rec( 
                                                          content := " by reve\
rsing the orientation of every edge specified by\n    ", count := 
                                                            [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dges", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 85590, 
                                                          root := ~, 
                                                          start := 85578, 
                                                          stop := 85589 ), 
                                                      rec( 
                                                          content := ". If onl\
y one edge is to be reversed, then\n    ", count := [ 3, 3, 26, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphReverseEdge", count := [ 3, 3, 26, 7 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 26, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 85662, 
                                                          root := ~, 
                                                          start := 85637, 
                                                          stop := 85661 ), 
                                                      rec( 
                                                          content := " can be \
used instead. In this case, the second\n    argument should just be a single v\
ertex-pair, or the second and third\n    arguments should be the source and ra\
nge of an edge respectively. ", count := [ 3, 3, 26, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 26, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 85857, 
                                                          root := ~, 
                                                          start := 85853, 
                                                          stop := 85856 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that even though ", count := [ 3, 3, 26, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 26, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 85899, 
                                                          root := ~, 
                                                          start := 85885, 
                                                          stop := 85898 ), 
                                                      rec( 
                                                          content := " cannot \
have multiple edges, the\n    output may have multiple edges. ", 
                                                          count := 
                                                            [ 3, 3, 26, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 26, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 85972, 
                                                          root := ~, 
                                                          start := 85968, 
                                                          stop := 85971 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 85995, 
                                                          root := ~, 
                                                          start := 85981, 
                                                          stop := 85994 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 26, 9 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 86037, 
                                                          root := ~, 
                                                          start := 86007, 
                                                          stop := 86036 ), 
                                                      rec( 
                                                          content := ", then t\
he edges\n    are reversed in ", count := [ 3, 3, 26, 9 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 86088, 
                                                          root := ~, 
                                                          start := 86074, 
                                                          stop := 86087 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 3, 3, 26, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 86107, 
                                                          root := ~, 
                                                          start := 86093, 
                                                          stop := 86106 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 26, 9 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 86157, 
                                                          root := ~, 
                                                          start := 86119, 
                                                          stop := 86156 ), 
                                                      rec( 
                                                          content := ", an imm\
utable copy of ", count := [ 3, 3, 26, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 26, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 26, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 86194, 
                                                          root := ~, 
                                                          start := 86180, 
                                                          stop := 86193 ), 
                                                      rec( 
                                                          content := " with th\
e\n    specified edges reversed is returned.", count := [ 3, 3, 26, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 26, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 86249, 
                                                          root := ~, 
                                                          start := 86245, 
                                                          stop := 86248 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 3, 3, 26, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDiSparse6String(\".Tg?i@s?t_e?_qEsC\");\n<immutable digr\
aph with 21 vertices, 8 edges>\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 7 ], [\
 1, 8 ], [ 5, 21 ], [ 7, 19 ], [ 9, 1 ], \n  [ 11, 2 ], [ 21, 1 ] ]\ngap> new \
:= DigraphReverseEdge(D, [7, 19]);\n<immutable digraph with 21 vertices, 8 edg\
es>\ngap> DigraphEdges(new);\n[ [ 1, 2 ], [ 1, 7 ], [ 1, 8 ], [ 5, 21 ], [ 9, \
1 ], [ 11, 2 ], \n  [ 19, 7 ], [ 21, 1 ] ]\ngap> D2 := DigraphMutableCopy(new)\
;;\ngap> new := DigraphReverseEdges(D2, [[19, 7]]);;\ngap> D2 = new;\ntrue\nga\
p> D = new;\ntrue\n", count := [ 3, 3, 26, 11 ], name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 26, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 86832, 
                                                          root := ~, 
                                                          start := 86254, 
                                                          stop := 86831 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 26, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 26, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 86849, root := ~, 
                                                  start := 85186, 
                                                  stop := 86848 ) ], 
                                          count := [ 3, 3, 26, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 86863, root := ~, 
                                          start := 84836, stop := 86862 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 26, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D1, D2, ...",
                                                      Label := "for an\n    ar\
bitrary number of digraphs", Name := "DigraphDisjointUnion" ), content := 0, 
                                                  count := [ 3, 3, 27, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 86985, root := ~, 
                                                  start := 86884, 
                                                  stop := 86984 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "list", 
                                                      Label := "for a list of \
digraphs", Name := "DigraphDisjointUnion" ), content := 0, 
                                                  count := [ 3, 3, 27, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 87065, root := ~, 
                                                  start := 86988, 
                                                  stop := 87064 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 27, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 87097, root := ~, 
                                                  start := 87068, 
                                                  stop := 87096 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    In \
the first form, if ", count := [ 3, 3, 27, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 87149, 
                                                          root := ~, 
                                                          start := 87140, 
                                                          stop := 87148 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
2", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 87160, 
                                                          root := ~, 
                                                          start := 87151, 
                                                          stop := 87159 ), 
                                                      rec( 
                                                          content := ", etc. a\
re digraphs, then\n    ", count := [ 3, 3, 27, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDisjointUnion", count := [ 3, 3, 27, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 27, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87217, 
                                                          root := ~, 
                                                          start := 87190, 
                                                          stop := 87216 ), 
                                                      rec( 
                                                          content := " returns\
 their disjoint union.\n\n    In the second form, if ", count := 
                                                            [ 3, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 87287, 
                                                          root := ~, 
                                                          start := 87276, 
                                                          stop := 87286 ), 
                                                      rec( 
                                                          content := " is a no\
n-empty list of digraphs, then\n    ", count := [ 3, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDisjointUnion", count := [ 3, 3, 27, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 27, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87357, 
                                                          root := ~, 
                                                          start := 87330, 
                                                          stop := 87356 ), 
                                                      rec( 
                                                          content := " returns\
 the disjoint union of the digraphs\n    contained in the list.  ", 
                                                          count := 
                                                            [ 3, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 27, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 87433, 
                                                          root := ~, 
                                                          start := 87429, 
                                                          stop := 87432 ), 
                                                      rec( 
                                                          content := "\n\n    \
For a disjoint union of digraphs, the vertex set is the disjoint union of\n   \
 the vertex sets, and the edge list is the disjoint union of the edge lists.\n\
    ", count := [ 3, 3, 27, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 87601, 
                                                          root := ~, 
                                                          start := 87597, 
                                                          stop := 87600 ), 
                                                      rec( 
                                                          content := "\n\n    \
More specifically, for a collection of digraphs ", count := [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 87664, 
                                                          root := ~, 
                                                          start := 87655, 
                                                          stop := 87663 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
2", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 87675, 
                                                          root := ~, 
                                                          start := 87666, 
                                                          stop := 87674 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
..", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87691, 
                                                          root := ~, 
                                                          start := 87681, 
                                                          stop := 87690 ), 
                                                      rec( 
                                                          content := ", the di\
sjoint union with have\n    ", count := [ 3, 3, 27, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphNrVertices(", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87751, 
                                                          root := ~, 
                                                          start := 87726, 
                                                          stop := 87750 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 87760, 
                                                          root := ~, 
                                                          start := 87751, 
                                                          stop := 87759 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87768, 
                                                          root := ~, 
                                                          start := 87760, 
                                                          stop := 87767 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "+\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87777, 
                                                          root := ~, 
                                                          start := 87769, 
                                                          stop := 87776 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphNrVertices(", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87807, 
                                                          root := ~, 
                                                          start := 87782, 
                                                          stop := 87806 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
2", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 87816, 
                                                          root := ~, 
                                                          start := 87807, 
                                                          stop := 87815 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87824, 
                                                          root := ~, 
                                                          start := 87816, 
                                                          stop := 87823 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "+\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87833, 
                                                          root := ~, 
                                                          start := 87825, 
                                                          stop := 87832 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
..", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87844, 
                                                          root := ~, 
                                                          start := 87834, 
                                                          stop := 87843 ), 
                                                      rec( 
                                                          content := " vertice\
s.\n    The edges of ", count := [ 3, 3, 27, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 87881, 
                                                          root := ~, 
                                                          start := 87872, 
                                                          stop := 87880 ), 
                                                      rec( 
                                                          content := " will re\
main unchanged, whilst the edges of the\n    ", count := [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87941, 
                                                          root := ~, 
                                                          start := 87933, 
                                                          stop := 87940 ), 
                                                      rec( 
                                                          content := "th digra\
ph, ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 87961, 
                                                          root := ~, 
                                                          start := 87953, 
                                                          stop := 87960 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i]", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 87971, 
                                                          root := ~, 
                                                          start := 87961, 
                                                          stop := 87970 ), 
                                                      rec( 
                                                          content := ", will b\
e changed so that they\n    belong to the vertices of the disjoint union corre\
sponding to\n    ", count := [ 3, 3, 27, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 88080, 
                                                          root := ~, 
                                                          start := 88072, 
                                                          stop := 88079 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i]", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 88090, 
                                                          root := ~, 
                                                          start := 88080, 
                                                          stop := 88089 ), 
                                                      rec( 
                                                          content := ".  In pa\
rticular, the edges of ", count := [ 3, 3, 27, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 88129, 
                                                          root := ~, 
                                                          start := 88121, 
                                                          stop := 88128 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i]", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 88139, 
                                                          root := ~, 
                                                          start := 88129, 
                                                          stop := 88138 ), 
                                                      rec( 
                                                          content := " will\n \
   have their source and range increased by\n    ", count := [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphNrVertices(", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 88219, 
                                                          root := ~, 
                                                          start := 88194, 
                                                          stop := 88218 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 88228, 
                                                          root := ~, 
                                                          start := 88219, 
                                                          stop := 88227 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 88236, 
                                                          root := ~, 
                                                          start := 88228, 
                                                          stop := 88235 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "+\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 88245, 
                                                          root := ~, 
                                                          start := 88237, 
                                                          stop := 88244 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
..", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 88256, 
                                                          root := ~, 
                                                          start := 88246, 
                                                          stop := 88255 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "+\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 88265, 
                                                          root := ~, 
                                                          start := 88257, 
                                                          stop := 88264 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphNrVertices(", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 27, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 88295, 
                                                          root := ~, 
                                                          start := 88270, 
                                                          stop := 88294 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 88303, 
                                                          root := ~, 
                                                          start := 88295, 
                                                          stop := 88302 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i-1])", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 88316, 
                                                          root := ~, 
                                                          start := 88303, 
                                                          stop := 88315 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 3, 27, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 27, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 88327, 
                                                          root := ~, 
                                                          start := 88323, 
                                                          stop := 88326 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that previously set ", count := [ 3, 3, 27, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 3, 3, 27, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 88391, 
                                                          root := ~, 
                                                          start := 88358, 
                                                          stop := 88390 ), 
                                                      rec( 
                                                          content := " will be\
 lost.", count := [ 3, 3, 27, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 88409, 
                                                          root := ~, 
                                                          start := 88405, 
                                                          stop := 88408 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the first digraph ", count := [ 3, 3, 27, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 88445, 
                                                          root := ~, 
                                                          start := 88436, 
                                                          stop := 88444 ), 
                                                      rec( content := " [", 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist[1]", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 88461, 
                                                          root := ~, 
                                                          start := 88447, 
                                                          stop := 88460 ), 
                                                      rec( 
                                                          content := "] belong\
s to ", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 27, 9 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 88508, 
                                                          root := ~, 
                                                          start := 88474, 
                                                          stop := 88507 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 88524, 
                                                          root := ~, 
                                                          start := 88515, 
                                                          stop := 88523 ), 
                                                      rec( content := " [", 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist[1]", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 88540, 
                                                          root := ~, 
                                                          start := 88526, 
                                                          stop := 88539 ), 
                                                      rec( 
                                                          content := "] is mod\
ified in\n    place to contain the appropriate vertices and edges. If ", 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 27, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 88631, 
                                                          root := ~, 
                                                          start := 88617, 
                                                          stop := 88630 ), 
                                                      rec( 
                                                          content := " belongs\
\n    to ", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 27, 9 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 88679, 
                                                          root := ~, 
                                                          start := 88647, 
                                                          stop := 88678 ), 
                                                      rec( 
                                                          content := ", a new \
immutable digraph containing the\n    appropriate vertices and edges is return\
ed.\n", count := [ 3, 3, 27, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D1 := CycleDigraph(3);\n<immutable cycle digraph with 3 vertices>\ngap> \
OutNeighbours(D1);\n[ [ 2 ], [ 3 ], [ 1 ] ]\ngap> D2 := CompleteDigraph(3);\n<\
immutable complete digraph with 3 vertices>\ngap> OutNeighbours(D2);\n[ [ 2, 3\
 ], [ 1, 3 ], [ 1, 2 ] ]\ngap> union := DigraphDisjointUnion(D1, D2);\n<immuta\
ble digraph with 6 vertices, 9 edges>\ngap> OutNeighbours(union);\n[ [ 2 ], [ \
3 ], [ 1 ], [ 5, 6 ], [ 4, 6 ], [ 4, 5 ] ]\n", count := [ 3, 3, 27, 10 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 27, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 89221, 
                                                          root := ~, 
                                                          start := 88768, 
                                                          stop := 89220 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 27, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 27, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 89238, root := ~, 
                                                  start := 87100, 
                                                  stop := 89237 ) ], 
                                          count := [ 3, 3, 27, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 89252, root := ~, 
                                          start := 86869, stop := 89251 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 27, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D1, D2, ...",
                                                      Label := "for a positive\
 number of digraphs", Name := "DigraphEdgeUnion" ), content := 0, 
                                                  count := [ 3, 3, 28, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 89368, root := ~, 
                                                  start := 89273, 
                                                  stop := 89367 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "list", 
                                                      Label := "for a list of \
digraphs", Name := "DigraphEdgeUnion" ), content := 0, 
                                                  count := [ 3, 3, 28, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 89444, root := ~, 
                                                  start := 89371, 
                                                  stop := 89443 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 28, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 89476, root := ~, 
                                                  start := 89447, 
                                                  stop := 89475 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    In \
the first form, if ", count := [ 3, 3, 28, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 89528, 
                                                          root := ~, 
                                                          start := 89519, 
                                                          stop := 89527 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
2", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 89539, 
                                                          root := ~, 
                                                          start := 89530, 
                                                          stop := 89538 ), 
                                                      rec( 
                                                          content := ", etc. a\
re digraphs, then\n    ", count := [ 3, 3, 28, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEdgeUnion", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "C", 
                                                          next := 89592, 
                                                          root := ~, 
                                                          start := 89569, 
                                                          stop := 89591 ), 
                                                      rec( 
                                                          content := " returns\
 their edge union.\n\n    In the second form, if ", count := [ 3, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 89658, 
                                                          root := ~, 
                                                          start := 89647, 
                                                          stop := 89657 ), 
                                                      rec( 
                                                          content := " is a no\
n-empty list of digraphs, then\n    ", count := [ 3, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEdgeUnion", count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 3, 3, 28, 5 ], mathmode := "Text", name := "C", 
                                                          next := 89724, 
                                                          root := ~, 
                                                          start := 89701, 
                                                          stop := 89723 ), 
                                                      rec( 
                                                          content := " returns\
 the edge union of the digraphs contained\n    in the list.  ", 
                                                          count := 
                                                            [ 3, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 28, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 89796, 
                                                          root := ~, 
                                                          start := 89792, 
                                                          stop := 89795 ), 
                                                      rec( 
                                                          content := "\n\n    \
The vertex set of the edge union of a collection of digraphs is the\n    ", 
                                                          count := 
                                                            [ 3, 3, 28, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
nion", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 28, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 89886, 
                                                          root := ~, 
                                                          start := 89874, 
                                                          stop := 89885 ), 
                                                      rec( 
                                                          content := " of the \
vertex sets, whilst the edge list of the edge union is\n    the ", 
                                                          count := 
                                                            [ 3, 3, 28, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
oncatenation", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 28, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 89977, 
                                                          root := ~, 
                                                          start := 89957, 
                                                          stop := 89976 ), 
                                                      rec( 
                                                          content := " of the \
edge lists.  The number of vertices of the\n    edge union is equal to the ", 
                                                          count := 
                                                            [ 3, 3, 28, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
aximum", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 28, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 90073, 
                                                          root := ~, 
                                                          start := 90059, 
                                                          stop := 90072 ), 
                                                      rec( 
                                                          content := " number \
of vertices of one of the\n    digraphs, whilst the number of edges of the edg\
e union will equal the\n    ", count := [ 3, 3, 28, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
um", count := [ 3, 3, 28, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 28, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 90195, 
                                                          root := ~, 
                                                          start := 90185, 
                                                          stop := 90194 ), 
                                                      rec( 
                                                          content := " of the \
number of edges of each digraph. ", count := [ 3, 3, 28, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 28, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 90240, 
                                                          root := ~, 
                                                          start := 90236, 
                                                          stop := 90239 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that previously set ", count := [ 3, 3, 28, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 3, 3, 28, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 90304, 
                                                          root := ~, 
                                                          start := 90271, 
                                                          stop := 90303 ), 
                                                      rec( 
                                                          content := " will be\
 lost.\n    ", count := [ 3, 3, 28, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 90327, 
                                                          root := ~, 
                                                          start := 90323, 
                                                          stop := 90326 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the first digraph ", count := [ 3, 3, 28, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 90363, 
                                                          root := ~, 
                                                          start := 90354, 
                                                          stop := 90362 ), 
                                                      rec( content := " [", 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist[1]", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 90379, 
                                                          root := ~, 
                                                          start := 90365, 
                                                          stop := 90378 ), 
                                                      rec( 
                                                          content := "] belong\
s to ", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 28, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 90426, 
                                                          root := ~, 
                                                          start := 90392, 
                                                          stop := 90425 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 90442, 
                                                          root := ~, 
                                                          start := 90433, 
                                                          stop := 90441 ), 
                                                      rec( content := " [", 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist[1]", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 90458, 
                                                          root := ~, 
                                                          start := 90444, 
                                                          stop := 90457 ), 
                                                      rec( 
                                                          content := "] is mod\
ified in\n    place to contain the appropriate vertices and edges. If ", 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 28, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 90549, 
                                                          root := ~, 
                                                          start := 90535, 
                                                          stop := 90548 ), 
                                                      rec( 
                                                          content := " belongs\
\n    to ", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 28, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 90597, 
                                                          root := ~, 
                                                          start := 90565, 
                                                          stop := 90596 ), 
                                                      rec( 
                                                          content := ", a new \
immutable digraph containing the\n    appropriate vertices and edges is return\
ed.\n", count := [ 3, 3, 28, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(10);\n<immutable cycle digraph with 10 vertices>\ngap>\
 DigraphEdgeUnion(D, D);\n<immutable multidigraph with 10 vertices, 20 edges>\
\ngap> D1 := Digraph([[2], [1]]);\n<immutable digraph with 2 vertices, 2 edges\
>\ngap> D2 := Digraph([[2, 3], [2], [1]]);\n<immutable digraph with 3 vertices\
, 4 edges>\ngap> union := DigraphEdgeUnion(D1, D2);\n<immutable multidigraph w\
ith 3 vertices, 6 edges>\ngap> OutNeighbours(union);\n[ [ 2, 2, 3 ], [ 1, 2 ],\
 [ 1 ] ]\ngap> union = DigraphByEdges(\n> Concatenation(DigraphEdges(D1), Digr\
aphEdges(D2)));\ntrue\n", count := [ 3, 3, 28, 9 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 28, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 91270, 
                                                          root := ~, 
                                                          start := 90686, 
                                                          stop := 91269 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 28, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 28, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 91287, root := ~, 
                                                  start := 89479, 
                                                  stop := 91286 ) ], 
                                          count := [ 3, 3, 28, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 91301, root := ~, 
                                          start := 89258, stop := 91300 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 28, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D1, D2, ...",
                                                      Label := "for a positive\
 number of digraphs", Name := "DigraphJoin" ), content := 0, 
                                                  count := [ 3, 3, 29, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 91412, root := ~, 
                                                  start := 91322, 
                                                  stop := 91411 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "list", 
                                                      Label := "for a list of \
digraphs", Name := "DigraphJoin" ), content := 0, count := [ 3, 3, 29, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 91483, root := ~, 
                                                  start := 91415, 
                                                  stop := 91482 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 29, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 91515, root := ~, 
                                                  start := 91486, 
                                                  stop := 91514 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    In \
the first form, if ", count := [ 3, 3, 29, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 91567, 
                                                          root := ~, 
                                                          start := 91558, 
                                                          stop := 91566 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
2", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 91578, 
                                                          root := ~, 
                                                          start := 91569, 
                                                          stop := 91577 ), 
                                                      rec( 
                                                          content := ", etc. a\
re digraphs, then\n    ", count := [ 3, 3, 29, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphJoin", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 91626, 
                                                          root := ~, 
                                                          start := 91608, 
                                                          stop := 91625 ), 
                                                      rec( 
                                                          content := " returns\
 their join.\n\n    In the second form, if ", count := [ 3, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 91686, 
                                                          root := ~, 
                                                          start := 91675, 
                                                          stop := 91685 ), 
                                                      rec( 
                                                          content := " is a no\
n-empty list of digraphs,\n    then ", count := [ 3, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphJoin", count := [ 3, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 91747, 
                                                          root := ~, 
                                                          start := 91729, 
                                                          stop := 91746 ), 
                                                      rec( 
                                                          content := " returns\
 the join of the digraphs contained in the\n    list. ", count := 
                                                            [ 3, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 91812, 
                                                          root := ~, 
                                                          start := 91808, 
                                                          stop := 91811 ), 
                                                      rec( 
                                                          content := "\n\n    \
The join of a collection of digraphs ", count := [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 91864, 
                                                          root := ~, 
                                                          start := 91855, 
                                                          stop := 91863 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
2", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 91875, 
                                                          root := ~, 
                                                          start := 91866, 
                                                          stop := 91874 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
..", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 91887, 
                                                          root := ~, 
                                                          start := 91877, 
                                                          stop := 91886 ), 
                                                      rec( 
                                                          content := " is\n   \
 formed by first taking the ", count := [ 3, 3, 29, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
DisjointUnion", Label := "for a list of digraphs" ), content := 0, 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 91993, 
                                                          root := ~, 
                                                          start := 91922, 
                                                          stop := 91992 ), 
                                                      rec( 
                                                          content := " of the \
collection.\n\n    In the disjoint union, if ", count := [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 \\neq j", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 92059, 
                                                          root := ~, 
                                                          start := 92044, 
                                                          stop := 92058 ), 
                                                      rec( 
                                                          content := " then th\
ere are no edges between\n    vertices corresponding to digraphs ", 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 92139, 
                                                          root := ~, 
                                                          start := 92131, 
                                                          stop := 92138 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i]", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 92149, 
                                                          root := ~, 
                                                          start := 92139, 
                                                          stop := 92148 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 92166, 
                                                          root := ~, 
                                                          start := 92158, 
                                                          stop := 92165 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
j]", count := [ 3, 3, 29, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 92176, 
                                                          root := ~, 
                                                          start := 92166, 
                                                          stop := 92175 ), 
                                                      rec( 
                                                          content := " in the \
collection; the join is created by including\n    all such edges.", 
                                                          count := 
                                                            [ 3, 3, 29, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 29, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 92252, 
                                                          root := ~, 
                                                          start := 92248, 
                                                          stop := 92251 ), 
                                                      rec( 
                                                          content := "\n\n    \
For example, the join of two empty digraphs is a complete bipartite\n    digra\
ph.", count := [ 3, 3, 29, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 29, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 92342, 
                                                          root := ~, 
                                                          start := 92338, 
                                                          stop := 92341 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that previously set ", count := [ 3, 3, 29, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 3, 3, 29, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 92406, 
                                                          root := ~, 
                                                          start := 92373, 
                                                          stop := 92405 ), 
                                                      rec( 
                                                          content := " will be\
 lost.\n    ", count := [ 3, 3, 29, 8 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 92429, 
                                                          root := ~, 
                                                          start := 92425, 
                                                          stop := 92428 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the first digraph ", count := [ 3, 3, 29, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 92465, 
                                                          root := ~, 
                                                          start := 92456, 
                                                          stop := 92464 ), 
                                                      rec( content := " [", 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist[1]", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 92481, 
                                                          root := ~, 
                                                          start := 92467, 
                                                          stop := 92480 ), 
                                                      rec( 
                                                          content := "] belong\
s to ", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 3, 29, 9 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 92528, 
                                                          root := ~, 
                                                          start := 92494, 
                                                          stop := 92527 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 92544, 
                                                          root := ~, 
                                                          start := 92535, 
                                                          stop := 92543 ), 
                                                      rec( content := " [", 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist[1]", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 92560, 
                                                          root := ~, 
                                                          start := 92546, 
                                                          stop := 92559 ), 
                                                      rec( 
                                                          content := "] is mod\
ified in\n    place to contain the appropriate vertices and edges. If ", 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 29, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 92651, 
                                                          root := ~, 
                                                          start := 92637, 
                                                          stop := 92650 ), 
                                                      rec( 
                                                          content := " belongs\
\n    to ", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 3, 29, 9 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 92699, 
                                                          root := ~, 
                                                          start := 92667, 
                                                          stop := 92698 ), 
                                                      rec( 
                                                          content := ", a new \
immutable digraph containing the\n    appropriate vertices and edges is return\
ed.\n", count := [ 3, 3, 29, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(3);\n<immutable complete digraph with 3 vertices>\n\
gap> IsCompleteDigraph(DigraphJoin(D, D));\ntrue\ngap> D2 := CycleDigraph(3);\
\n<immutable cycle digraph with 3 vertices>\ngap> DigraphJoin(D, D2);\n<immuta\
ble digraph with 6 vertices, 27 edges>\n", count := [ 3, 3, 29, 10 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 29, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 93084, 
                                                          root := ~, 
                                                          start := 92788, 
                                                          stop := 93083 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 29, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 29, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 93101, root := ~, 
                                                  start := 91518, 
                                                  stop := 93100 ) ], 
                                          count := [ 3, 3, 29, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 93115, root := ~, 
                                          start := 91307, stop := 93114 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 29, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "gr1, gr2, ...", 
                                                      Label := "for a positive\
 number of digraphs", Name := "DigraphCartesianProduct" ), content := 0, 
                                                  count := [ 3, 3, 30, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 93240, root := ~, 
                                                  start := 93136, 
                                                  stop := 93239 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "list", 
                                                      Label := "for a list of \
digraphs", Name := "DigraphCartesianProduct" ), content := 0, 
                                                  count := [ 3, 3, 30, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 93327, root := ~, 
                                                  start := 93243, 
                                                  stop := 93326 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 30, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 93359, root := ~, 
                                                  start := 93330, 
                                                  stop := 93358 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    In \
the first form, if ", count := [ 3, 3, 30, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r1", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 93412, 
                                                          root := ~, 
                                                          start := 93402, 
                                                          stop := 93411 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 30, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r2", count := [ 3, 3, 30, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 93424, 
                                                          root := ~, 
                                                          start := 93414, 
                                                          stop := 93423 ), 
                                                      rec( 
                                                          content := ", etc. a\
re digraphs, then\n    ", count := [ 3, 3, 30, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphCartesianProduct", count := [ 3, 3, 30, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 30, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 93484, 
                                                          root := ~, 
                                                          start := 93454, 
                                                          stop := 93483 ), 
                                                      rec( 
                                                          content := " returns\
 a digraph isomorphic to their\n    Cartesian product.\n    ", 
                                                          count := 
                                                            [ 3, 3, 30, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 30, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 93554, 
                                                          root := ~, 
                                                          start := 93550, 
                                                          stop := 93553 ), 
                                                      rec( 
                                                          content := "\n\n    \
In the second form, if ", count := [ 3, 3, 30, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 3, 30, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 93594, 
                                                          root := ~, 
                                                          start := 93583, 
                                                          stop := 93593 ), 
                                                      rec( 
                                                          content := " is a no\
n-empty list of digraphs,\n    then ", count := [ 3, 3, 30, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphCartesianProduct", count := [ 3, 3, 30, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 30, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 93667, 
                                                          root := ~, 
                                                          start := 93637, 
                                                          stop := 93666 ), 
                                                      rec( 
                                                          content := " returns\
 a digraph isomorphic to the \n    Cartesian product of the digraphs contained\
 in the list.\n    ", count := [ 3, 3, 30, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 93774, 
                                                          root := ~, 
                                                          start := 93770, 
                                                          stop := 93773 ), 
                                                      rec( 
                                                          content := "\n \n   \
 Mathematically, the Cartesian product of two digraphs ", count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 93843, 
                                                          root := ~, 
                                                          start := 93835, 
                                                          stop := 93842 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 93853, 
                                                          root := ~, 
                                                          start := 93845, 
                                                          stop := 93852 ), 
                                                      rec( 
                                                          content := "\n    is\
 a digraph with vertex set ", count := [ 3, 3, 30, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
artesian(DigraphVertices(G),\n    DigraphVertices(H))", count := [ 3, 3, 30, 
                                                                      7 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 93947, 
                                                          root := ~, 
                                                          start := 93887, 
                                                          stop := 93946 ), 
                                                      rec( 
                                                          content := " such th\
at there is an edge from ", count := [ 3, 3, 30, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u, u']", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 93994, 
                                                          root := ~, 
                                                          start := 93980, 
                                                          stop := 93993 ), 
                                                      rec( 
                                                          content := " to\n   \
 ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
v, v']", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94016, 
                                                          root := ~, 
                                                          start := 94002, 
                                                          stop := 94015 ), 
                                                      rec( content := " iff ",
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
u = v ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94035, 
                                                          root := ~, 
                                                          start := 94021, 
                                                          stop := 94034 ), 
                                                      rec( 
                                                          content := " and the\
re is an edge from ", count := [ 3, 3, 30, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
'", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94071, 
                                                          root := ~, 
                                                          start := 94062, 
                                                          stop := 94070 ), 
                                                      rec( 
                                                          content := " to\n   \
 ", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
'", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94088, 
                                                          root := ~, 
                                                          start := 94079, 
                                                          stop := 94087 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94100, 
                                                          root := ~, 
                                                          start := 94092, 
                                                          stop := 94099 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
u' = v'", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94119, 
                                                          root := ~, 
                                                          start := 94104, 
                                                          stop := 94118 ), 
                                                      rec( 
                                                          content := " and the\
re is an edge from\n    ", count := [ 3, 3, 30, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94158, 
                                                          root := ~, 
                                                          start := 94150, 
                                                          stop := 94157 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94170, 
                                                          root := ~, 
                                                          start := 94162, 
                                                          stop := 94169 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 3, 30, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94182, 
                                                          root := ~, 
                                                          start := 94174, 
                                                          stop := 94181 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 30, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 94192, 
                                                          root := ~, 
                                                          start := 94188, 
                                                          stop := 94191 ), 
                                                      rec( 
                                                          content := "\n\n    \
Due to technical reasons, the digraph ", count := [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94244, 
                                                          root := ~, 
                                                          start := 94236, 
                                                          stop := 94243 ), 
                                                      rec( 
                                                          content := " returne\
d by\n    ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphCartesianProduct", count := [ 3, 3, 30, 8 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94291, 
                                                          root := ~, 
                                                          start := 94261, 
                                                          stop := 94290 ), 
                                                      rec( 
                                                          content := " has ver\
tex set\n    ", count := [ 3, 3, 30, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 ..  DigraphNrVertices(G)*DigraphNrVertices(H)]", count := [ 3, 3, 30, 8 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94367, 
                                                          root := ~, 
                                                          start := 94311, 
                                                          stop := 94366 ), 
                                                      rec( 
                                                          content := " instead\
, and the\n     exact\n    method of encoding pairs of vertices into integers \
is implementation\n    specific.  The original vertex pair can be somewhat reg\
ained by using\n    ", count := [ 3, 3, 30, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
CartesianProductProjections" ), content := 0, count := [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 94595, 
                                                          root := ~, 
                                                          start := 94547, 
                                                          stop := 94594 ), 
                                                      rec( 
                                                          content := ". In add\
ition,\n    ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 3, 3, 30, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 94647, 
                                                          root := ~, 
                                                          start := 94614, 
                                                          stop := 94646 ), 
                                                      rec( 
                                                          content := " are pre\
served: if vertex pair\n    ", count := [ 3, 3, 30, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u,u']", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94695, 
                                                          root := ~, 
                                                          start := 94682, 
                                                          stop := 94694 ), 
                                                      rec( 
                                                          content := " was enc\
oded as ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94719, 
                                                          root := ~, 
                                                          start := 94711, 
                                                          stop := 94718 ), 
                                                      rec( 
                                                          content := " then th\
e vertex label of ", count := [ 3, 3, 30, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94753, 
                                                          root := ~, 
                                                          start := 94745, 
                                                          stop := 94752 ), 
                                                      rec( 
                                                          content := "\n    wi\
ll be the pair of vertex labels of ", count := [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94803, 
                                                          root := ~, 
                                                          start := 94795, 
                                                          stop := 94802 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
'", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94817, 
                                                          root := ~, 
                                                          start := 94808, 
                                                          stop := 94816 ), 
                                                      rec( 
                                                          content := " i.e.\n \
   ", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphVertexLabel(D,i) = [DigraphVertexLabel(G,u),\n      DigraphVertexLabel(H\
,u')]", count := [ 3, 3, 30, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 94917, 
                                                          root := ~, 
                                                          start := 94827, 
                                                          stop := 94916 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 30, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 30, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 94927, 
                                                          root := ~, 
                                                          start := 94923, 
                                                          stop := 94926 ), 
                                                      rec( 
                                                          content := "\n\n    \
As the Cartesian product is associative, the Cartesian product of a collection\
 \n    of digraphs ", count := [ 3, 3, 30, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r1", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 95039, 
                                                          root := ~, 
                                                          start := 95029, 
                                                          stop := 95038 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 30, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r2", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 95051, 
                                                          root := ~, 
                                                          start := 95041, 
                                                          stop := 95050 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 30, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
..", count := [ 3, 3, 30, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 95063, 
                                                          root := ~, 
                                                          start := 95053, 
                                                          stop := 95062 ), 
                                                      rec( 
                                                          content := " is comp\
uted in the obvious \n    fashion. \n    ", count := [ 3, 3, 30, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 30, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 95114, 
                                                          root := ~, 
                                                          start := 95110, 
                                                          stop := 95113 ), 
                                                      rec( content := "\n\n", 
                                                          count := 
                                                            [ 3, 3, 30, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := ChainDigraph(4);\n<immutable chain digraph with 4 vertices>\ngap> \
gr2 := CycleDigraph(3);\n<immutable cycle digraph with 3 vertices>\ngap> gr3 :\
= DigraphCartesianProduct(gr, gr2);\n<immutable digraph with 12 vertices, 21 e\
dges>\ngap> IsIsomorphicDigraph(gr3, \n> Digraph([[2, 5], [3, 6], [4, 7], [8],\
 \n>          [6, 9], [7, 10], [8, 11], [12],\n>          [10, 1], [11, 2], [1\
2, 3], [4]]));\ntrue\n", count := [ 3, 3, 30, 11 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 30, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 95548, 
                                                          root := ~, 
                                                          start := 95116, 
                                                          stop := 95547 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 30, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 30, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 95565, root := ~, 
                                                  start := 93362, 
                                                  stop := 95564 ) ], 
                                          count := [ 3, 3, 30, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 95579, root := ~, 
                                          start := 93121, stop := 95578 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 30, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "gr1, gr2, ...", 
                                                      Label := "for a positive\
 number of digraphs", Name := "DigraphDirectProduct" ), content := 0, 
                                                  count := [ 3, 3, 31, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 95701, root := ~, 
                                                  start := 95600, 
                                                  stop := 95700 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "list", 
                                                      Label := "for a list of \
digraphs", Name := "DigraphDirectProduct" ), content := 0, 
                                                  count := [ 3, 3, 31, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 95785, root := ~, 
                                                  start := 95704, 
                                                  stop := 95784 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 31, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 95817, root := ~, 
                                                  start := 95788, 
                                                  stop := 95816 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    In \
the first form, if ", count := [ 3, 3, 31, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r1", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 95870, 
                                                          root := ~, 
                                                          start := 95860, 
                                                          stop := 95869 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r2", count := [ 3, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 95882, 
                                                          root := ~, 
                                                          start := 95872, 
                                                          stop := 95881 ), 
                                                      rec( 
                                                          content := ", etc. a\
re digraphs, then\n    ", count := [ 3, 3, 31, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDirectProduct", count := [ 3, 3, 31, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 31, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 95939, 
                                                          root := ~, 
                                                          start := 95912, 
                                                          stop := 95938 ), 
                                                      rec( 
                                                          content := " returns\
 a digraph isomorphic to their direct\n    product.\n    ", 
                                                          count := 
                                                            [ 3, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 96006, 
                                                          root := ~, 
                                                          start := 96002, 
                                                          stop := 96005 ), 
                                                      rec( 
                                                          content := "\n\n    \
In the second form, if ", count := [ 3, 3, 31, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 3, 31, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 96046, 
                                                          root := ~, 
                                                          start := 96035, 
                                                          stop := 96045 ), 
                                                      rec( 
                                                          content := " is a no\
n-empty list of digraphs, then\n    ", count := [ 3, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDirectProduct", count := [ 3, 3, 31, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 31, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96116, 
                                                          root := ~, 
                                                          start := 96089, 
                                                          stop := 96115 ), 
                                                      rec( 
                                                          content := " returns\
 a digraph isomorphic to the direct\n    product of the digraphs contained in \
the list.\n    ", count := [ 3, 3, 31, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 96219, 
                                                          root := ~, 
                                                          start := 96215, 
                                                          stop := 96218 ), 
                                                      rec( 
                                                          content := "\n\n    \
Mathematically, the direct product of two digraphs ", count := [ 3, 3, 31, 7 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96284, 
                                                          root := ~, 
                                                          start := 96276, 
                                                          stop := 96283 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96294, 
                                                          root := ~, 
                                                          start := 96286, 
                                                          stop := 96293 ), 
                                                      rec( 
                                                          content := " is a\n \
   digraph with vertex set ", count := [ 3, 3, 31, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
artesian(DigraphVertices(G),\n    DigraphVertices(H))", count := [ 3, 3, 31, 
                                                                      7 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96388, 
                                                          root := ~, 
                                                          start := 96328, 
                                                          stop := 96387 ), 
                                                      rec( 
                                                          content := " such th\
at there is an edge from ", count := [ 3, 3, 31, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u, u']", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96435, 
                                                          root := ~, 
                                                          start := 96421, 
                                                          stop := 96434 ), 
                                                      rec( 
                                                          content := "\n    to\
 ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
v, v']", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96457, 
                                                          root := ~, 
                                                          start := 96443, 
                                                          stop := 96456 ), 
                                                      rec( 
                                                          content := " iff the\
re is an edge from ", count := [ 3, 3, 31, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96492, 
                                                          root := ~, 
                                                          start := 96484, 
                                                          stop := 96491 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96504, 
                                                          root := ~, 
                                                          start := 96496, 
                                                          stop := 96503 ), 
                                                      rec( 
                                                          content := " in\n   \
 ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96520, 
                                                          root := ~, 
                                                          start := 96512, 
                                                          stop := 96519 ), 
                                                      rec( 
                                                          content := " and an \
edge from ", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
'", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96547, 
                                                          root := ~, 
                                                          start := 96538, 
                                                          stop := 96546 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
'", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96560, 
                                                          root := ~, 
                                                          start := 96551, 
                                                          stop := 96559 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96572, 
                                                          root := ~, 
                                                          start := 96564, 
                                                          stop := 96571 ), 
                                                      rec( 
                                                          content := ". \n    \
", count := [ 3, 3, 31, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 96583, 
                                                          root := ~, 
                                                          start := 96579, 
                                                          stop := 96582 ), 
                                                      rec( 
                                                          content := " \n\n   \
 Due to technical reasons, the digraph ", count := [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96636, 
                                                          root := ~, 
                                                          start := 96628, 
                                                          stop := 96635 ), 
                                                      rec( 
                                                          content := " returne\
d by\n    ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDirectProduct", count := [ 3, 3, 31, 8 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96680, 
                                                          root := ~, 
                                                          start := 96653, 
                                                          stop := 96679 ), 
                                                      rec( 
                                                          content := " has ver\
tex set\n    ", count := [ 3, 3, 31, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 ..  DigraphNrVertices(G)*DigraphNrVertices(H)]", count := [ 3, 3, 31, 8 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 96756, 
                                                          root := ~, 
                                                          start := 96700, 
                                                          stop := 96755 ), 
                                                      rec( 
                                                          content := " instead\
, and the\n    exact method of encoding pairs of vertices into integers is imp\
lementation\n    specific.  The original vertex pair can be somewhat regained \
by using\n    ", count := [ 3, 3, 31, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
DirectProductProjections" ), content := 0, count := [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 96976, 
                                                          root := ~, 
                                                          start := 96931, 
                                                          stop := 96975 ), 
                                                      rec( 
                                                          content := ". In add\
ition\n    ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 3, 3, 31, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 97027, 
                                                          root := ~, 
                                                          start := 96994, 
                                                          stop := 97026 ), 
                                                      rec( 
                                                          content := " are pre\
served: if vertex pair\n    ", count := [ 3, 3, 31, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u,u']", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 97075, 
                                                          root := ~, 
                                                          start := 97062, 
                                                          stop := 97074 ), 
                                                      rec( 
                                                          content := " was enc\
oded as ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 97099, 
                                                          root := ~, 
                                                          start := 97091, 
                                                          stop := 97098 ), 
                                                      rec( 
                                                          content := " then th\
e vertex label of ", count := [ 3, 3, 31, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 97133, 
                                                          root := ~, 
                                                          start := 97125, 
                                                          stop := 97132 ), 
                                                      rec( 
                                                          content := "\n    wi\
ll be the pair of vertex labels of ", count := [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 97183, 
                                                          root := ~, 
                                                          start := 97175, 
                                                          stop := 97182 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
'", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 97197, 
                                                          root := ~, 
                                                          start := 97188, 
                                                          stop := 97196 ), 
                                                      rec( 
                                                          content := " i.e.\n \
   ", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphVertexLabel(D,i) = [DigraphVertexLabel(G,u),\n    DigraphVertexLabel(H,u\
')]", count := [ 3, 3, 31, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 97295, 
                                                          root := ~, 
                                                          start := 97207, 
                                                          stop := 97294 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 31, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 97305, 
                                                          root := ~, 
                                                          start := 97301, 
                                                          stop := 97304 ), 
                                                      rec( 
                                                          content := "\n\n    \
As the direct product is associative, the direct product of a collection \n   \
 of digraphs ", count := [ 3, 3, 31, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r1", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 97411, 
                                                          root := ~, 
                                                          start := 97401, 
                                                          stop := 97410 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 31, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r2", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 97423, 
                                                          root := ~, 
                                                          start := 97413, 
                                                          stop := 97422 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 31, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
..", count := [ 3, 3, 31, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 31, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 97435, 
                                                          root := ~, 
                                                          start := 97425, 
                                                          stop := 97434 ), 
                                                      rec( 
                                                          content := " is comp\
uted in the obvious \n    fashion. \n    ", count := [ 3, 3, 31, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 31, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 97486, 
                                                          root := ~, 
                                                          start := 97482, 
                                                          stop := 97485 ), 
                                                      rec( content := "\n\n", 
                                                          count := 
                                                            [ 3, 3, 31, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := ChainDigraph(4);\n<immutable chain digraph with 4 vertices>\ngap> \
gr2 := CycleDigraph(3);\n<immutable cycle digraph with 3 vertices>\ngap> gr3 :\
= DigraphDirectProduct(gr, gr2);\n<immutable digraph with 12 vertices, 9 edges\
>\ngap> IsIsomorphicDigraph(gr3, \n> Digraph([[6], [7], [8], [], \n>          \
[10], [11], [12], [],\n>          [2], [3], [4], []]));\ntrue\n", count := 
                                                                    [ 3, 3, 
                                                                      31, 11 ]
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 31, 11 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 97883, 
                                                          root := ~, 
                                                          start := 97488, 
                                                          stop := 97882 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 31, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 31, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 97900, root := ~, 
                                                  start := 95820, 
                                                  stop := 97899 ) ], 
                                          count := [ 3, 3, 31, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 97914, root := ~, 
                                          start := 95585, stop := 97913 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 31, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphCartesia\
nProductProjections" ), content := 0, count := [ 3, 3, 32, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 97998, root := ~, 
                                                  start := 97935, 
                                                  stop := 97997 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 transformations.", count := [ 3, 3, 32, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 32, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 98046, root := ~, 
                                                  start := 98001, 
                                                  stop := 98045 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 32, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 98084, 
                                                          root := ~, 
                                                          start := 98070, 
                                                          stop := 98083 ), 
                                                      rec( 
                                                          content := " is a Ca\
rtesian product digraph, \n    ", count := [ 3, 3, 32, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph = DigraphCartesianProduct(gr_1, gr_2, ... )", count := [ 3, 3, 32, 3 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 98180, 
                                                          root := ~, 
                                                          start := 98122, 
                                                          stop := 98179 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphCartesianProductProjections", count := [ 3, 3, 32, 3 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 32, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 98232, 
                                                          root := ~, 
                                                          start := 98191, 
                                                          stop := 98231 ), 
                                                      rec( 
                                                          content := " returns\
 a list ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roj", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 32, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 98259, 
                                                          root := ~, 
                                                          start := 98248, 
                                                          stop := 98258 ), 
                                                      rec( 
                                                          content := "\n    su\
ch that ", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roj[i]", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 32, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 98288, 
                                                          root := ~, 
                                                          start := 98274, 
                                                          stop := 98287 ), 
                                                      rec( 
                                                          content := " is the \
projection onto the ", count := [ 3, 3, 32, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 32, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 32, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 98324, 
                                                          root := ~, 
                                                          start := 98316, 
                                                          stop := 98323 ), 
                                                      rec( 
                                                          content := "-th\n   \
 coordinate of the product.\n    ", count := [ 3, 3, 32, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 32, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 98367, 
                                                          root := ~, 
                                                          start := 98363, 
                                                          stop := 98366 ), 
                                                      rec( 
                                                          content := "\n\n    \
A projection is an idempotent endomorphism of ", count := [ 3, 3, 32, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 32, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 98433, 
                                                          root := ~, 
                                                          start := 98419, 
                                                          stop := 98432 ), 
                                                      rec( 
                                                          content := ". If\n  \
  ", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r1, gr2, ...", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 32, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 98462, 
                                                          root := ~, 
                                                          start := 98442, 
                                                          stop := 98461 ), 
                                                      rec( 
                                                          content := " are all\
 loopless digraphs, then the induced \n    subdigraph of ", 
                                                          count := 
                                                            [ 3, 3, 32, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 32, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 98540, 
                                                          root := ~, 
                                                          start := 98526, 
                                                          stop := 98539 ), 
                                                      rec( 
                                                          content := " on the \
image of ", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roj[i]", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 32, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 98571, 
                                                          root := ~, 
                                                          start := 98557, 
                                                          stop := 98570 ), 
                                                      rec( 
                                                          content := " is \n  \
  isomorphic to ", count := [ 3, 3, 32, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r_i", count := [ 3, 3, 32, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 32, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 98605, 
                                                          root := ~, 
                                                          start := 98594, 
                                                          stop := 98604 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 32, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 32, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 98615, 
                                                          root := ~, 
                                                          start := 98611, 
                                                          stop := 98614 ), 
                                                      rec( 
                                                          content := "\n\n    \
Currently this attribute is only set upon creating an immutable \n    digraph \
via ", count := [ 3, 3, 32, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphCartesianProduct", count := [ 3, 3, 32, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 32, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 98732, 
                                                          root := ~, 
                                                          start := 98702, 
                                                          stop := 98731 ), 
                                                      rec( 
                                                          content := " and the\
re is no way \n    of calculating it for other digraphs.\n    ", 
                                                          count := 
                                                            [ 3, 3, 32, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 32, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 98804, 
                                                          root := ~, 
                                                          start := 98800, 
                                                          stop := 98803 ), 
                                                      rec( 
                                                          content := "\n\n    \
For more information see\n    ", count := [ 3, 3, 32, 6 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
CartesianProduct", Label := "for a list of digraphs" ), content := 0, 
                                                          count := 
                                                            [ 3, 3, 32, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 98907, 
                                                          root := ~, 
                                                          start := 98839, 
                                                          stop := 98906 ), 
                                                      rec( 
                                                          content := " \n\n   \
 ", count := [ 3, 3, 32, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphCartesianProduct(ChainDigraph(3), CycleDigraph(4),\n> Digrap\
h([[2], [2]]));;\ngap> HasDigraphCartesianProductProjections(D);\ntrue\ngap> p\
roj := DigraphCartesianProductProjections(D);; Length(proj);\n3\ngap> IsIdempo\
tent(proj[2]);\ntrue\ngap> RankOfTransformation(proj[3]);\n2\ngap> S := ImageS\
etOfTransformation(proj[2]);;\ngap> IsIsomorphicDigraph(CycleDigraph(4), Induc\
edSubdigraph(D, S));\ntrue\n", count := [ 3, 3, 32, 7 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 32, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 99350, 
                                                          root := ~, 
                                                          start := 98914, 
                                                          stop := 99349 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 32, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 32, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 99367, root := ~, 
                                                  start := 98049, 
                                                  stop := 99366 ) ], 
                                          count := [ 3, 3, 32, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 99381, root := ~, 
                                          start := 97920, stop := 99380 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 32, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphDirectPr\
oductProjections" ), content := 0, count := [ 3, 3, 33, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 99462, root := ~, 
                                                  start := 99402, 
                                                  stop := 99461 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 transformations.", count := [ 3, 3, 33, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 33, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 99510, root := ~, 
                                                  start := 99465, 
                                                  stop := 99509 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 33, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 99548, 
                                                          root := ~, 
                                                          start := 99534, 
                                                          stop := 99547 ), 
                                                      rec( 
                                                          content := " is a di\
rect product digraph, \n    ", count := [ 3, 3, 33, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph = DigraphDirectProduct(gr_1, gr_2, ... )", count := [ 3, 3, 33, 3 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 99638, 
                                                          root := ~, 
                                                          start := 99583, 
                                                          stop := 99637 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDirectProductProjections", count := [ 3, 3, 33, 3 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 33, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 99687, 
                                                          root := ~, 
                                                          start := 99649, 
                                                          stop := 99686 ), 
                                                      rec( 
                                                          content := " returns\
 a list ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roj", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 33, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 99714, 
                                                          root := ~, 
                                                          start := 99703, 
                                                          stop := 99713 ), 
                                                      rec( 
                                                          content := "\n    su\
ch that ", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roj[i]", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 33, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 99743, 
                                                          root := ~, 
                                                          start := 99729, 
                                                          stop := 99742 ), 
                                                      rec( 
                                                          content := " is the \
projection onto the ", count := [ 3, 3, 33, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 33, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 33, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 99779, 
                                                          root := ~, 
                                                          start := 99771, 
                                                          stop := 99778 ), 
                                                      rec( 
                                                          content := "-th\n   \
 coordinate of the product.\n    ", count := [ 3, 3, 33, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 99822, 
                                                          root := ~, 
                                                          start := 99818, 
                                                          stop := 99821 ), 
                                                      rec( 
                                                          content := "\n\n    \
A projection is an idempotent endomorphism of ", count := [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 99888, 
                                                          root := ~, 
                                                          start := 99874, 
                                                          stop := 99887 ), 
                                                      rec( 
                                                          content := ". If\n  \
  ", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r1, gr2, ...", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 99917, 
                                                          root := ~, 
                                                          start := 99897, 
                                                          stop := 99916 ), 
                                                      rec( 
                                                          content := " are all\
 loopless digraphs, then the image \n    of ", count := [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 99982, 
                                                          root := ~, 
                                                          start := 99968, 
                                                          stop := 99981 ), 
                                                      rec( 
                                                          content := " under "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roj[i]", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 100003, 
                                                          root := ~, 
                                                          start := 99989, 
                                                          stop := 100002 ), 
                                                      rec( 
                                                          content := " is isom\
orphic to ", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
r_i", count := [ 3, 3, 33, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 100032, 
                                                          root := ~, 
                                                          start := 100021, 
                                                          stop := 100031 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 33, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 33, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 100042, 
                                                          root := ~, 
                                                          start := 100038, 
                                                          stop := 100041 ), 
                                                      rec( 
                                                          content := "\n\n    \
Currently this attribute is only set upon creating an immutable\n    digraph v\
ia ", count := [ 3, 3, 33, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDirectProduct", count := [ 3, 3, 33, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 33, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 100155, 
                                                          root := ~, 
                                                          start := 100128, 
                                                          stop := 100154 ), 
                                                      rec( 
                                                          content := " and the\
re is no way of \n    calculating it for other digraphs.\n    ", 
                                                          count := 
                                                            [ 3, 3, 33, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 33, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 100227, 
                                                          root := ~, 
                                                          start := 100223, 
                                                          stop := 100226 ), 
                                                      rec( 
                                                          content := "\n\n    \
For more information, see\n    ", count := [ 3, 3, 33, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
DirectProduct", Label := "for a list of digraphs" ), content := 0, 
                                                          count := 
                                                            [ 3, 3, 33, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 100328, 
                                                          root := ~, 
                                                          start := 100263, 
                                                          stop := 100327 ), 
                                                      rec( 
                                                          content := " \n\n   \
 ", count := [ 3, 3, 33, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphDirectProduct(ChainDigraph(3), CycleDigraph(4),\n> Digraph([\
[2], [2]]));;\ngap> HasDigraphDirectProductProjections(D);\ntrue\ngap> proj :=\
 DigraphDirectProductProjections(D);; Length(proj);\n3\ngap> IsIdempotent(proj\
[2]);\ntrue\ngap> RankOfTransformation(proj[3]);\n2\ngap> P := DigraphRemoveAl\
lMultipleEdges(\n> ReducedDigraph(OnDigraphs(D, proj[2])));; \ngap> IsIsomorph\
icDigraph(CycleDigraph(4), P);\ntrue\n", count := [ 3, 3, 33, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 33, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 100780, 
                                                          root := ~, 
                                                          start := 100335, 
                                                          stop := 100779 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 33, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 33, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 100797, root := ~, 
                                                  start := 99513, 
                                                  stop := 100796 ) ], 
                                          count := [ 3, 3, 33, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 100811, root := ~, 
                                          start := 99387, stop := 100810 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 33, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "LineDigraph" ),
                                                  content := 0, 
                                                  count := [ 3, 3, 34, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 100872, root := ~, 
                                                  start := 100832, 
                                                  stop := 100871 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "EdgeDigraph" ),
                                                  content := 0, 
                                                  count := [ 3, 3, 34, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 100915, root := ~, 
                                                  start := 100875, 
                                                  stop := 100914 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 34, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 100947, root := ~, 
                                                  start := 100918, 
                                                  stop := 100946 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Giv\
en a digraph ", count := [ 3, 3, 34, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 100998, 
                                                          root := ~, 
                                                          start := 100984, 
                                                          stop := 100997 ), 
                                                      rec( 
                                                          content := ", the op\
eration returns the digraph\n    obtained by associating a vertex with each ed\
ge of ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 101103, 
                                                          root := ~, 
                                                          start := 101089, 
                                                          stop := 101102 ), 
                                                      rec( 
                                                          content := ", and\n \
   creating an edge from a vertex ", count := [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 101152, 
                                                          root := ~, 
                                                          start := 101144, 
                                                          stop := 101151 ), 
                                                      rec( 
                                                          content := " to a ve\
rtex ", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 101173, 
                                                          root := ~, 
                                                          start := 101165, 
                                                          stop := 101172 ), 
                                                      rec( 
                                                          content := " if and \
only\n    if the terminal vertex of the edge associated with ", 
                                                          count := 
                                                            [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 101249, 
                                                          root := ~, 
                                                          start := 101241, 
                                                          stop := 101248 ), 
                                                      rec( 
                                                          content := " is the \
start\n    vertex of the edge associated with ", count := [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 3, 3, 34, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 101310, 
                                                          root := ~, 
                                                          start := 101302, 
                                                          stop := 101309 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 34, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 34, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 101315, 
                                                          root := ~, 
                                                          start := 101311, 
                                                          stop := 101314 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that the returned digraph is always a new immutable digraph, and the\n   \
 argument ", count := [ 3, 3, 34, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 34, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 34, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 101422, 
                                                          root := ~, 
                                                          start := 101408, 
                                                          stop := 101421 ), 
                                                      rec( 
                                                          content := " is neve\
r modified.\n    ", count := [ 3, 3, 34, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> LineDigraph(CompleteDigraph(3));\n<immutable digraph with 6 vertices, 12\
 edges>\ngap> LineDigraph(ChainDigraph(3));\n<immutable digraph with 2 vertice\
s, 1 edge>\n", count := [ 3, 3, 34, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 34, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 101641, 
                                                          root := ~, 
                                                          start := 101446, 
                                                          stop := 101640 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 34, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 34, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 101658, root := ~, 
                                                  start := 100950, 
                                                  stop := 101657 ) ], 
                                          count := [ 3, 3, 34, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 101672, root := ~, 
                                          start := 100817, stop := 101671 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 34, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "LineUndirectedD\
igraph" ), content := 0, count := [ 3, 3, 35, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 101743, root := ~, 
                                                  start := 101693, 
                                                  stop := 101742 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "EdgeUndirectedD\
igraph" ), content := 0, count := [ 3, 3, 35, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 101796, root := ~, 
                                                  start := 101746, 
                                                  stop := 101795 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 35, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 101828, root := ~, 
                                                  start := 101799, 
                                                  stop := 101827 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Giv\
en a symmetric digraph ", count := [ 3, 3, 35, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 35, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 101889, 
                                                          root := ~, 
                                                          start := 101875, 
                                                          stop := 101888 ), 
                                                      rec( 
                                                          content := ", the op\
eration returns the\n    symmetric digraph obtained by associating a vertex wi\
th each edge of\n    ", count := [ 3, 3, 35, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 35, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 35, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 102008, 
                                                          root := ~, 
                                                          start := 101994, 
                                                          stop := 102007 ), 
                                                      rec( 
                                                          content := ", ignori\
ng directions and multiplicites, and adding an edge\n    between two vertices \
if and only if the corresponding edges have a vertex in\n    common.", 
                                                          count := 
                                                            [ 3, 3, 35, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 35, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 102164, 
                                                          root := ~, 
                                                          start := 102160, 
                                                          stop := 102163 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that the returned digraph is always a new immutable digraph, and the\n   \
 argument ", count := [ 3, 3, 35, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 35, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 35, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 102271, 
                                                          root := ~, 
                                                          start := 102257, 
                                                          stop := 102270 ), 
                                                      rec( 
                                                          content := " is neve\
r modified.\n    ", count := [ 3, 3, 35, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> LineUndirectedDigraph(CompleteDigraph(3));\n<immutable digraph with 3 ve\
rtices, 6 edges>\ngap> LineUndirectedDigraph(DigraphSymmetricClosure(ChainDigr\
aph(3)));\n<immutable digraph with 2 vertices, 2 edges>\n", count := 
                                                                    [ 3, 3, 
                                                                      35, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 35, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 102535, 
                                                          root := ~, 
                                                          start := 102295, 
                                                          stop := 102534 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 35, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 35, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 102552, root := ~, 
                                                  start := 101831, 
                                                  stop := 102551 ) ], 
                                          count := [ 3, 3, 35, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 102566, root := ~, 
                                          start := 101678, stop := 102565 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 35, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DoubleDigraph" 
                                                     ), content := 0, 
                                                  count := [ 3, 3, 36, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 102629, root := ~, 
                                                  start := 102587, 
                                                  stop := 102628 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 36, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 102661, root := ~, 
                                                  start := 102632, 
                                                  stop := 102660 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Let\
 ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 102700, 
                                                          root := ~, 
                                                          start := 102686, 
                                                          stop := 102699 ), 
                                                      rec( 
                                                          content := " be a di\
graph with vertex set ", count := [ 3, 3, 36, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 102738, 
                                                          root := ~, 
                                                          start := 102730, 
                                                          stop := 102737 ), 
                                                      rec( 
                                                          content := ". This f\
unction\n    returns the double digraph of ", count := [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 102802, 
                                                          root := ~, 
                                                          start := 102788, 
                                                          stop := 102801 ), 
                                                      rec( 
                                                          content := ". The ve\
rtex set of the double\n    digraph is the orginal vertex set together with a \
duplicate. The edges are\n    ", count := [ 3, 3, 36, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u_1, v_2]", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 102933, 
                                                          root := ~, 
                                                          start := 102916, 
                                                          stop := 102932 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u_2, v_1]", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 102955, 
                                                          root := ~, 
                                                          start := 102938, 
                                                          stop := 102954 ), 
                                                      rec( 
                                                          content := " if and \
only if ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u, v]", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 102984, 
                                                          root := ~, 
                                                          start := 102971, 
                                                          stop := 102983 ), 
                                                      rec( 
                                                          content := " is an\n\
    edge in ", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 36, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 103017, 
                                                          root := ~, 
                                                          start := 103003, 
                                                          stop := 103016 ), 
                                                      rec( 
                                                          content := ", togeth\
er with the original edges and their\n    duplicates.", count := 
                                                            [ 3, 3, 36, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 36, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 103081, 
                                                          root := ~, 
                                                          start := 103077, 
                                                          stop := 103080 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 36, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 103104, 
                                                          root := ~, 
                                                          start := 103090, 
                                                          stop := 103103 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then ", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 36, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 103136, 
                                                          root := ~, 
                                                          start := 103122, 
                                                          stop := 103135 ), 
                                                      rec( 
                                                          content := " is modi\
fied in-place. If\n    ", count := [ 3, 3, 36, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 36, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 103180, 
                                                          root := ~, 
                                                          start := 103166, 
                                                          stop := 103179 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph constructed as\n    described above is ret\
urned.\n    ", count := [ 3, 3, 36, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gamma := Digraph([[2], [3], [1]]);\n<immutable digraph with 3 vertices, \
3 edges>\ngap> DoubleDigraph(gamma);\n<immutable digraph with 6 vertices, 12 e\
dges>\n", count := [ 3, 3, 36, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 36, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 103466, 
                                                          root := ~, 
                                                          start := 103276, 
                                                          stop := 103465 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 36, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 36, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 103483, root := ~, 
                                                  start := 102664, 
                                                  stop := 103482 ) ], 
                                          count := [ 3, 3, 36, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 103497, root := ~, 
                                          start := 102572, stop := 103496 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 36, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "BipartiteDouble\
Digraph" ), content := 0, count := [ 3, 3, 37, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 103569, root := ~, 
                                                  start := 103518, 
                                                  stop := 103568 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 37, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 103601, root := ~, 
                                                  start := 103572, 
                                                  stop := 103600 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Let\
 ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 103640, 
                                                          root := ~, 
                                                          start := 103626, 
                                                          stop := 103639 ), 
                                                      rec( 
                                                          content := " be a di\
graph with vertex set ", count := [ 3, 3, 37, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 103678, 
                                                          root := ~, 
                                                          start := 103670, 
                                                          stop := 103677 ), 
                                                      rec( 
                                                          content := ". This f\
unction\n    returns the bipartite double digraph of ", count := 
                                                            [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 103752, 
                                                          root := ~, 
                                                          start := 103738, 
                                                          stop := 103751 ), 
                                                      rec( 
                                                          content := ". The ve\
rtex set of\n    the double digraph is the original vertex set together with a\
 duplicate. The\n    edges are ", count := [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u_1, v_2]", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 103884, 
                                                          root := ~, 
                                                          start := 103867, 
                                                          stop := 103883 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u_2, v_1]", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 103906, 
                                                          root := ~, 
                                                          start := 103889, 
                                                          stop := 103905 ), 
                                                      rec( 
                                                          content := " if and \
only if ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u,\n      v]", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 103941, 
                                                          root := ~, 
                                                          start := 103922, 
                                                          stop := 103940 ), 
                                                      rec( 
                                                          content := " is an e\
dge in ", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 37, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 37, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 103970, 
                                                          root := ~, 
                                                          start := 103956, 
                                                          stop := 103969 ), 
                                                      rec( 
                                                          content := ". The re\
sulting graph is bipartite,\n    since the orignal edges are not included in t\
he resulting digraph.", count := [ 3, 3, 37, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 37, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 104080, 
                                                          root := ~, 
                                                          start := 104076, 
                                                          stop := 104079 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 37, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 104103, 
                                                          root := ~, 
                                                          start := 104089, 
                                                          stop := 104102 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then ", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 37, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 104135, 
                                                          root := ~, 
                                                          start := 104121, 
                                                          stop := 104134 ), 
                                                      rec( 
                                                          content := " is modi\
fied in-place. If\n    ", count := [ 3, 3, 37, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 37, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 104179, 
                                                          root := ~, 
                                                          start := 104165, 
                                                          stop := 104178 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph constructed as\n    described above is ret\
urned.\n    ", count := [ 3, 3, 37, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gamma := Digraph([[2], [3], [1]]);\n<immutable digraph with 3 vertices, \
3 edges>\ngap> BipartiteDoubleDigraph(gamma);\n<immutable digraph with 6 verti\
ces, 6 edges>\n", count := [ 3, 3, 37, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 37, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 104473, 
                                                          root := ~, 
                                                          start := 104275, 
                                                          stop := 104472 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 37, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 37, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 104490, root := ~, 
                                                  start := 103604, 
                                                  stop := 104489 ) ], 
                                          count := [ 3, 3, 37, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 104504, root := ~, 
                                          start := 103503, stop := 104503 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 37, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphAddAllLo\
ops" ), content := 0, count := [ 3, 3, 38, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 104572, root := ~, 
                                                  start := 104525, 
                                                  stop := 104571 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphAddAllLo\
opsAttr" ), content := 0, count := [ 3, 3, 38, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 104626, root := ~, 
                                                  start := 104575, 
                                                  stop := 104625 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 38, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 104658, root := ~, 
                                                  start := 104629, 
                                                  stop := 104657 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    For\
 a digraph ", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 38, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 104707, 
                                                          root := ~, 
                                                          start := 104693, 
                                                          stop := 104706 ), 
                                                      rec( 
                                                          content := " this op\
eration returns a new digraph constructed\n    from ", count := 
                                                            [ 3, 3, 38, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 38, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 104780, 
                                                          root := ~, 
                                                          start := 104766, 
                                                          stop := 104779 ), 
                                                      rec( 
                                                          content := ", such t\
hat a loop is added for every vertex which did not\n    have a loop in ", 
                                                          count := 
                                                            [ 3, 3, 38, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 38, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 38, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 104872, 
                                                          root := ~, 
                                                          start := 104858, 
                                                          stop := 104871 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 38, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 38, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 104877, 
                                                          root := ~, 
                                                          start := 104873, 
                                                          stop := 104876 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 38, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 104900, 
                                                          root := ~, 
                                                          start := 104886, 
                                                          stop := 104899 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the loops are\
 added to the loopless vertices of the mutable digraph\n    ", 
                                                          count := 
                                                            [ 3, 3, 38, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 38, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 105058, 
                                                          root := ~, 
                                                          start := 105044, 
                                                          stop := 105057 ), 
                                                      rec( 
                                                          content := " in-plac\
e.\n    ", count := [ 3, 3, 38, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := EmptyDigraph(13);\n<immutable empty digraph with 13 vertices>\ngap>\
 D := DigraphAddAllLoops(D);\n<immutable reflexive digraph with 13 vertices, 1\
3 edges>\ngap> OutNeighbours(D);\n[ [ 1 ], [ 2 ], [ 3 ], [ 4 ], [ 5 ], [ 6 ], \
[ 7 ], [ 8 ], [ 9 ], \n  [ 10 ], [ 11 ], [ 12 ], [ 13 ] ]\ngap> D := Digraph([\
[1, 2, 3], [1, 3], [1]]);\n<immutable digraph with 3 vertices, 6 edges>\ngap> \
D := DigraphAddAllLoops(D);\n<immutable reflexive digraph with 3 vertices, 8 e\
dges>\ngap> OutNeighbours(D);\n[ [ 1, 2, 3 ], [ 1, 3, 2 ], [ 1, 3 ] ]\ngap> D \
:= CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edg\
es>\ngap> DigraphAddAllLoops(D);\n<mutable digraph with 3 vertices, 6 edges>\n\
gap> D;\n<mutable digraph with 3 vertices, 6 edges>\n", count := [ 3, 3, 38, 
                                                                      7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 38, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 105840, 
                                                          root := ~, 
                                                          start := 105073, 
                                                          stop := 105839 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 38, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 38, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 105857, root := ~, 
                                                  start := 104661, 
                                                  stop := 105856 ) ], 
                                          count := [ 3, 3, 38, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 105871, root := ~, 
                                          start := 104510, stop := 105870 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 38, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, i", 
                                                      Label := "for digraph an\
d int", Name := "DistanceDigraph" ), content := 0, count := [ 3, 3, 39, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 105975, root := ~, 
                                                  start := 105892, 
                                                  stop := 105974 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list", 
                                                      Label := "for digraph an\
d list", Name := "DistanceDigraph" ), content := 0, count := [ 3, 3, 39, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 106065, root := ~, 
                                                  start := 105978, 
                                                  stop := 106064 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 39, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 106097, root := ~, 
                                                  start := 106068, 
                                                  stop := 106096 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
 first argument is a digraph, the second argument is a non-negative\n    integ\
er or a list of positive integers. This operation returns a digraph on\n    th\
e same set of vertices as ", count := [ 3, 3, 39, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 39, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 106315, 
                                                          root := ~, 
                                                          start := 106301, 
                                                          stop := 106314 ), 
                                                      rec( 
                                                          content := ", with t\
wo vertices being adjacent\n    if and only if the distance between them in ",
                                                          count := 
                                                            [ 3, 3, 39, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 39, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 106412, 
                                                          root := ~, 
                                                          start := 106398, 
                                                          stop := 106411 ), 
                                                      rec( 
                                                          content := " equals \
", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 39, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 106428, 
                                                          root := ~, 
                                                          start := 106420, 
                                                          stop := 106427 ), 
                                                      rec( 
                                                          content := "\n    or\
 is a number in ", count := [ 3, 3, 39, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 3, 3, 39, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 39, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 106462, 
                                                          root := ~, 
                                                          start := 106451, 
                                                          stop := 106461 ), 
                                                      rec( 
                                                          content := ".  See "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 39, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and two vertices", Oper := "DigraphShortestDistance" ), content := 0, 
                                                          count := 
                                                            [ 3, 3, 39, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 106549, 
                                                          root := ~, 
                                                          start := 106469, 
                                                          stop := 106548 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 3, 39, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 39, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 106555, 
                                                          root := ~, 
                                                          start := 106551, 
                                                          stop := 106554 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 39, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 106578, 
                                                          root := ~, 
                                                          start := 106564, 
                                                          stop := 106577 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then ", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 39, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 106610, 
                                                          root := ~, 
                                                          start := 106596, 
                                                          stop := 106609 ), 
                                                      rec( 
                                                          content := " is modi\
fied in-place. If\n    ", count := [ 3, 3, 39, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 39, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 106654, 
                                                          root := ~, 
                                                          start := 106640, 
                                                          stop := 106653 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph constructed as\n    described above is ret\
urned.\n    ", count := [ 3, 3, 39, 6 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph := DigraphFromSparse6String(\n> \":]n?AL`BC_DEbEF`GIaGHdIJeGKcKL\
_@McDHfILaBJfHMjKM\");\n<immutable digraph with 30 vertices, 90 edges>\ngap> D\
istanceDigraph(digraph, 1);\n<immutable digraph with 30 vertices, 90 edges>\ng\
ap> DistanceDigraph(digraph, [1, 2]);\n<immutable digraph with 30 vertices, 27\
0 edges>\n", count := [ 3, 3, 39, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 39, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 107094, 
                                                          root := ~, 
                                                          start := 106750, 
                                                          stop := 107093 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 39, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 39, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 107111, root := ~, 
                                                  start := 106100, 
                                                  stop := 107110 ) ], 
                                          count := [ 3, 3, 39, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 107125, root := ~, 
                                          start := 105877, stop := 107124 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 39, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, k", 
                                                      Name := "DigraphClosure"\
 ), content := 0, count := [ 3, 3, 40, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 107192, root := ~, 
                                                  start := 107146, 
                                                  stop := 107191 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 40, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 107224, root := ~, 
                                                  start := 107195, 
                                                  stop := 107223 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Giv\
en a symmetric loopless digraph with no multiple edges ", count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 107317, 
                                                          root := ~, 
                                                          start := 107303, 
                                                          stop := 107316 ), 
                                                      rec( 
                                                          content := ",\n    t\
he ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "k", count := [ 3, 3, 40, 3 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 40, 3 ], 
                                                                  mathmode := \
"Text", name := "A", next := 107338, root := ~, start := 107330, stop := 10733\
7 ), rec( content := "-closure of ", count := [ 3, 3, 40, 3 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          conte\
nt := "digraph", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "A", 
                                                                  next := 1073\
64, root := ~, start := 107350, stop := 107363 ) ], count := [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 107368, 
                                                          root := ~, 
                                                          start := 107327, 
                                                          stop := 107367 ), 
                                                      rec( 
                                                          content := " is defi\
ned to be the unique\n    smallest symmetric loopless digraph ", 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 107445, 
                                                          root := ~, 
                                                          start := 107437, 
                                                          stop := 107444 ), 
                                                      rec( 
                                                          content := " with no\
 multiple edges on the\n    vertices of ", count := [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 107506, 
                                                          root := ~, 
                                                          start := 107492, 
                                                          stop := 107505 ), 
                                                      rec( 
                                                          content := " that co\
ntains all the edges of ", count := [ 3, 3, 40, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 107552, 
                                                          root := ~, 
                                                          start := 107538, 
                                                          stop := 107551 ), 
                                                      rec( 
                                                          content := "\n    an\
d satsifies the property that the sum of the degrees of every two\n    non-adj\
acenct vertices in ", count := [ 3, 3, 40, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 107663, 
                                                          root := ~, 
                                                          start := 107655, 
                                                          stop := 107662 ), 
                                                      rec( 
                                                          content := " is less\
 than ", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 3, 40, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 107685, 
                                                          root := ~, 
                                                          start := 107677, 
                                                          stop := 107684 ), 
                                                      rec( 
                                                          content := ". See ",
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsSymme\
tricDigraph" ), content := 0, count := [ 3, 3, 40, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 107727, 
                                                          root := ~, 
                                                          start := 107691, 
                                                          stop := 107726 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ 3, 3, 40, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 107758, 
                                                          root := ~, 
                                                          start := 107729, 
                                                          stop := 107757 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsMulti\
Digraph" ), content := 0, count := [ 3, 3, 40, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 107792, 
                                                          root := ~, 
                                                          start := 107760, 
                                                          stop := 107791 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "OutDegr\
eeOfVertex" ), content := 0, count := [ 3, 3, 40, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 107829, 
                                                          root := ~, 
                                                          start := 107798, 
                                                          stop := 107828 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 3, 40, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 40, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 107835, 
                                                          root := ~, 
                                                          start := 107831, 
                                                          stop := 107834 ), 
                                                      rec( 
                                                          content := "\n\n    \
The operation ", count := [ 3, 3, 40, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphClosure", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 40, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 107876, 
                                                          root := ~, 
                                                          start := 107855, 
                                                          stop := 107875 ), 
                                                      rec( 
                                                          content := " returns\
 the ", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 3, 40, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 107897, 
                                                          root := ~, 
                                                          start := 107889, 
                                                          stop := 107896 ), 
                                                      rec( 
                                                          content := "-closure\
 of\n    ", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 40, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 40, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 107927, 
                                                          root := ~, 
                                                          start := 107913, 
                                                          stop := 107926 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 3, 40, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(6);\n<immutable complete digraph with 6 vertices>\n\
gap> D := DigraphRemoveEdges(D, [[1, 2], [2, 1]]);\n<immutable digraph with 6 \
vertices, 28 edges>\ngap> closure := DigraphClosure(D, 6);\n<immutable digraph\
 with 6 vertices, 30 edges>\ngap> IsCompleteDigraph(closure);\ntrue\n", 
                                                                  count := 
                                                                    [ 3, 3, 
                                                                      40, 5 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 40, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 108259, 
                                                          root := ~, 
                                                          start := 107933, 
                                                          stop := 108258 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 40, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 40, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 108276, root := ~, 
                                                  start := 107227, 
                                                  stop := 108275 ) ], 
                                          count := [ 3, 3, 40, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 108290, root := ~, 
                                          start := 107131, stop := 108289 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 3, 40, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMycielsk\
ian" ), content := 0, count := [ 3, 3, 41, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 108358, root := ~, 
                                                  start := 108311, 
                                                  stop := 108357 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMycielsk\
ianAttr" ), content := 0, count := [ 3, 3, 41, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 108412, root := ~, 
                                                  start := 108361, 
                                                  stop := 108411 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 3, 41, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 108444, root := ~, 
                                                  start := 108415, 
                                                  stop := 108443 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 41, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 108482, 
                                                          root := ~, 
                                                          start := 108468, 
                                                          stop := 108481 ), 
                                                      rec( 
                                                          content := " is a sy\
mmetric digraph, then\n    ", count := [ 3, 3, 41, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphMycielskian", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 3, 3, 41, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 108541, 
                                                          root := ~, 
                                                          start := 108516, 
                                                          stop := 108540 ), 
                                                      rec( 
                                                          content := " returns\
 the Mycielskian of ", count := [ 3, 3, 41, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 41, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 41, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 108583, 
                                                          root := ~, 
                                                          start := 108569, 
                                                          stop := 108582 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 41, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 41, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 108588, 
                                                          root := ~, 
                                                          start := 108584, 
                                                          stop := 108587 ), 
                                                      rec( 
                                                          content := "\n    \n\
    The Mycielskian of a symmetric digraph is a larger symmetric digraph\n    \
constructed from it, which has a larger chromatic number. For further\n    inf\
ormation, see ", count := [ 3, 3, 41, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttps://en.wikipedia.org/wiki/Mycielskian", count := [ 3, 3, 41, 6 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 3, 41, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 108814, 
                                                          root := ~, 
                                                          start := 108762, 
                                                          stop := 108813 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 3, 3, 41, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 41, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 108819, 
                                                          root := ~, 
                                                          start := 108815, 
                                                          stop := 108818 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 41, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 108842, 
                                                          root := ~, 
                                                          start := 108828, 
                                                          stop := 108841 ), 
                                                      rec( 
                                                          content := " is immu\
table, then a new immutable digraph is returned.\n    Otherwise, the mutable d\
igraph ", count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 3, 3, 41, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 3, 41, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 108948, 
                                                          root := ~, 
                                                          start := 108934, 
                                                          stop := 108947 ), 
                                                      rec( 
                                                          content := " is chan\
ged in-place into\n    its Mycielskian.", count := [ 3, 3, 41, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 3, 41, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 108998, 
                                                          root := ~, 
                                                          start := 108994, 
                                                          stop := 108997 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 3, 41, 8 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(2);\n<immutable cycle digraph with 2 vertices>\ngap> C\
hromaticNumber(D);\n2\ngap> D := DigraphMycielskian(D);\n<immutable digraph wi\
th 5 vertices, 10 edges>\ngap> ChromaticNumber(D);\n3\ngap> D := DigraphMyciel\
skian(D);\n<immutable digraph with 11 vertices, 40 edges>\ngap> ChromaticNumbe\
r(D);\n4\ngap> D := CompleteBipartiteDigraph(IsMutable, 2, 3);\n<mutable digra\
ph with 5 vertices, 12 edges>\ngap> DigraphMycielskian(D);\n<mutable digraph w\
ith 11 vertices, 46 edges>\ngap> D;\n<mutable digraph with 11 vertices, 46 edg\
es>\n", count := [ 3, 3, 41, 9 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 3, 41, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 109568, 
                                                          root := ~, 
                                                          start := 109004, 
                                                          stop := 109567 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 3, 41, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 3, 41, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 109585, root := ~, 
                                                  start := 108447, 
                                                  stop := 109584 ) ], 
                                          count := [ 3, 3, 41, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 109599, root := ~, 
                                          start := 108296, stop := 109598 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 3, 3, 41, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 3, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 109613, 
                                  root := ~, start := 43573, stop := 109612 ),
                              rec( content := "\n\n  ", 
                                  count := [ 3, 3, 41, 10 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Random digraphs",
                                                  count := [ 3, 4, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 3, 4, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 109660, 
                                          root := ~, start := 109626, 
                                          stop := 109659 ), 
                                      rec( content := "\n    ", 
                                          count := [ 3, 4, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]n[, p]",
                                                      Name := "RandomDigraph" 
                                                     ), content := 0, 
                                                  count := [ 3, 4, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 109729, root := ~, 
                                                  start := 109680, 
                                                  stop := 109728 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 4, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 109761, root := ~, 
                                                  start := 109732, 
                                                  stop := 109760 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
the optional first argument ", count := [ 3, 4, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 109824, 
                                                          root := ~, 
                                                          start := 109813, 
                                                          stop := 109823 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 4, 1, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 109970, 
                                                          root := ~, 
                                                          start := 109959, 
                                                          stop := 109969 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 4, 1, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 110004, 
                                                          root := ~, 
                                                          start := 109974, 
                                                          stop := 110003 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 110072, 
                                                          root := ~, 
                                                          start := 110061, 
                                                          stop := 110071 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 4, 1, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 110112, 
                                                          root := ~, 
                                                          start := 110076, 
                                                          stop := 110111 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 110197, 
                                                          root := ~, 
                                                          start := 110186, 
                                                          stop := 110196 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 4, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 4, 1, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 110257, 
                                                          root := ~, 
                                                          start := 110219, 
                                                          stop := 110256 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 110281, 
                                                          root := ~, 
                                                          start := 110277, 
                                                          stop := 110280 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 110298, 
                                                          root := ~, 
                                                          start := 110290, 
                                                          stop := 110297 ), 
                                                      rec( 
                                                          content := " is a po\
sitive integer, then this function returns a random\n    digraph with ", 
                                                          count := 
                                                            [ 3, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 110383, 
                                                          root := ~, 
                                                          start := 110375, 
                                                          stop := 110382 ), 
                                                      rec( 
                                                          content := " vertice\
s and without multiple edges. The result\n    may or may not have loops.", 
                                                          count := 
                                                            [ 3, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 110466, 
                                                          root := ~, 
                                                          start := 110462, 
                                                          stop := 110465 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional second argument ", count := [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 110512, 
                                                          root := ~, 
                                                          start := 110504, 
                                                          stop := 110511 ), 
                                                      rec( 
                                                          content := " is a fl\
oat with value\n    ", count := [ 3, 4, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
 \\leq ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 110553, 
                                                          root := ~, 
                                                          start := 110539, 
                                                          stop := 110552 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
p ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 110564, 
                                                          root := ~, 
                                                          start := 110554, 
                                                          stop := 110563 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
\\leq 1", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 110579, 
                                                          root := ~, 
                                                          start := 110565, 
                                                          stop := 110578 ), 
                                                      rec( 
                                                          content := ", then a\
n edge will exist between each\n    pair of vertices with probability approxim\
ately ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 110678, 
                                                          root := ~, 
                                                          start := 110670, 
                                                          stop := 110677 ), 
                                                      rec( 
                                                          content := ".\n    I\
f ", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 3, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 110695, 
                                                          root := ~, 
                                                          start := 110687, 
                                                          stop := 110694 ), 
                                                      rec( 
                                                          content := " is not \
specified, then a random probability will be assumed\n    (chosen with uniform\
 probability).\n    ", count := [ 3, 4, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RandomDigraph(1000);\n<immutable digraph with 1000 vertices, 364444 edge\
s>\ngap> RandomDigraph(10000, 0.023);\n<immutable digraph with 10000 vertices,\
 2300438 edges>\ngap> RandomDigraph(IsMutableDigraph, 1000, 1 / 2);\n<mutable \
digraph with 1000 vertices, 499739 edges>\n", count := [ 3, 4, 1, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 4, 1, 6 ], mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 111093, 
                                                          root := ~, 
                                                          start := 110799, 
                                                          stop := 111092 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 4, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 4, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 111110, root := ~, 
                                                  start := 109764, 
                                                  stop := 111109 ) ], 
                                          count := [ 3, 4, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 111124, root := ~, 
                                          start := 109665, stop := 111123 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 4, 1, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "n[, m]", 
                                                      Name := "RandomMultiDigr\
aph" ), content := 0, count := [ 3, 4, 2, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 111191, root := ~, 
                                                  start := 111145, 
                                                  stop := 111190 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 4, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 111223, root := ~, 
                                                  start := 111194, 
                                                  stop := 111222 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 111255, 
                                                          root := ~, 
                                                          start := 111247, 
                                                          stop := 111254 ), 
                                                      rec( 
                                                          content := " is a po\
sitive integer, then this function returns a random\n    digraph with ", 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 111340, 
                                                          root := ~, 
                                                          start := 111332, 
                                                          stop := 111339 ), 
                                                      rec( 
                                                          content := " vertice\
s. If the optional second argument\n    ", count := [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 111395, 
                                                          root := ~, 
                                                          start := 111387, 
                                                          stop := 111394 ), 
                                                      rec( 
                                                          content := " is a po\
sitive integer, then the digraph will have ", count := [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 111454, 
                                                          root := ~, 
                                                          start := 111446, 
                                                          stop := 111453 ), 
                                                      rec( 
                                                          content := "\n    ed\
ges. If ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 111477, 
                                                          root := ~, 
                                                          start := 111469, 
                                                          stop := 111476 ), 
                                                      rec( 
                                                          content := " is not \
specified, then the number of edges will be\n    chosen randomly (with uniform\
 probability) from the range\n    ", count := [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. ", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 111608, 
                                                          root := ~, 
                                                          start := 111595, 
                                                          stop := 111607 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "{\
n \\choose 2}", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 111628, 
                                                          root := ~, 
                                                          start := 111608, 
                                                          stop := 111627 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "]\
", count := [ 3, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 111636, 
                                                          root := ~, 
                                                          start := 111628, 
                                                          stop := 111635 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 111646, 
                                                          root := ~, 
                                                          start := 111642, 
                                                          stop := 111645 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used by this function chooses each edge from the set of\n    all po\
ssible edges with uniform probability. No effort is made to avoid\n    creatin\
g multiple edges, so it is possible (but not guaranteed) that the\n    result \
will have multiple edges. The result may or may not have loops.", 
                                                          count := 
                                                            [ 3, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 4, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 111950, 
                                                          root := ~, 
                                                          start := 111946, 
                                                          stop := 111949 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 3, 4, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RandomMultiDigraph(1000);\n<immutable multidigraph with 1000 vertices, 2\
16659 edges>\ngap> RandomMultiDigraph(1000, 950);\n<immutable multidigraph wit\
h 1000 vertices, 950 edges>\n", count := [ 3, 4, 2, 6 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 112159, 
                                                          root := ~, 
                                                          start := 111955, 
                                                          stop := 112158 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 4, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 4, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 112176, root := ~, 
                                                  start := 111226, 
                                                  stop := 112175 ) ], 
                                          count := [ 3, 4, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 112190, root := ~, 
                                          start := 111130, stop := 112189 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 4, 2, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]n", 
                                                      Name := "RandomTournamen\
t" ), content := 0, count := [ 3, 4, 3, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 112258, root := ~, 
                                                  start := 112211, 
                                                  stop := 112257 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 4, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 112290, root := ~, 
                                                  start := 112261, 
                                                  stop := 112289 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
the optional first argument ", count := [ 3, 4, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 112353, 
                                                          root := ~, 
                                                          start := 112342, 
                                                          stop := 112352 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 4, 3, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 112499, 
                                                          root := ~, 
                                                          start := 112488, 
                                                          stop := 112498 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 4, 3, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 112533, 
                                                          root := ~, 
                                                          start := 112503, 
                                                          stop := 112532 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 112601, 
                                                          root := ~, 
                                                          start := 112590, 
                                                          stop := 112600 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 4, 3, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 112641, 
                                                          root := ~, 
                                                          start := 112605, 
                                                          stop := 112640 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 112726, 
                                                          root := ~, 
                                                          start := 112715, 
                                                          stop := 112725 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 4, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 4, 3, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 112786, 
                                                          root := ~, 
                                                          start := 112748, 
                                                          stop := 112785 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 4, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 4, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 112810, 
                                                          root := ~, 
                                                          start := 112806, 
                                                          stop := 112809 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 112827, 
                                                          root := ~, 
                                                          start := 112819, 
                                                          stop := 112826 ), 
                                                      rec( 
                                                          content := " is a no\
n-negative integer, this function returns a random\n    tournament with ", 
                                                          count := 
                                                            [ 3, 4, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 112914, 
                                                          root := ~, 
                                                          start := 112906, 
                                                          stop := 112913 ), 
                                                      rec( 
                                                          content := " vertice\
s. See ", count := [ 3, 4, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsTourn\
ament" ), content := 0, count := [ 3, 4, 3, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 112955, 
                                                          root := ~, 
                                                          start := 112929, 
                                                          stop := 112954 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 4, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 4, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 112961, 
                                                          root := ~, 
                                                          start := 112957, 
                                                          stop := 112960 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 3, 4, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RandomTournament(10);\n<immutable tournament with 10 vertices>\ngap> Ran\
domTournament(IsMutableDigraph, 10);\n<mutable digraph with 1000 vertices, 500\
601 edges>\n", count := [ 3, 4, 3, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 4, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 113153, 
                                                          root := ~, 
                                                          start := 112966, 
                                                          stop := 113152 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 4, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 4, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 113170, root := ~, 
                                                  start := 112293, 
                                                  stop := 113169 ) ], 
                                          count := [ 3, 4, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 113184, root := ~, 
                                          start := 112196, stop := 113183 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 4, 3, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "n", 
                                                      Name := "RandomLattice" 
                                                     ), content := 0, 
                                                  count := [ 3, 4, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 113241, root := ~, 
                                                  start := 113205, 
                                                  stop := 113240 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 4, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 113273, root := ~, 
                                                  start := 113244, 
                                                  stop := 113272 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
the optional first argument ", count := [ 3, 4, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 113336, 
                                                          root := ~, 
                                                          start := 113325, 
                                                          stop := 113335 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 4, 4, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 113482, 
                                                          root := ~, 
                                                          start := 113471, 
                                                          stop := 113481 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 4, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 113516, 
                                                          root := ~, 
                                                          start := 113486, 
                                                          stop := 113515 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 113584, 
                                                          root := ~, 
                                                          start := 113573, 
                                                          stop := 113583 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 4, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 113624, 
                                                          root := ~, 
                                                          start := 113588, 
                                                          stop := 113623 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 113709, 
                                                          root := ~, 
                                                          start := 113698, 
                                                          stop := 113708 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 4, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 4, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 113769, 
                                                          root := ~, 
                                                          start := 113731, 
                                                          stop := 113768 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 4, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 113793, 
                                                          root := ~, 
                                                          start := 113789, 
                                                          stop := 113792 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 113810, 
                                                          root := ~, 
                                                          start := 113802, 
                                                          stop := 113809 ), 
                                                      rec( 
                                                          content := " is a po\
sitive integer, this function return a random lattice\n    with ", 
                                                          count := 
                                                            [ 3, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 113889, 
                                                          root := ~, 
                                                          start := 113881, 
                                                          stop := 113888 ), 
                                                      rec( 
                                                          content := " vertice\
s, where it is guaranteed that ", count := [ 3, 4, 4, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 113936, 
                                                          root := ~, 
                                                          start := 113928, 
                                                          stop := 113935 ), 
                                                      rec( 
                                                          content := " is betw\
een\n    ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 113960, 
                                                          root := ~, 
                                                          start := 113952, 
                                                          stop := 113959 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
 * ", count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 4, 4, 4 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 4, 4, 4 ], 
                                                                  mathmode := \
"Text", name := "A", next := 113980, root := ~, start := 113972, stop := 11397\
9 ) ], count := [ 3, 4, 4, 4 ], mathmode := "Text", name := "C", 
                                                          next := 113984, 
                                                          root := ~, 
                                                          start := 113965, 
                                                          stop := 113983 ), 
                                                      rec( 
                                                          content := ". See ",
                                                          count := 
                                                            [ 3, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsLatti\
ceDigraph" ), content := 0, count := [ 3, 4, 4, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 114020, 
                                                          root := ~, 
                                                          start := 113990, 
                                                          stop := 114019 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 4, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 4, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 114026, 
                                                          root := ~, 
                                                          start := 114022, 
                                                          stop := 114025 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 3, 4, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> RandomLattice(10);\n<immutable lattice digraph with 10 vertices, 39 edge\
s>\ngap> RandomLattice(IsMutableDigraph, 10);\n<mutable digraph with 12 vertic\
es, 52 edges>\n", count := [ 3, 4, 4, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 4, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 114221, 
                                                          root := ~, 
                                                          start := 114031, 
                                                          stop := 114220 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 4, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 4, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 114238, root := ~, 
                                                  start := 113276, 
                                                  stop := 114237 ) ], 
                                          count := [ 3, 4, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 114252, root := ~, 
                                          start := 113190, stop := 114251 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 3, 4, 4, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 4, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 114266, 
                                  root := ~, start := 109617, stop := 114265 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 3, 4, 4, 7 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Standard examples\
", count := [ 3, 5, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                             ], count := [ 3, 5, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 114315, 
                                          root := ~, start := 114279, 
                                          stop := 114314 ), 
                                      rec( content := "\n    ", 
                                          count := [ 3, 5, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]n", 
                                                      Name := "ChainDigraph" )
                                                    , content := 0, 
                                                  count := [ 3, 5, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 114378, root := ~, 
                                                  start := 114335, 
                                                  stop := 114377 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 5, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 114410, root := ~, 
                                                  start := 114381, 
                                                  stop := 114409 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 114442, 
                                                          root := ~, 
                                                          start := 114434, 
                                                          stop := 114441 ), 
                                                      rec( 
                                                          content := " is a po\
sitive integer, this function returns a chain\n    with ", 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 114513, 
                                                          root := ~, 
                                                          start := 114505, 
                                                          stop := 114512 ), 
                                                      rec( 
                                                          content := " vertice\
s and ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "n", count := [ 3, 5, 1, 3 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], 
                                                                  mathmode := \
"Text", name := "A", next := 114538, root := ~, start := 114530, stop := 11453\
7 ), rec( content := " - 1", count := [ 3, 5, 1, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 1, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 114546, 
                                                          root := ~, 
                                                          start := 114527, 
                                                          stop := 114545 ), 
                                                      rec( 
                                                          content := " edges.\\
n    Specifically,\n    for each vertex ", count := [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 114600, 
                                                          root := ~, 
                                                          start := 114592, 
                                                          stop := 114599 ), 
                                                      rec( 
                                                          content := " (with "
                                                            , 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 114615, 
                                                          root := ~, 
                                                          start := 114607, 
                                                          stop := 114614 ), 
                                                      rec( content := " < ", 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 114629, 
                                                          root := ~, 
                                                          start := 114621, 
                                                          stop := 114628 ), 
                                                      rec( 
                                                          content := "), there\
 is a directed\n    edge with source ", count := [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 114681, 
                                                          root := ~, 
                                                          start := 114673, 
                                                          stop := 114680 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 + 1", count := [ 3, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 114704, 
                                                          root := ~, 
                                                          start := 114692, 
                                                          stop := 114703 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 114710, 
                                                          root := ~, 
                                                          start := 114706, 
                                                          stop := 114709 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional first argument ", count := [ 3, 5, 1, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 114758, 
                                                          root := ~, 
                                                          start := 114747, 
                                                          stop := 114757 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 5, 1, 4 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 114904, 
                                                          root := ~, 
                                                          start := 114893, 
                                                          stop := 114903 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 5, 1, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 114938, 
                                                          root := ~, 
                                                          start := 114908, 
                                                          stop := 114937 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 115006, 
                                                          root := ~, 
                                                          start := 114995, 
                                                          stop := 115005 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 1, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 115046, 
                                                          root := ~, 
                                                          start := 115010, 
                                                          stop := 115045 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 115131, 
                                                          root := ~, 
                                                          start := 115120, 
                                                          stop := 115130 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 5, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 1, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 115191, 
                                                          root := ~, 
                                                          start := 115153, 
                                                          stop := 115190 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 115215, 
                                                          root := ~, 
                                                          start := 115211, 
                                                          stop := 115214 ), 
                                                      rec( 
                                                          content := "\n\n    \
The ", count := [ 3, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
ReflexiveTransitiveClosure" ), content := 0, count := [ 3, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 115272, 
                                                          root := ~, 
                                                          start := 115225, 
                                                          stop := 115271 ), 
                                                      rec( 
                                                          content := " of a ch\
ain represents a\n    total order.\n    ", count := [ 3, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> ChainDigraph(42);\n<immutable chain digraph with 42 vertices>\ngap> Chai\
nDigraph(IsMutableDigraph, 10);\n<mutable digraph with 10 vertices, 9 edges>\n\
", count := [ 3, 5, 1, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 115501, 
                                                          root := ~, 
                                                          start := 115318, 
                                                          stop := 115500 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 5, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 5, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 115518, root := ~, 
                                                  start := 114413, 
                                                  stop := 115517 ) ], 
                                          count := [ 3, 5, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 115532, root := ~, 
                                          start := 114320, stop := 115531 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 5, 1, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]n", 
                                                      Name := "CompleteDigraph\
" ), content := 0, count := [ 3, 5, 2, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 115599, root := ~, 
                                                  start := 115553, 
                                                  stop := 115598 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 5, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 115631, root := ~, 
                                                  start := 115602, 
                                                  stop := 115630 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 115663, 
                                                          root := ~, 
                                                          start := 115655, 
                                                          stop := 115662 ), 
                                                      rec( 
                                                          content := " is a no\
n-negative integer, this function returns the complete\n    digraph with ", 
                                                          count := 
                                                            [ 3, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 115751, 
                                                          root := ~, 
                                                          start := 115743, 
                                                          stop := 115750 ), 
                                                      rec( 
                                                          content := " vertice\
s. See ", count := [ 3, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsCompl\
eteDigraph" ), content := 0, count := [ 3, 5, 2, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 115797, 
                                                          root := ~, 
                                                          start := 115766, 
                                                          stop := 115796 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 115803, 
                                                          root := ~, 
                                                          start := 115799, 
                                                          stop := 115802 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional first argument ", count := [ 3, 5, 2, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 115851, 
                                                          root := ~, 
                                                          start := 115840, 
                                                          stop := 115850 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 5, 2, 4 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 115997, 
                                                          root := ~, 
                                                          start := 115986, 
                                                          stop := 115996 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 116031, 
                                                          root := ~, 
                                                          start := 116001, 
                                                          stop := 116030 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 116099, 
                                                          root := ~, 
                                                          start := 116088, 
                                                          stop := 116098 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 116139, 
                                                          root := ~, 
                                                          start := 116103, 
                                                          stop := 116138 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 116224, 
                                                          root := ~, 
                                                          start := 116213, 
                                                          stop := 116223 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 116284, 
                                                          root := ~, 
                                                          start := 116246, 
                                                          stop := 116283 ), 
                                                      rec( 
                                                          content := " is used\
 by default.\n    ", count := [ 3, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> CompleteDigraph(20);\n<immutable complete digraph with 20 vertices>\ngap\
> CompleteDigraph(IsMutableDigraph, 10);\n<mutable digraph with 10 vertices, 9\
0 edges>\n", count := [ 3, 5, 2, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 3, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 116502, 
                                                          root := ~, 
                                                          start := 116309, 
                                                          stop := 116501 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 5, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 5, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 116519, root := ~, 
                                                  start := 115634, 
                                                  stop := 116518 ) ], 
                                          count := [ 3, 5, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 116533, root := ~, 
                                          start := 115538, stop := 116532 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 5, 2, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]m, n", 
                                                      Name := "CompleteBiparti\
teDigraph" ), content := 0, count := [ 3, 5, 3, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 116612, root := ~, 
                                                  start := 116554, 
                                                  stop := 116611 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 5, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 116644, root := ~, 
                                                  start := 116615, 
                                                  stop := 116643 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A c\
omplete bipartite digraph is a digraph whose vertices\n    can be partitioned \
into two non-empty vertex sets, such there exists\n    a unique edge with sour\
ce ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 116833, 
                                                          root := ~, 
                                                          start := 116825, 
                                                          stop := 116832 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 116852, 
                                                          root := ~, 
                                                          start := 116844, 
                                                          stop := 116851 ), 
                                                      rec( 
                                                          content := " if and \
only if\n    ", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 116880, 
                                                          root := ~, 
                                                          start := 116872, 
                                                          stop := 116879 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 3, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 116893, 
                                                          root := ~, 
                                                          start := 116885, 
                                                          stop := 116892 ), 
                                                      rec( 
                                                          content := " lie in \
different vertex sets. ", count := [ 3, 5, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 116928, 
                                                          root := ~, 
                                                          start := 116924, 
                                                          stop := 116927 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 116945, 
                                                          root := ~, 
                                                          start := 116937, 
                                                          stop := 116944 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 116958, 
                                                          root := ~, 
                                                          start := 116950, 
                                                          stop := 116957 ), 
                                                      rec( 
                                                          content := " are pos\
itive integers, this function\n    returns the complete bipartite digraph with\
 vertex sets of sizes\n    ", count := [ 3, 5, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 117077, 
                                                          root := ~, 
                                                          start := 117069, 
                                                          stop := 117076 ), 
                                                      rec( 
                                                          content := " (contai\
ning the vertices ", count := [ 3, 5, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. m]", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 117118, 
                                                          root := ~, 
                                                          start := 117103, 
                                                          stop := 117117 ), 
                                                      rec( 
                                                          content := ") and\n \
   ", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 117136, 
                                                          root := ~, 
                                                          start := 117128, 
                                                          stop := 117135 ), 
                                                      rec( 
                                                          content := " (contai\
ning the vertices ", count := [ 3, 5, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
m + 1 .. m + n]", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "C", 
                                                          next := 117185, 
                                                          root := ~, 
                                                          start := 117162, 
                                                          stop := 117184 ), 
                                                      rec( 
                                                          content := ").\n    \
", count := [ 3, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 117196, 
                                                          root := ~, 
                                                          start := 117192, 
                                                          stop := 117195 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional first argument ", count := [ 3, 5, 3, 5 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 117244, 
                                                          root := ~, 
                                                          start := 117233, 
                                                          stop := 117243 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 5, 3, 5 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 117390, 
                                                          root := ~, 
                                                          start := 117379, 
                                                          stop := 117389 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 5, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 117424, 
                                                          root := ~, 
                                                          start := 117394, 
                                                          stop := 117423 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 117492, 
                                                          root := ~, 
                                                          start := 117481, 
                                                          stop := 117491 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 117532, 
                                                          root := ~, 
                                                          start := 117496, 
                                                          stop := 117531 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 117617, 
                                                          root := ~, 
                                                          start := 117606, 
                                                          stop := 117616 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 5, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 117677, 
                                                          root := ~, 
                                                          start := 117639, 
                                                          stop := 117676 ), 
                                                      rec( 
                                                          content := " is used\
 by default.\n\n    ", count := [ 3, 5, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> CompleteBipartiteDigraph(2, 3);\n<immutable complete bipartite digraph w\
ith bicomponent sizes 2 and 3>\ngap> CompleteBipartiteDigraph(IsMutableDigraph\
, 3, 2);\n<mutable digraph with 5 vertices, 12 edges>\n", count := [ 3, 5, 3, 
                                                                      6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 3, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 117941, 
                                                          root := ~, 
                                                          start := 117703, 
                                                          stop := 117940 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 5, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 5, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 117958, root := ~, 
                                                  start := 116647, 
                                                  stop := 117957 ) ], 
                                          count := [ 3, 5, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 117972, root := ~, 
                                          start := 116539, stop := 117971 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 3, 5, 3, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]orders",
                                                      Name := "CompleteMultipa\
rtiteDigraph" ), content := 0, count := [ 3, 5, 4, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 118062, root := ~, 
                                                  start := 117997, 
                                                  stop := 118061 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 5, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 118096, root := ~, 
                                                  start := 118067, 
                                                  stop := 118095 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      F\
or a list ", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
rders", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 118145, 
                                                          root := ~, 
                                                          start := 118132, 
                                                          stop := 118144 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 3, 5, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 118157, 
                                                          root := ~, 
                                                          start := 118149, 
                                                          stop := 118156 ), 
                                                      rec( 
                                                          content := " positiv\
e integers,\n      this function returns the digraph containing ", 
                                                          count := 
                                                            [ 3, 5, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 118236, 
                                                          root := ~, 
                                                          start := 118228, 
                                                          stop := 118235 ), 
                                                      rec( 
                                                          content := " indepen\
dent sets\n      of vertices of orders ", count := [ 3, 5, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "l", count := [ 3, 5, 4, 3 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], 
                                                                  mathmode := \
"Text", name := "A", next := 118294, root := ~, start := 118286, stop := 11829\
3 ), rec( content := "[1] .. ", count := [ 3, 5, 4, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "l\
", count := [ 3, 5, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                                     ], 
                                                                  count := 
                                                                    [ 3, 5, 
                                                                      4, 3 ], 
                                                                  mathmode := \
"Text", name := "A", next := 118309, root := ~, start := 118301, stop := 11830\
8 ), rec( content := "[n]]", count := [ 3, 5, 4, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 4, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 118317, 
                                                          root := ~, 
                                                          start := 118282, 
                                                          stop := 118316 ), 
                                                      rec( 
                                                          content := ". Moreov\
er,\n      each vertex is adjacent to every other not contained in the\n      \
same independent set.\n      ", count := [ 3, 5, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 118433, 
                                                          root := ~, 
                                                          start := 118429, 
                                                          stop := 118432 ), 
                                                      rec( 
                                                          content := "\n\n    \
  If the optional first argument ", count := [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 118483, 
                                                          root := ~, 
                                                          start := 118472, 
                                                          stop := 118482 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n      specify the category or representation the digrap\
h being created will\n      belong to. For example, if ", count := 
                                                            [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 118633, 
                                                          root := ~, 
                                                          start := 118622, 
                                                          stop := 118632 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 5, 4, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 118667, 
                                                          root := ~, 
                                                          start := 118637, 
                                                          stop := 118666 ), 
                                                      rec( 
                                                          content := ",\n     \
 then the digraph being created will be mutable, if ", count := [ 3, 5, 4, 4 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 118737, 
                                                          root := ~, 
                                                          start := 118726, 
                                                          stop := 118736 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 4, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 118779, 
                                                          root := ~, 
                                                          start := 118741, 
                                                          stop := 118778 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n      If the optional first argument ", 
                                                          count := 
                                                            [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 118866, 
                                                          root := ~, 
                                                          start := 118855, 
                                                          stop := 118865 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 5, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 4, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 118928, 
                                                          root := ~, 
                                                          start := 118888, 
                                                          stop := 118927 ), 
                                                      rec( 
                                                          content := " is used\
 by default.\n      ", count := [ 3, 5, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> CompleteMultipartiteDigraph([5, 4, 2]);\n<immutable complete multipartit\
e digraph with 11 vertices, 76 edges>\ngap> CompleteMultipartiteDigraph(IsMuta\
bleDigraph, [5, 4, 2]);\n<mutable digraph with 11 vertices, 76 edges>\n", 
                                                                  count := 
                                                                    [ 3, 5, 
                                                                      4, 5 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 4, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 119209, 
                                                          root := ~, 
                                                          start := 118955, 
                                                          stop := 119208 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 5, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 5, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 119226, root := ~, 
                                                  start := 118101, 
                                                  stop := 119225 ) ], 
                                          count := [ 3, 5, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 119240, root := ~, 
                                          start := 117980, stop := 119239 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 5, 4, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]n", 
                                                      Name := "CycleDigraph" )
                                                    , content := 0, 
                                                  count := [ 3, 5, 5, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 119304, root := ~, 
                                                  start := 119261, 
                                                  stop := 119303 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 5, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 119336, root := ~, 
                                                  start := 119307, 
                                                  stop := 119335 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 119368, 
                                                          root := ~, 
                                                          start := 119360, 
                                                          stop := 119367 ), 
                                                      rec( 
                                                          content := " is a po\
sitive integer, this function returns a ", count := [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ycle", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 119428, 
                                                          root := ~, 
                                                          start := 119416, 
                                                          stop := 119427 ), 
                                                      rec( 
                                                          content := "\n    di\
graph with ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 119454, 
                                                          root := ~, 
                                                          start := 119446, 
                                                          stop := 119453 ), 
                                                      rec( 
                                                          content := " vertice\
s and ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 119476, 
                                                          root := ~, 
                                                          start := 119468, 
                                                          stop := 119475 ), 
                                                      rec( 
                                                          content := " edges. \
Specifically,\n    for each vertex ", count := [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 119526, 
                                                          root := ~, 
                                                          start := 119518, 
                                                          stop := 119525 ), 
                                                      rec( 
                                                          content := " (with "
                                                            , 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 119541, 
                                                          root := ~, 
                                                          start := 119533, 
                                                          stop := 119540 ), 
                                                      rec( content := " < ", 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 119555, 
                                                          root := ~, 
                                                          start := 119547, 
                                                          stop := 119554 ), 
                                                      rec( 
                                                          content := "), there\
 is a directed\n    edge with source ", count := [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 119607, 
                                                          root := ~, 
                                                          start := 119599, 
                                                          stop := 119606 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 + 1", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 119630, 
                                                          root := ~, 
                                                          start := 119618, 
                                                          stop := 119629 ), 
                                                      rec( 
                                                          content := ". In add\
ition, there is\n    an edge with source ", count := [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 119686, 
                                                          root := ~, 
                                                          start := 119678, 
                                                          stop := 119685 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 3, 5, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 119705, 
                                                          root := ~, 
                                                          start := 119697, 
                                                          stop := 119704 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 5, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 119711, 
                                                          root := ~, 
                                                          start := 119707, 
                                                          stop := 119710 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional first argument ", count := [ 3, 5, 5, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 119759, 
                                                          root := ~, 
                                                          start := 119748, 
                                                          stop := 119758 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 5, 5, 4 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 119905, 
                                                          root := ~, 
                                                          start := 119894, 
                                                          stop := 119904 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 5, 5, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 119939, 
                                                          root := ~, 
                                                          start := 119909, 
                                                          stop := 119938 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 5, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 120007, 
                                                          root := ~, 
                                                          start := 119996, 
                                                          stop := 120006 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 5, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 120047, 
                                                          root := ~, 
                                                          start := 120011, 
                                                          stop := 120046 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 5, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 120132, 
                                                          root := ~, 
                                                          start := 120121, 
                                                          stop := 120131 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 5, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 5, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 120190, 
                                                          root := ~, 
                                                          start := 120154, 
                                                          stop := 120189 ), 
                                                      rec( 
                                                          content := " is used\
 by default.\n  ", count := [ 3, 5, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> CycleDigraph(1);\n<immutable digraph with 1 vertex, 1 edge>\ngap> CycleD\
igraph(123);\n<immutable cycle digraph with 123 vertices>\ngap> CycleDigraph(I\
sMutableDigraph, 10);\n<mutable digraph with 10 vertices, 10 edges>\n", 
                                                                  count := 
                                                                    [ 3, 5, 
                                                                      5, 5 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 5, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 120463, 
                                                          root := ~, 
                                                          start := 120213, 
                                                          stop := 120462 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 5, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 5, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 120480, root := ~, 
                                                  start := 119339, 
                                                  stop := 120479 ) ], 
                                          count := [ 3, 5, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 120494, root := ~, 
                                          start := 119246, stop := 120493 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 5, 5, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]n", 
                                                      Name := "EmptyDigraph" )
                                                    , content := 0, 
                                                  count := [ 3, 5, 6, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 120558, root := ~, 
                                                  start := 120515, 
                                                  stop := 120557 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]n", 
                                                      Name := "NullDigraph" ),
                                                  content := 0, 
                                                  count := [ 3, 5, 6, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 120603, root := ~, 
                                                  start := 120561, 
                                                  stop := 120602 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 5, 6, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 120635, root := ~, 
                                                  start := 120606, 
                                                  stop := 120634 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 120667, 
                                                          root := ~, 
                                                          start := 120659, 
                                                          stop := 120666 ), 
                                                      rec( 
                                                          content := " is a no\
n-negative integer, this function returns the\n    ", count := [ 3, 5, 6, 5 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
mpty", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 120737, 
                                                          root := ~, 
                                                          start := 120725, 
                                                          stop := 120736 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 3, 5, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
ull", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 120752, 
                                                          root := ~, 
                                                          start := 120741, 
                                                          stop := 120751 ), 
                                                      rec( 
                                                          content := " digraph\
 with ", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 120774, 
                                                          root := ~, 
                                                          start := 120766, 
                                                          stop := 120773 ), 
                                                      rec( 
                                                          content := " vertice\
s. An empty\n    digraph is one with no edges.\n    ", count := [ 3, 5, 6, 5 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 120836, 
                                                          root := ~, 
                                                          start := 120832, 
                                                          stop := 120835 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the optional first argument ", count := [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 120890, 
                                                          root := ~, 
                                                          start := 120879, 
                                                          stop := 120889 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 5, 6, 6 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 121036, 
                                                          root := ~, 
                                                          start := 121025, 
                                                          stop := 121035 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 5, 6, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 121070, 
                                                          root := ~, 
                                                          start := 121040, 
                                                          stop := 121069 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 121138, 
                                                          root := ~, 
                                                          start := 121127, 
                                                          stop := 121137 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 6, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 121178, 
                                                          root := ~, 
                                                          start := 121142, 
                                                          stop := 121177 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 121263, 
                                                          root := ~, 
                                                          start := 121252, 
                                                          stop := 121262 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 5, 6, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 6, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 121323, 
                                                          root := ~, 
                                                          start := 121285, 
                                                          stop := 121322 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 5, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 121347, 
                                                          root := ~, 
                                                          start := 121343, 
                                                          stop := 121346 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "N\
ullDigraph", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 121371, 
                                                          root := ~, 
                                                          start := 121353, 
                                                          stop := 121370 ), 
                                                      rec( 
                                                          content := " is a sy\
nonym for ", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "E\
mptyDigraph", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 121408, 
                                                          root := ~, 
                                                          start := 121389, 
                                                          stop := 121407 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 5, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> EmptyDigraph(20);\n<immutable empty digraph with 20 vertices>\ngap> Null\
Digraph(10);\n<immutable empty digraph with 10 vertices>\ngap> EmptyDigraph(Is\
MutableDigraph, 10);\n<mutable empty digraph with 10 vertices>", count := 
                                                                    [ 3, 5, 
                                                                      6, 8 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 6, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 121659, 
                                                          root := ~, 
                                                          start := 121415, 
                                                          stop := 121658 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 5, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 5, 6, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 121676, root := ~, 
                                                  start := 120638, 
                                                  stop := 121675 ) ], 
                                          count := [ 3, 5, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 121690, root := ~, 
                                          start := 120500, stop := 121689 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 5, 6, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]n, k", 
                                                      Name := "JohnsonDigraph"\
 ), content := 0, count := [ 3, 5, 7, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 121759, root := ~, 
                                                  start := 121711, 
                                                  stop := 121758 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 5, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 121791, root := ~, 
                                                  start := 121762, 
                                                  stop := 121790 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 121823, 
                                                          root := ~, 
                                                          start := 121815, 
                                                          stop := 121822 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 3, 5, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 121836, 
                                                          root := ~, 
                                                          start := 121828, 
                                                          stop := 121835 ), 
                                                      rec( 
                                                          content := " are non\
-negative integers, then this operation\n    returns a symmetric digraph which\
 corresponds to the undirected ", count := [ 3, 5, 7, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "J\
ohnson\n    graph", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "E", 
                                                          next := 121976, 
                                                          root := ~, 
                                                          start := 121952, 
                                                          stop := 121975 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 5, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "J\
(n, k)", count := [ 3, 5, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 121991, 
                                                          root := ~, 
                                                          start := 121977, 
                                                          stop := 121990 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 5, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 121997, 
                                                          root := ~, 
                                                          start := 121993, 
                                                          stop := 121996 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional first argument ", count := [ 3, 5, 7, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 122045, 
                                                          root := ~, 
                                                          start := 122034, 
                                                          stop := 122044 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 5, 7, 4 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 122191, 
                                                          root := ~, 
                                                          start := 122180, 
                                                          stop := 122190 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 5, 7, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 122225, 
                                                          root := ~, 
                                                          start := 122195, 
                                                          stop := 122224 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 122293, 
                                                          root := ~, 
                                                          start := 122282, 
                                                          stop := 122292 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 7, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 122333, 
                                                          root := ~, 
                                                          start := 122297, 
                                                          stop := 122332 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 122418, 
                                                          root := ~, 
                                                          start := 122407, 
                                                          stop := 122417 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 5, 7, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 7, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 122478, 
                                                          root := ~, 
                                                          start := 122440, 
                                                          stop := 122477 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 5, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 122502, 
                                                          root := ~, 
                                                          start := 122498, 
                                                          stop := 122501 ), 
                                                      rec( 
                                                          content := "\n\n    \
The ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "J\
ohnson graph", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 122532, 
                                                          root := ~, 
                                                          start := 122512, 
                                                          stop := 122531 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 5, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "J\
(n, k)", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 122547, 
                                                          root := ~, 
                                                          start := 122533, 
                                                          stop := 122546 ), 
                                                      rec( 
                                                          content := " has ver\
tices given by all the\n    ", count := [ 3, 5, 7, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 122590, 
                                                          root := ~, 
                                                          start := 122582, 
                                                          stop := 122589 ), 
                                                      rec( 
                                                          content := "-subsets\
 of the range ", count := [ 3, 5, 7, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1 .. ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 5, 7, 5 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 122629, root := ~, start := 122621, stop := 12262\
8 ), rec( content := "]", count := [ 3, 5, 7, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 122634, 
                                                          root := ~, 
                                                          start := 122612, 
                                                          stop := 122633 ), 
                                                      rec( 
                                                          content := ", and tw\
o vertices are\n      connected by an edge iff their intersection has size ", 
                                                          count := 
                                                            [ 3, 5, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "k", count := [ 3, 5, 7, 5 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 122727, root := ~, start := 122719, stop := 12272\
6 ), rec( content := " - 1", count := [ 3, 5, 7, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 7, 5 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 122735, 
                                                          root := ~, 
                                                          start := 122716, 
                                                          stop := 122734 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 3, 5, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := JohnsonDigraph(3, 1);\n<immutable symmetric digraph with 3 vertice\
s, 6 edges>\ngap> OutNeighbours(gr);\n[ [ 2, 3 ], [ 1, 3 ], [ 1, 2 ] ]\ngap> g\
r := JohnsonDigraph(4, 2);\n<immutable symmetric digraph with 6 vertices, 24 e\
dges>\ngap> OutNeighbours(gr);\n[ [ 2, 3, 4, 5 ], [ 1, 3, 4, 6 ], [ 1, 2, 5, 6\
 ], [ 1, 2, 5, 6 ], \n  [ 1, 3, 4, 6 ], [ 2, 3, 4, 5 ] ]\ngap> JohnsonDigraph(\
1, 0);\n<immutable empty digraph with 1 vertex>\ngap> JohnsonDigraph(IsMutable\
Digraph, 1, 0);\n<mutable empty digraph with 1 vertex>\n", count := [ 3, 5, 
                                                                      7, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 7, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 123284, 
                                                          root := ~, 
                                                          start := 122742, 
                                                          stop := 123283 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 5, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 5, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 123301, root := ~, 
                                                  start := 121794, 
                                                  stop := 123300 ) ], 
                                          count := [ 3, 5, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 123315, root := ~, 
                                          start := 121696, stop := 123314 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 5, 7, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt]", 
                                                      Name := "PetersenGraph" 
                                                     ), content := 0, 
                                                  count := [ 3, 5, 8, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 123377, root := ~, 
                                                  start := 123336, 
                                                  stop := 123376 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 5, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 5, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 123409, root := ~, 
                                                  start := 123380, 
                                                  stop := 123408 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\n    F\
rom ", count := [ 3, 5, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttps://en.wikipedia.org/wiki/Petersen_graph", count := [ 3, 5, 8, 3 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 123491, 
                                                          root := ~, 
                                                          start := 123436, 
                                                          stop := 123490 ), 
                                                      rec( content := ":", 
                                                          count := 
                                                            [ 3, 5, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 123496, 
                                                          root := ~, 
                                                          start := 123492, 
                                                          stop := 123495 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 5, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "T\
he Petersen graph is an undirected graph with 10 vertices and 15 edges.\n    I\
t is a small graph that serves as a useful example and counterexample for\n   \
 many problems in graph theory. The Petersen graph is named after Julius\n    \
Petersen, who in 1898 constructed it to be the smallest bridgeless cubic\n    \
graph with no three-edge-coloring.", count := [ 3, 5, 8, 4 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Q", 
                                                          next := 123852, 
                                                          root := ~, 
                                                          start := 123502, 
                                                          stop := 123851 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 123856, 
                                                          root := ~, 
                                                          start := 123852, 
                                                          stop := 123855 ), 
                                                      rec( 
                                                          content := "\n    \n\
    If the optional first argument ", count := [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 123908, 
                                                          root := ~, 
                                                          start := 123897, 
                                                          stop := 123907 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 5, 8, 5 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 124054, 
                                                          root := ~, 
                                                          start := 124043, 
                                                          stop := 124053 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 5, 8, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 124088, 
                                                          root := ~, 
                                                          start := 124058, 
                                                          stop := 124087 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 124156, 
                                                          root := ~, 
                                                          start := 124145, 
                                                          stop := 124155 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 8, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 124196, 
                                                          root := ~, 
                                                          start := 124160, 
                                                          stop := 124195 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 124281, 
                                                          root := ~, 
                                                          start := 124270, 
                                                          stop := 124280 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 5, 8, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 8, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 124341, 
                                                          root := ~, 
                                                          start := 124303, 
                                                          stop := 124340 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 5, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 124365, 
                                                          root := ~, 
                                                          start := 124361, 
                                                          stop := 124364 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 3, 5, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "General\
isedPetersenGraph" ), content := 0, count := [ 3, 5, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 124418, 
                                                          root := ~, 
                                                          start := 124380, 
                                                          stop := 124417 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 3, 5, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> ChromaticNumber(PetersenGraph());\n3\ngap> PetersenGraph(IsMutableDigrap\
h);\n<mutable digraph with 10 vertices, 30 edges>\n", count := [ 3, 5, 8, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 8, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 124577, 
                                                          root := ~, 
                                                          start := 124421, 
                                                          stop := 124576 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 5, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 5, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 124594, root := ~, 
                                                  start := 123412, 
                                                  stop := 124593 ) ], 
                                          count := [ 3, 5, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 124608, root := ~, 
                                          start := 123321, stop := 124607 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 3, 5, 8, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "[filt, ]n, k", 
                                                      Name := "GeneralisedPete\
rsenGraph" ), content := 0, count := [ 3, 5, 9, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 124687, root := ~, 
                                                  start := 124629, 
                                                  stop := 124686 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 3, 5, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 124719, root := ~, 
                                                  start := 124690, 
                                                  stop := 124718 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 124751, 
                                                          root := ~, 
                                                          start := 124743, 
                                                          stop := 124750 ), 
                                                      rec( 
                                                          content := " is a po\
sitive integer and ", count := [ 3, 5, 9, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 124786, 
                                                          root := ~, 
                                                          start := 124778, 
                                                          stop := 124785 ), 
                                                      rec( 
                                                          content := " is a no\
n-negative\n    integer less than ", count := [ 3, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "n", count := [ 3, 5, 9, 3 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], 
                                                                  mathmode := \
"Text", name := "A", next := 124838, root := ~, start := 124830, stop := 12483\
7 ), rec( content := " / 2", count := [ 3, 5, 9, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 124846, 
                                                          root := ~, 
                                                          start := 124827, 
                                                          stop := 124845 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns\n    the ", count := [ 3, 5, 9, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
eneralised Petersen graph", count := [ 3, 5, 9, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 124917, 
                                                          root := ~, 
                                                          start := 124884, 
                                                          stop := 124916 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 3, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
PG(", count := [ 3, 5, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 3, 5, 9, 3 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], 
                                                                  mathmode := \
"Text", name := "A", next := 124933, root := ~, start := 124925, stop := 12493\
2 ), rec( content := ", k)", count := [ 3, 5, 9, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 9, 3 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 124941, 
                                                          root := ~, 
                                                          start := 124918, 
                                                          stop := 124940 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 3, 5, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 124947, 
                                                          root := ~, 
                                                          start := 124943, 
                                                          stop := 124946 ), 
                                                      rec( 
                                                          content := "\n\n    \
From\n    ", count := [ 3, 5, 9, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttps://en.wikipedia.org/wiki/Generalized_Petersen_graph", count := [ 3, 5, 9, 
                                                                      4 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 3, 5, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 125029, 
                                                          root := ~, 
                                                          start := 124962, 
                                                          stop := 125028 ), 
                                                      rec( 
                                                          content := ":\n    "
                                                            , 
                                                          count := 
                                                            [ 3, 5, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 125039, 
                                                          root := ~, 
                                                          start := 125035, 
                                                          stop := 125038 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 3, 5, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "T\
he generalized Petersen graphs are a family of cubic\n    graphs formed by con\
necting the vertices of a regular polygon to the\n    corresponding vertices o\
f a star polygon. They include the Petersen graph\n    and generalize one of t\
he ways of constructing the Petersen graph. The\n    generalized Petersen grap\
h family was introduced in 1950 by H. S. M.\n    Coxeter and was given its nam\
e in 1969 by Mark Watkins.", count := [ 3, 5, 9, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 9, 5 ], mathmode := "Text", 
                                                          name := "Q", 
                                                          next := 125464, 
                                                          root := ~, 
                                                          start := 125045, 
                                                          stop := 125463 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 3, 5, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 125473, 
                                                          root := ~, 
                                                          start := 125469, 
                                                          stop := 125472 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional first argument ", count := [ 3, 5, 9, 6 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 125521, 
                                                          root := ~, 
                                                          start := 125510, 
                                                          stop := 125520 ), 
                                                      rec( 
                                                          content := " is pres\
ent, then this should\n    specify the category or representation the digraph \
being created will\n    belong to. For example, if ", count := [ 3, 5, 9, 6 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 125667, 
                                                          root := ~, 
                                                          start := 125656, 
                                                          stop := 125666 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 3, 5, 9, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 125701, 
                                                          root := ~, 
                                                          start := 125671, 
                                                          stop := 125700 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen the digraph being created will be mutable, if ", count := [ 3, 5, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 125769, 
                                                          root := ~, 
                                                          start := 125758, 
                                                          stop := 125768 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 3, 5, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 9, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 125809, 
                                                          root := ~, 
                                                          start := 125773, 
                                                          stop := 125808 ), 
                                                      rec( 
                                                          content := ", then t\
he digraph will be immutable. \n    If the optional first argument ", 
                                                          count := 
                                                            [ 3, 5, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 3, 5, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 125894, 
                                                          root := ~, 
                                                          start := 125883, 
                                                          stop := 125893 ), 
                                                      rec( 
                                                          content := " is not \
present, then ", count := [ 3, 5, 9, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 3, 5, 9, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 125954, 
                                                          root := ~, 
                                                          start := 125916, 
                                                          stop := 125953 ), 
                                                      rec( 
                                                          content := " is used\
 by default.", count := [ 3, 5, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 3, 5, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 125978, 
                                                          root := ~, 
                                                          start := 125974, 
                                                          stop := 125977 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 3, 5, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Peterse\
nGraph" ), content := 0, count := [ 3, 5, 9, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 126020, 
                                                          root := ~, 
                                                          start := 125993, 
                                                          stop := 126019 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 3, 5, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> GeneralisedPetersenGraph(7, 2);\n<immutable symmetric digraph with 14 ve\
rtices, 42 edges>\ngap> GeneralisedPetersenGraph(40, 1);\n<immutable symmetric\
 digraph with 80 vertices, 240 edges>\ngap> D := GeneralisedPetersenGraph(5, 2\
);\n<immutable symmetric digraph with 10 vertices, 30 edges>\ngap> IsIsomorphi\
cDigraph(D, PetersenGraph());\ntrue\ngap> GeneralisedPetersenGraph(IsMutableDi\
graph, 9, 4);\n<mutable digraph with 18 vertices, 54 edges>\n", count := 
                                                                    [ 3, 5, 
                                                                      9, 8 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 3, 5, 9, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 126495, 
                                                          root := ~, 
                                                          start := 126023, 
                                                          stop := 126494 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 3, 5, 9, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 3, 5, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 126512, root := ~, 
                                                  start := 124722, 
                                                  stop := 126511 ) ], 
                                          count := [ 3, 5, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 126526, root := ~, 
                                          start := 124614, stop := 126525 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 3, 5, 9, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 3, 5, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 126540, 
                                  root := ~, start := 114270, stop := 126539 )
                                , 
                              rec( content := "\n\n", count := [ 3, 5, 9, 9 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 3, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 126552, root := ~, start := 19173, 
                          stop := 126551 ), 
                      rec( content := "\n ", count := [ 3, 5, 9, 9 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " creating ", count := [ 3, 5, 9, 9 ], 
                          mathmode := "Text", name := "XMLCOMMENT", root := ~ 
                         ), 
                      rec( content := "\n  ", count := [ 3, 5, 9, 9 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Label := "Operators" ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Operators", 
                                          count := [ 4, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 4, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 126629, 
                                  root := ~, start := 126601, stop := 126628 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 4, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Operators for dig\
raphs", count := [ 4, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 4, 1, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 126683, 
                                          root := ~, start := 126642, 
                                          stop := 126682 ), 
                                      rec( content := "\n    ", 
                                          count := [ 4, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "digraph1", count := [ 4, 1, 0, 4 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 4 ], 
                                                                  mathmode := \
"Text", name := "A", next := 126724, root := ~, start := 126709, stop := 12672\
3 ), rec( content := " = ", count := [ 4, 1, 0, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "d\
igraph2", count := [ 4, 1, 0, 4 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 4, 1, 0, 4 ], mathmode := "Text", name := "A", 
                                                                  next := 1267\
42, root := ~, start := 126727, stop := 126741 ) ], count := [ 4, 1, 0, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 126746, 
                                                          root := ~, 
                                                          start := 126706, 
                                                          stop := 126745 ) ], 
                                                  count := [ 4, 1, 0, 4 ], 
                                                  name := "Mark", 
                                                  next := 126753, root := ~, 
                                                  start := 126700, 
                                                  stop := 126752 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec( Key := "=" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "=", count := [ 4, 1, 0, 5 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], 
                                                                  mathmode := \
"Text", name := "C", next := 126796, root := ~, start := 126788, stop := 12679\
5 ), rec( content := " (for digraphs)", count := [ 4, 1, 0, 5 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Index", 
                                                          next := 126819, 
                                                          root := ~, 
                                                          start := 126773, 
                                                          stop := 126818 ), 
                                                      rec( 
                                                          content := "\n      \
 returns ", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 126846, 
                                                          root := ~, 
                                                          start := 126835, 
                                                          stop := 126845 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 4, 1, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 126865, 
                                                          root := ~, 
                                                          start := 126850, 
                                                          stop := 126864 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 4, 1, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 126885, 
                                                          root := ~, 
                                                          start := 126870, 
                                                          stop := 126884 ), 
                                                      rec( 
                                                          content := " have th\
e same\n       vertices, and ", count := [ 4, 1, 0, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEdges(", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "digraph1", count := [ 4, 1, 0, 5 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 126952, root := ~, start := 126937, stop := 12695\
1 ), rec( content := ") =\n         DigraphEdges(", count := [ 4, 1, 0, 5 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph2", count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 4, 1, 0, 5 ], mathmode := "Text", name := "A", 
                                                                  next := 1269\
93, root := ~, start := 126978, stop := 126992 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 4, 1, 
                                                                      0, 5 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 126998, 
                                                          root := ~, 
                                                          start := 126921, 
                                                          stop := 126997 ), 
                                                      rec( 
                                                          content := ", up to \
some re-ordering of the edge\n       lists. ", count := [ 4, 1, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 4, 1, 0, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 127053, 
                                                          root := ~, 
                                                          start := 127049, 
                                                          stop := 127052 ), 
                                                      rec( 
                                                          content := "\n\n    \
   Note that this operator does not compare the vertex labels\n       of ", 
                                                          count := 
                                                            [ 4, 1, 0, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 0, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 127146, 
                                                          root := ~, 
                                                          start := 127131, 
                                                          stop := 127145 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 4, 1, 0, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 0, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 127166, 
                                                          root := ~, 
                                                          start := 127151, 
                                                          stop := 127165 ), 
                                                      rec( 
                                                          content := ".\n     \
", count := [ 4, 1, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 4, 1, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 127180, root := ~, 
                                                  start := 126759, 
                                                  stop := 127179 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "digraph1", count := [ 4, 1, 0, 7 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 7 ], 
                                                                  mathmode := \
"Text", name := "A", next := 127211, root := ~, start := 127196, stop := 12721\
0 ), rec( content := " < ", count := [ 4, 1, 0, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "d\
igraph2", count := [ 4, 1, 0, 7 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 4, 1, 0, 7 ], mathmode := "Text", name := "A", 
                                                                  next := 1272\
32, root := ~, start := 127217, stop := 127231 ) ], count := [ 4, 1, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 127236, 
                                                          root := ~, 
                                                          start := 127193, 
                                                          stop := 127235 ) ], 
                                                  count := [ 4, 1, 0, 7 ], 
                                                  name := "Mark", 
                                                  next := 127243, root := ~, 
                                                  start := 127187, 
                                                  stop := 127242 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
", count := [ 4, 1, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec( Key := "<" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "<", count := [ 4, 1, 0, 8 ], mathmode \
:= "Text", name := "PCDATA", next := 6, root := ~ ) ], count := [ 4, 1, 0, 8 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "C", next := 127292, root := ~, start := 127281, stop := 12729\
1 ), rec( content := " (for digraphs)", count := [ 4, 1, 0, 8 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Index", 
                                                          next := 127315, 
                                                          root := ~, 
                                                          start := 127263, 
                                                          stop := 127314 ), 
                                                      rec( 
                                                          content := "\n\n    \
   This operator returns ", count := [ 4, 1, 0, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 4, 1, 0, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 0, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 127357, 
                                                          root := ~, 
                                                          start := 127346, 
                                                          stop := 127356 ), 
                                                      rec( 
                                                          content := " if one \
of the following holds:\n\n       ", count := [ 4, 1, 0, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n           The number ", count := [ \
4, 1, 0, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "n_1", count := [ 4, 1, 0, 10 ], \
mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 10 ],
                                                                          math\
mode := "Text", name := "M", next := 127452, root := ~, start := 127442, stop \
:= 127451 ), rec( content := " of vertices in ", count := [ 4, 1, 0, 10 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "digraph1", count := [ 4, 1, 0, 10 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 10 ], mathmode := "T\
ext", name := "A", next := 127483, root := ~, start := 127468, stop := 127482 
                                                                         ), 
                                                                      rec( 
                                                                          cont\
ent := " is less than\n           the number ", count := [ 4, 1, 0, 10 ], math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "n_2", count := [ 4, 1, 0, 10 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 10 ], mathmode := "Text",
                                                                          name\
 := "M", next := 127529, root := ~, start := 127519, stop := 127528 ), 
                                                                      rec( 
                                                                          cont\
ent := " of vertices in ", count := [ 4, 1, 0, 10 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conten\
t := "digraph2", count := [ 4, 1, 0, 10 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 4, 1, 0, 10 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 127560, root := ~, start := 127545, stop := 127559 ), rec( content := ";\n\
         ", count := [ 4, 1, 0, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 4, 1, 0, 10 ], name := "Item", next := 127578, 
                                                                  root := ~, 
                                                                  start := 127\
413, stop := 127577 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n           ", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "n_\
1 = n_2", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "M", next := \
127622, root := ~, start := 127606, stop := 127621 ), rec( content := ", and t\
he number ", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "m_1", count\
 := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 4, 1, 0, 12 ], mathmode := "Text", name := "M", next := 127649, root :=\
 ~, start := 127639, stop := 127648 ), rec( content := " of edges in\n        \
   ", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := \
~ ), rec( attributes := rec(  ), content := [ rec( content := "digraph1", coun\
t := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 4, 1, 0, 12 ], mathmode := "Text", name := "A", next := 127688, root :=\
 ~, start := 127673, stop := 127687 ), rec( content := " is less than the numb\
er ", count := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := \
~ ), rec( attributes := rec(  ), content := [ rec( content := "m_2", count := \
[ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\
 [ 4, 1, 0, 12 ], mathmode := "Text", name := "M", next := 127723, root := ~, 
                                                                          star\
t := 127713, stop := 127722 ), rec( content := " of edges in\n           ", 
                                                                          coun\
t := [ 4, 1, 0, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "digraph2", count := [ 4, 1, 0\
, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, \
0, 12 ], mathmode := "Text", name := "A", next := 127762, root := ~, start := \
127747, stop := 127761 ), rec( content := ";\n         ", count := [ 4, 1, 0, \
12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 
                                                                      0, 12 ],
                                                                  name := "Ite\
m", next := 127780, root := ~, start := 127588, stop := 127779 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n           ", count := [ 4, 1, 0, 1\
4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\
(  ), content := [ rec( content := "n_1 = n_2", count := [ 4, 1, 0, 14 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 14 ], 
                                                                          math\
mode := "Text", name := "M", next := 127824, root := ~, start := 127808, stop \
:= 127823 ), rec( content := ", ", count := [ 4, 1, 0, 14 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec\
( content := "m_1 = m_2", count := [ 4, 1, 0, 14 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ 4, 1, 0, 14 ], mathmode := "Text", name \
:= "M", next := 127842, root := ~, start := 127826, stop := 127841 ), rec( 
                                                                          cont\
ent := ", and\n           ", count := [ 4, 1, 0, 14 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "DigraphEdges(", count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :=\
 "digraph1", count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "A", next \
:= 127890, root := ~, start := 127875, stop := 127889 ), rec( content := ")", \
count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ],
                                                                          coun\
t := [ 4, 1, 0, 14 ], mathmode := "Text", name := "C", next := 127895, root :=\
 ~, start := 127859, stop := 127894 ), rec( content := " is less than\n       \
    ", count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root :=\
 ~ ), rec( attributes := rec(  ), content := [ rec( content := "DigraphEdges("\
, count := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ),\
 rec( attributes := rec(  ), content := [ rec( content := "digraph2", count :=\
 [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\
= [ 4, 1, 0, 14 ], mathmode := "Text", name := "A", next := 127951, root := ~,\
 start := 127936, stop := 127950 ), rec( content := ")", count := [ 4, 1, 0, 1\
4 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 0, \
14 ], mathmode := "Text", name := "C", next := 127956, root := ~, start := 127\
920, stop := 127955 ), rec( content := " after having both of these sets\n    \
       have been sorted with respect to the lexicographical order.\n         "
                                                                            , 
                                                                          coun\
t := [ 4, 1, 0, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 4, 1, 
                                                                      0, 14 ],
                                                                  name := "Ite\
m", next := 128076, root := ~, start := 127790, stop := 128075 ) ], 
                                                          count := 
                                                            [ 4, 1, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 128091, 
                                                          root := ~, 
                                                          start := 127397, 
                                                          stop := 128090 ), 
                                                      rec( 
                                                          content := "\n     "
                                                            , 
                                                          count := 
                                                            [ 4, 1, 0, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 4, 1, 0, 8 ], 
                                                  name := "Item", 
                                                  next := 128104, root := ~, 
                                                  start := 127249, 
                                                  stop := 128103 ) ], 
                                          count := [ 4, 1, 0, 4 ], 
                                          mathmode := "Text", name := "List", 
                                          next := 128115, root := ~, 
                                          start := 126688, stop := 128114 ), 
                                      rec( content := "\n\n   ", 
                                          count := [ 4, 1, 0, 18 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "super, sub", 
                                                      Name := "IsSubdigraph" )
                                                    , content := 0, 
                                                  count := [ 4, 1, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 128179, root := ~, 
                                                  start := 128135, 
                                                  stop := 128178 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 128202, 
                                                          root := ~, 
                                                          start := 128191, 
                                                          stop := 128201 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 128218, 
                                                          root := ~, 
                                                          start := 128206, 
                                                          stop := 128217 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 4, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 128229, root := ~, 
                                                  start := 128182, 
                                                  stop := 128228 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128265, 
                                                          root := ~, 
                                                          start := 128253, 
                                                          stop := 128264 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ub", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128280, 
                                                          root := ~, 
                                                          start := 128270, 
                                                          stop := 128279 ), 
                                                      rec( 
                                                          content := " are dig\
raphs, then this operation returns\n    ", count := [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 128338, 
                                                          root := ~, 
                                                          start := 128327, 
                                                          stop := 128337 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ub", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128352, 
                                                          root := ~, 
                                                          start := 128342, 
                                                          stop := 128351 ), 
                                                      rec( 
                                                          content := " is a su\
bdigraph of ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128384, 
                                                          root := ~, 
                                                          start := 128372, 
                                                          stop := 128383 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 128402, 
                                                          root := ~, 
                                                          start := 128390, 
                                                          stop := 128401 ), 
                                                      rec( 
                                                          content := "\n    if\
 it is not. ", count := [ 4, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 128425, 
                                                          root := ~, 
                                                          start := 128421, 
                                                          stop := 128424 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ub", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128451, 
                                                          root := ~, 
                                                          start := 128441, 
                                                          stop := 128450 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ubdigraph", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 128474, 
                                                          root := ~, 
                                                          start := 128457, 
                                                          stop := 128473 ), 
                                                      rec( 
                                                          content := " of a di\
graph ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128500, 
                                                          root := ~, 
                                                          start := 128488, 
                                                          stop := 128499 ), 
                                                      rec( 
                                                          content := " if\n   \
 ", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ub", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128518, 
                                                          root := ~, 
                                                          start := 128508, 
                                                          stop := 128517 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128535, 
                                                          root := ~, 
                                                          start := 128523, 
                                                          stop := 128534 ), 
                                                      rec( 
                                                          content := " share t\
he same number of vertices, and the\n    collection of edges of ", 
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128618, 
                                                          root := ~, 
                                                          start := 128606, 
                                                          stop := 128617 ), 
                                                      rec( 
                                                          content := " (includ\
ing repeats) contains the\n    collection of edges of ", count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ub", count := [ 4, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128689, 
                                                          root := ~, 
                                                          start := 128679, 
                                                          stop := 128688 ), 
                                                      rec( 
                                                          content := " (includ\
ing repeats).  ", count := [ 4, 1, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 128716, 
                                                          root := ~, 
                                                          start := 128712, 
                                                          stop := 128715 ), 
                                                      rec( 
                                                          content := "\n\n    \
In other words, ", count := [ 4, 1, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ub", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128748, 
                                                          root := ~, 
                                                          start := 128738, 
                                                          stop := 128747 ), 
                                                      rec( 
                                                          content := " is a su\
bdigraph of ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 128780, 
                                                          root := ~, 
                                                          start := 128768, 
                                                          stop := 128779 ), 
                                                      rec( 
                                                          content := " if and \
only if\n    ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphNrVertices(", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "su\
b", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 4, 1, 
                                                                      1, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 128831, root := ~, start := 128821, stop := 12883\
0 ), rec( content := ") = DigraphNrVertices(", count := [ 4, 1, 1, 5 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "super", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ) ], count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "A", 
                                                                  next := 1288\
65, root := ~, start := 128853, stop := 128864 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 4, 1, 
                                                                      1, 5 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 128870, 
                                                          root := ~, 
                                                          start := 128800, 
                                                          stop := 128869 ), 
                                                      rec( 
                                                          content := ", and\n \
   for each pair of vertices ", count := [ 4, 1, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 128914, 
                                                          root := ~, 
                                                          start := 128906, 
                                                          stop := 128913 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 128927, 
                                                          root := ~, 
                                                          start := 128919, 
                                                          stop := 128926 ), 
                                                      rec( 
                                                          content := ", there \
are at least as many\n    edges of the form ", count := [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i, j]", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 128991, 
                                                          root := ~, 
                                                          start := 128978, 
                                                          stop := 128990 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 129007, 
                                                          root := ~, 
                                                          start := 128995, 
                                                          stop := 129006 ), 
                                                      rec( 
                                                          content := " as ther\
e are in ", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ub", count := [ 4, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 129034, 
                                                          root := ~, 
                                                          start := 129024, 
                                                          stop := 129033 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 4, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 4, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 129044, 
                                                          root := ~, 
                                                          start := 129040, 
                                                          stop := 129043 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 4, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> g := Digraph([[2, 3], [1], [2, 3]]);\n<immutable digraph with 3 vertices\
, 5 edges>\ngap> h := Digraph([[2, 3], [], [2]]);\n<immutable digraph with 3 v\
ertices, 3 edges>\ngap> IsSubdigraph(g, h);\ntrue\ngap> IsSubdigraph(h, g);\nf\
alse\ngap> IsSubdigraph(CompleteDigraph(4), CycleDigraph(4));\ntrue\ngap> IsSu\
bdigraph(CycleDigraph(4), ChainDigraph(4));\ntrue\ngap> g := Digraph([[2, 2], \
[1]]);\n<immutable multidigraph with 2 vertices, 3 edges>\ngap> h := Digraph([\
[2], [1]]);\n<immutable digraph with 2 vertices, 2 edges>\ngap> IsSubdigraph(g\
, h);\ntrue\ngap> IsSubdigraph(h, g);\nfalse", count := [ 4, 1, 1, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 1, 1, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 129652, 
                                                          root := ~, 
                                                          start := 129050, 
                                                          stop := 129651 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 4, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 4, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 129669, root := ~, 
                                                  start := 128232, 
                                                  stop := 129668 ) ], 
                                          count := [ 4, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 129683, root := ~, 
                                          start := 128120, stop := 129682 ), 
                                      rec( content := "\n\n   ", 
                                          count := [ 4, 1, 1, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "super, sub", 
                                                      Name := "IsUndirectedSpa\
nningTree" ), content := 0, count := [ 4, 1, 2, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 129759, root := ~, 
                                                  start := 129703, 
                                                  stop := 129758 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "super, sub", 
                                                      Name := "IsUndirectedSpa\
nningForest" ), content := 0, count := [ 4, 1, 2, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 129820, root := ~, 
                                                  start := 129762, 
                                                  stop := 129819 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 129843, 
                                                          root := ~, 
                                                          start := 129832, 
                                                          stop := 129842 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 129859, 
                                                          root := ~, 
                                                          start := 129847, 
                                                          stop := 129858 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 4, 1, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 129870, root := ~, 
                                                  start := 129823, 
                                                  stop := 129869 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
 operation ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sUndirectedSpanningTree", count := [ 4, 1, 2, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 129936, 
                                                          root := ~, 
                                                          start := 129905, 
                                                          stop := 129935 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 129956, 
                                                          root := ~, 
                                                          start := 129945, 
                                                          stop := 129955 ), 
                                                      rec( 
                                                          content := " if the\\
n    digraph ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ub", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 129986, 
                                                          root := ~, 
                                                          start := 129976, 
                                                          stop := 129985 ), 
                                                      rec( 
                                                          content := " is an u\
ndirected spanning tree of the digraph\n    ", count := [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 130049, 
                                                          root := ~, 
                                                          start := 130037, 
                                                          stop := 130048 ), 
                                                      rec( 
                                                          content := ", and th\
e operation ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sUndirectedSpanningForest", count := [ 4, 1, 2, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 1, 2, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 130102, 
                                                          root := ~, 
                                                          start := 130069, 
                                                          stop := 130101 ), 
                                                      rec( 
                                                          content := " returns\
\n    ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 130126, 
                                                          root := ~, 
                                                          start := 130115, 
                                                          stop := 130125 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ub", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 130152, 
                                                          root := ~, 
                                                          start := 130142, 
                                                          stop := 130151 ), 
                                                      rec( 
                                                          content := " is an u\
ndirected spanning forest of\n    the digraph ", count := [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 130217, 
                                                          root := ~, 
                                                          start := 130205, 
                                                          stop := 130216 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 4, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 4, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 130223, 
                                                          root := ~, 
                                                          start := 130219, 
                                                          stop := 130222 ), 
                                                      rec( 
                                                          content := "\n\n    \
An ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
ndirected spanning tree", count := [ 4, 1, 2, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 1, 2, 6 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 130263, 
                                                          root := ~, 
                                                          start := 130232, 
                                                          stop := 130262 ), 
                                                      rec( 
                                                          content := " of a di\
graph ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 130289, 
                                                          root := ~, 
                                                          start := 130277, 
                                                          stop := 130288 ), 
                                                      rec( 
                                                          content := " is a su\
bdigraph\n    of ", count := [ 4, 1, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 130325, 
                                                          root := ~, 
                                                          start := 130313, 
                                                          stop := 130324 ), 
                                                      rec( 
                                                          content := " that is\
 an undirected tree (see ", count := [ 4, 1, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsSubdi\
graph" ), content := 0, count := [ 4, 1, 2, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 130385, 
                                                          root := ~, 
                                                          start := 130358, 
                                                          stop := 130384 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 4, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsUndir\
ectedTree" ), content := 0, count := [ 4, 1, 2, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 130425, 
                                                          root := ~, 
                                                          start := 130394, 
                                                          stop := 130424 ), 
                                                      rec( 
                                                          content := "). Note \
that a digraph whose ", count := [ 4, 1, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Maximal\
SymmetricSubdigraph" ), content := 0, count := [ 4, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 130500, 
                                                          root := ~, 
                                                          start := 130454, 
                                                          stop := 130499 ), 
                                                      rec( 
                                                          content := " is not \
connected has no undirected\n    spanning trees (see ", count := 
                                                            [ 4, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsConne\
ctedDigraph" ), content := 0, count := [ 4, 1, 2, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 130592, 
                                                          root := ~, 
                                                          start := 130560, 
                                                          stop := 130591 ), 
                                                      rec( content := "). ", 
                                                          count := 
                                                            [ 4, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 130599, 
                                                          root := ~, 
                                                          start := 130595, 
                                                          stop := 130598 ), 
                                                      rec( 
                                                          content := "\n\n    \
An ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
ndirected spanning forest", count := [ 4, 1, 2, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 4, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 130641, 
                                                          root := ~, 
                                                          start := 130608, 
                                                          stop := 130640 ), 
                                                      rec( 
                                                          content := " of a di\
graph ", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 130667, 
                                                          root := ~, 
                                                          start := 130655, 
                                                          stop := 130666 ), 
                                                      rec( 
                                                          content := " is a\n \
   subdigraph of ", count := [ 4, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 130703, 
                                                          root := ~, 
                                                          start := 130691, 
                                                          stop := 130702 ), 
                                                      rec( 
                                                          content := " that is\
 an undirected forest (see ", count := [ 4, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsSubdi\
graph" ), content := 0, count := [ 4, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 130770, 
                                                          root := ~, 
                                                          start := 130738, 
                                                          stop := 130769 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsUndir\
ectedForest" ), content := 0, count := [ 4, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 130807, 
                                                          root := ~, 
                                                          start := 130775, 
                                                          stop := 130806 ), 
                                                      rec( 
                                                          content := "), and i\
s not\n    contained in any larger such subdigraph of ", count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 130880, 
                                                          root := ~, 
                                                          start := 130868, 
                                                          stop := 130879 ), 
                                                      rec( 
                                                          content := ".  Equiv\
alently, an\n    undirected spanning forest is a subdigraph of ", 
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 130962, 
                                                          root := ~, 
                                                          start := 130950, 
                                                          stop := 130961 ), 
                                                      rec( 
                                                          content := " whose c\
onnected\n    components coincide with those of the ", count := [ 4, 1, 2, 7 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Maximal\
SymmetricSubdigraph" ), content := 0, count := [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 131067, 
                                                          root := ~, 
                                                          start := 131021, 
                                                          stop := 131066 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
uper", count := [ 4, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 131083, 
                                                          root := ~, 
                                                          start := 131071, 
                                                          stop := 131082 ), 
                                                      rec( 
                                                          content := " (see ",
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
ConnectedComponents" ), content := 0, count := [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 131135, 
                                                          root := ~, 
                                                          start := 131089, 
                                                          stop := 131134 ), 
                                                      rec( content := "). ", 
                                                          count := 
                                                            [ 4, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 4, 1, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 131142, 
                                                          root := ~, 
                                                          start := 131138, 
                                                          stop := 131141 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that an undirected spanning tree is an undirected spanning forest that\n \
   is connected.\n\n    ", count := [ 4, 1, 2, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(4);\n<immutable complete digraph with 4 vertices>\n\
gap> tree := Digraph([[3], [4], [1, 4], [2, 3]]);\n<immutable digraph with 4 v\
ertices, 6 edges>\ngap> IsSubdigraph(D, tree) and IsUndirectedTree(tree);\ntru\
e\ngap> IsUndirectedSpanningTree(D, tree);\ntrue\ngap> forest := EmptyDigraph(\
4);\n<immutable empty digraph with 4 vertices>\ngap> IsSubdigraph(D, forest) a\
nd IsUndirectedForest(forest);\ntrue\ngap> IsUndirectedSpanningForest(D, fores\
t);\nfalse\ngap> IsSubdigraph(tree, forest);\ntrue\ngap> D := DigraphDisjointU\
nion(CycleDigraph(2), CycleDigraph(2));\n<immutable digraph with 4 vertices, 4\
 edges>\ngap> IsUndirectedTree(D);\nfalse\ngap> IsUndirectedForest(D) and IsUn\
directedSpanningForest(D, D);\ntrue", count := [ 4, 1, 2, 9 ], name := "PCDATA\
", root := ~ ) ], count := [ 4, 1, 2, 9 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 131994, 
                                                          root := ~, 
                                                          start := 131247, 
                                                          stop := 131993 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 4, 1, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 4, 1, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 132011, root := ~, 
                                                  start := 129873, 
                                                  stop := 132010 ) ], 
                                          count := [ 4, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 132025, root := ~, 
                                          start := 129688, stop := 132024 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 4, 1, 2, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 4, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 132039, 
                                  root := ~, start := 126633, stop := 132038 )
                                , 
                              rec( content := "\n", count := [ 4, 1, 2, 10 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 4, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 132050, root := ~, start := 126574, 
                          stop := 132049 ), 
                      rec( content := "\n ", count := [ 4, 1, 2, 10 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " operators/hashs ", 
                          count := [ 4, 1, 2, 10 ], mathmode := "Text", 
                          name := "XMLCOMMENT", root := ~ ), 
                      rec( content := "\n  ", count := [ 4, 1, 2, 10 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( 
                          attributes := 
                            rec( Label := "Attributes and operations" ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "Attributes and operations\
", count := [ 5, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                     ], count := [ 5, 0, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 132166, root := ~, start := 132122, 
                                  stop := 132165 ), 
                              rec( content := "\n  ", count := [ 5, 0, 0, 3 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Vertices and edge\
s", count := [ 5, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                 ) ], count := [ 5, 1, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 132215, 
                                          root := ~, start := 132178, 
                                          stop := 132214 ), 
                                      rec( content := "\n    ", 
                                          count := [ 5, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphVertices\
" ), content := 0, count := [ 5, 1, 1, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 132279, root := ~, 
                                                  start := 132235, 
                                                  stop := 132278 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 integers.", count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 132320, root := ~, 
                                                  start := 132282, 
                                                  stop := 132319 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns the vertices of the digraph ", count := [ 5, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 132391, 
                                                          root := ~, 
                                                          start := 132377, 
                                                          stop := 132390 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 132397, 
                                                          root := ~, 
                                                          start := 132393, 
                                                          stop := 132396 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that the vertices of a digraph are always a range of\n    positive intege\
rs from ", count := [ 5, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 5, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 132496, 
                                                          root := ~, 
                                                          start := 132488, 
                                                          stop := 132495 ), 
                                                      rec( 
                                                          content := " to the \
number of vertices of the graph.\n    ", count := [ 5, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n>                  [\"a\", \"b\", \
\"b\"],\n>                  [\"b\", \"c\", \"a\"]);\n<immutable digraph with 3\
 vertices, 3 edges>\ngap> DigraphVertices(gr);\n[ 1 .. 3 ]\ngap> gr := Digraph\
([1, 2, 3, 4, 5, 7],\n>                  [1, 2, 2, 4, 4],\n>                  \
[2, 7, 5, 3, 7]);\n<immutable digraph with 6 vertices, 5 edges>\ngap> DigraphV\
ertices(gr);\n[ 1 .. 6 ]\ngap> DigraphVertices(RandomDigraph(100));\n[ 1 .. 10\
0 ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 ver\
tices, 3 edges>\ngap> DigraphVertices(D);\n[ 1 .. 3 ]\n", count := [ 5, 1, 1, 
                                                                      5 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 1, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 133137, 
                                                          root := ~, 
                                                          start := 132541, 
                                                          stop := 133136 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 133154, root := ~, 
                                                  start := 132323, 
                                                  stop := 133153 ) ], 
                                          count := [ 5, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 133168, root := ~, 
                                          start := 132220, stop := 133167 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 1, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphNrVertic\
es" ), content := 0, count := [ 5, 1, 2, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 133235, root := ~, 
                                                  start := 133189, 
                                                  stop := 133234 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r.", count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 5, 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 133268, root := ~, 
                                                  start := 133238, 
                                                  stop := 133267 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns the number of vertices of the digraph ", count := [ 5, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 133349, 
                                                          root := ~, 
                                                          start := 133335, 
                                                          stop := 133348 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 133355, 
                                                          root := ~, 
                                                          start := 133351, 
                                                          stop := 133354 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n>                  [\"a\", \"b\", \
\"b\"],\n>                  [\"b\", \"c\", \"a\"]);\n<immutable digraph with 3\
 vertices, 3 edges>\ngap> DigraphNrVertices(gr);\n3\ngap> gr := Digraph([1, 2,\
 3, 4, 5, 7],\n>                  [1, 2, 2, 4, 4],\n>                  [2, 7, \
5, 3, 7]);\n<immutable digraph with 6 vertices, 5 edges>\ngap> DigraphNrVertic\
es(gr);\n6\ngap> DigraphNrVertices(RandomDigraph(100));\n100\ngap> D := CycleD\
igraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap>\
 DigraphNrVertices(D);\n3\n", count := [ 5, 1, 2, 5 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 133929, 
                                                          root := ~, 
                                                          start := 133361, 
                                                          stop := 133928 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 133946, root := ~, 
                                                  start := 133271, 
                                                  stop := 133945 ) ], 
                                          count := [ 5, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 133960, root := ~, 
                                          start := 133174, stop := 133959 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 2, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphEdges" )
                                                    , content := 0, 
                                                  count := [ 5, 1, 3, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 134022, root := ~, 
                                                  start := 133981, 
                                                  stop := 134021 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 lists.", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 134060, root := ~, 
                                                  start := 134025, 
                                                  stop := 134059 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEdges", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 134100, 
                                                          root := ~, 
                                                          start := 134081, 
                                                          stop := 134099 ), 
                                                      rec( 
                                                          content := " returns\
 a list of edges of the digraph ", count := [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 134154, 
                                                          root := ~, 
                                                          start := 134140, 
                                                          stop := 134153 ), 
                                                      rec( 
                                                          content := ",\n    w\
here each edge is a pair of elements of ", count := [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Vertices" ), content := 0, count := [ 5, 1, 3, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 134230, 
                                                          root := ~, 
                                                          start := 134201, 
                                                          stop := 134229 ), 
                                                      rec( 
                                                          content := " of\n   \
 the form ", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
source,range]", count := [ 5, 1, 3, 3 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 134268, 
                                                          root := ~, 
                                                          start := 134247, 
                                                          stop := 134267 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 134278, 
                                                          root := ~, 
                                                          start := 134274, 
                                                          stop := 134277 ), 
                                                      rec( 
                                                          content := "\n\n    \
The entries of ", count := [ 5, 1, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEdges(", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 134319, 
                                                          root := ~, 
                                                          start := 134299, 
                                                          stop := 134318 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 134333, 
                                                          root := ~, 
                                                          start := 134319, 
                                                          stop := 134332 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 134341, 
                                                          root := ~, 
                                                          start := 134333, 
                                                          stop := 134340 ), 
                                                      rec( 
                                                          content := " are in \
one-to-one\n    corresponence with the edges of ", count := [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 134410, 
                                                          root := ~, 
                                                          start := 134396, 
                                                          stop := 134409 ), 
                                                      rec( 
                                                          content := ".  Hence\
\n    ", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEdges(", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 134443, 
                                                          root := ~, 
                                                          start := 134423, 
                                                          stop := 134442 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 134457, 
                                                          root := ~, 
                                                          start := 134443, 
                                                          stop := 134456 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 134465, 
                                                          root := ~, 
                                                          start := 134457, 
                                                          stop := 134464 ), 
                                                      rec( 
                                                          content := " is dupl\
icate-free if and only if\n    ", count := [ 5, 1, 3, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 134517, 
                                                          root := ~, 
                                                          start := 134503, 
                                                          stop := 134516 ), 
                                                      rec( 
                                                          content := " contain\
s no multiple edges. ", count := [ 5, 1, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 134550, 
                                                          root := ~, 
                                                          start := 134546, 
                                                          stop := 134549 ), 
                                                      rec( 
                                                          content := "\n\n    \
The entries of ", count := [ 5, 1, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEdges", count := [ 5, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 134590, 
                                                          root := ~, 
                                                          start := 134571, 
                                                          stop := 134589 ), 
                                                      rec( 
                                                          content := " are gua\
ranteed to be sorted by their\n    first component (i.e. by the source of each\
 edge), but they are not\n    necessarily then sorted by the second component.\
\n    ", count := [ 5, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := DigraphFromDiSparse6String(\".DaXbOe?EAM@G~\");\n<immutable multid\
igraph with 5 vertices, 16 edges>\ngap> edges := ShallowCopy(DigraphEdges(gr))\
;; Sort(edges);\ngap> edges;\n[ [ 1, 1 ], [ 1, 3 ], [ 1, 3 ], [ 1, 4 ], [ 1, 5\
 ], [ 2, 1 ], \n  [ 2, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], \
\n  [ 4, 2 ], [ 4, 4 ], [ 4, 5 ], [ 5, 1 ] ]\ngap> D := CycleDigraph(IsMutable\
Digraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> DigraphEdges(D)\
;\n[ [ 1, 2 ], [ 2, 3 ], [ 3, 1 ] ]\n", count := [ 5, 1, 3, 6 ], name := "PCDA\
TA", root := ~ ) ], count := [ 5, 1, 3, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 135280, 
                                                          root := ~, 
                                                          start := 134757, 
                                                          stop := 135279 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 135297, root := ~, 
                                                  start := 134063, 
                                                  stop := 135296 ) ], 
                                          count := [ 5, 1, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 135311, root := ~, 
                                          start := 133966, stop := 135310 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 3, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphNrEdges"\
 ), content := 0, count := [ 5, 1, 4, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 135375, root := ~, 
                                                  start := 135332, 
                                                  stop := 135374 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r.", count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 5, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 135408, root := ~, 
                                                  start := 135378, 
                                                  stop := 135407 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the number of edges of the digraph ", count := 
                                                            [ 5, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 135500, 
                                                          root := ~, 
                                                          start := 135486, 
                                                          stop := 135499 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([\n> [1, 3, 4, 5], [1, 2, 3, 5], [2, 4, 5], [2, 4, 5], [1]\
]);;\ngap> DigraphNrEdges(gr);\n15\ngap> gr := Digraph([\"a\", \"b\", \"c\"],\
\n>                  [\"a\", \"b\", \"b\"],\n>                  [\"b\", \"a\",\
 \"a\"]);\n<immutable multidigraph with 3 vertices, 3 edges>\ngap> DigraphNrEd\
ges(gr);\n3\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph wi\
th 3 vertices, 3 edges>\ngap> DigraphNrEdges(D);\n3\n", count := [ 5, 1, 4, 4 
                                                                     ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 4, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 135947, 
                                                          root := ~, 
                                                          start := 135506, 
                                                          stop := 135946 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 135964, root := ~, 
                                                  start := 135411, 
                                                  stop := 135963 ) ], 
                                          count := [ 5, 1, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 135978, root := ~, 
                                          start := 135317, stop := 135977 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphNrLoops"\
 ), content := 0, count := [ 5, 1, 5, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 136042, root := ~, 
                                                  start := 135999, 
                                                  stop := 136041 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r.", count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 5, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 136075, root := ~, 
                                                  start := 136045, 
                                                  stop := 136074 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the number of loops of the digraph ", count := 
                                                            [ 5, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 136167, 
                                                          root := ~, 
                                                          start := 136153, 
                                                          stop := 136166 ), 
                                                      rec( 
                                                          content := ". See ",
                                                          count := 
                                                            [ 5, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ 5, 1, 5, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 136202, 
                                                          root := ~, 
                                                          start := 136173, 
                                                          stop := 136201 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 136208, 
                                                          root := ~, 
                                                          start := 136204, 
                                                          stop := 136207 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 3], [1, 4], [3, 3, 5], [], [2, 5]]);\n<immutable multi\
digraph with 5 vertices, 9 edges>\ngap> DigraphNrLoops(D);\n3\ngap> D := Empty\
Digraph(5);\n<immutable empty digraph with 5 vertices>\ngap> DigraphNrLoops(D)\
;\n0\ngap> D := CompleteDigraph(5);\n<immutable complete digraph with 5 vertic\
es>\ngap> DigraphNrLoops(D);\n0\n", count := [ 5, 1, 5, 5 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 136577, 
                                                          root := ~, 
                                                          start := 136213, 
                                                          stop := 136576 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 136594, root := ~, 
                                                  start := 136078, 
                                                  stop := 136593 ) ], 
                                          count := [ 5, 1, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 136608, root := ~, 
                                          start := 135984, stop := 136607 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 5, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphSinks" )
                                                    , content := 0, 
                                                  count := [ 5, 1, 6, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 136670, root := ~, 
                                                  start := 136629, 
                                                  stop := 136669 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 vertices.", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 136711, root := ~, 
                                                  start := 136673, 
                                                  stop := 136710 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns a list of the sinks of the digraph\n    ", 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 136807, 
                                                          root := ~, 
                                                          start := 136793, 
                                                          stop := 136806 ), 
                                                      rec( 
                                                          content := ".\n    A\
 sink of a digraph is a vertex with out-degree zero.\n    See ", 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "OutDegr\
eeOfVertex" ), content := 0, count := [ 5, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 136906, 
                                                          root := ~, 
                                                          start := 136875, 
                                                          stop := 136905 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[3, 5, 2, 2], [3], [], [5, 2, 5, 3], []]);\n<immutable mu\
ltidigraph with 5 vertices, 9 edges>\ngap> DigraphSinks(gr);\n[ 3, 5 ]\ngap> D\
 := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 ed\
ges>\ngap> DigraphSinks(D);\n[  ]\n", count := [ 5, 1, 6, 4 ], name := "PCDATA\
", root := ~ ) ], count := [ 5, 1, 6, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 137204, 
                                                          root := ~, 
                                                          start := 136912, 
                                                          stop := 137203 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 137221, root := ~, 
                                                  start := 136714, 
                                                  stop := 137220 ) ], 
                                          count := [ 5, 1, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 137235, root := ~, 
                                          start := 136614, stop := 137234 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 6, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphSources"\
 ), content := 0, count := [ 5, 1, 7, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 137299, root := ~, 
                                                  start := 137256, 
                                                  stop := 137298 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 vertices.", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 137340, root := ~, 
                                                  start := 137302, 
                                                  stop := 137339 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns an immutable list of the sources of the digraph\n    ", 
                                                          count := 
                                                            [ 5, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 137449, 
                                                          root := ~, 
                                                          start := 137435, 
                                                          stop := 137448 ), 
                                                      rec( 
                                                          content := ".\n    A\
 source of a digraph is a vertex with in-degree zero.\n    See ", 
                                                          count := 
                                                            [ 5, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "InDegre\
eOfVertex" ), content := 0, count := [ 5, 1, 7, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 137548, 
                                                          root := ~, 
                                                          start := 137518, 
                                                          stop := 137547 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[3, 5, 2, 2], [3], [], [5, 2, 5, 3], []]);\n<immutable mu\
ltidigraph with 5 vertices, 9 edges>\ngap> DigraphSources(gr);\n[ 1, 4 ]\ngap>\
 D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 \
edges>\ngap> DigraphSources(D);\n[  ]\n", count := [ 5, 1, 7, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 7, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 137850, 
                                                          root := ~, 
                                                          start := 137554, 
                                                          stop := 137849 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 137867, root := ~, 
                                                  start := 137343, 
                                                  stop := 137866 ) ], 
                                          count := [ 5, 1, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 137881, root := ~, 
                                          start := 137241, stop := 137880 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 7, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphTopologi\
calSort" ), content := 0, count := [ 5, 1, 8, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 137953, root := ~, 
                                                  start := 137902, 
                                                  stop := 137952 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 positive integers, or ", count := [ 5, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 138008, 
                                                          root := ~, 
                                                          start := 137997, 
                                                          stop := 138007 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 138019, root := ~, 
                                                  start := 137956, 
                                                  stop := 138018 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 138057, 
                                                          root := ~, 
                                                          start := 138043, 
                                                          stop := 138056 ), 
                                                      rec( 
                                                          content := " is a di\
graph whose only directed cycles are loops, then\n    ", count := 
                                                            [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphTopologicalSort", count := [ 5, 1, 8, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 138147, 
                                                          root := ~, 
                                                          start := 138118, 
                                                          stop := 138146 ), 
                                                      rec( 
                                                          content := " returns\
 the vertices of ", count := [ 5, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 138186, 
                                                          root := ~, 
                                                          start := 138172, 
                                                          stop := 138185 ), 
                                                      rec( 
                                                          content := " ordered\
\n    so that every edge's source appears no earlier in the list than its rang\
e.\n    If the digraph ", count := [ 5, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 138307, 
                                                          root := ~, 
                                                          start := 138293, 
                                                          stop := 138306 ), 
                                                      rec( 
                                                          content := " contain\
s directed cycles of length greater\n    than ", count := [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 5, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 138368, 
                                                          root := ~, 
                                                          start := 138360, 
                                                          stop := 138367 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns ", count := [ 5, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 138409, 
                                                          root := ~, 
                                                          start := 138398, 
                                                          stop := 138408 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 138419, 
                                                          root := ~, 
                                                          start := 138415, 
                                                          stop := 138418 ), 
                                                      rec( 
                                                          content := "\n\n    \
See Section ", count := [ 5, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 138481, 
                                                          root := ~, 
                                                          start := 138437, 
                                                          stop := 138480 ), 
                                                      rec( 
                                                          content := " for the\
 definition\n    of a directed cycle, and the definition of a loop.\n\n    ", 
                                                          count := 
                                                            [ 5, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 138565, 
                                                          root := ~, 
                                                          start := 138561, 
                                                          stop := 138564 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used for this attribute has complexity ", count := [ 5, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 138634, 
                                                          root := ~, 
                                                          start := 138621, 
                                                          stop := 138633 ), 
                                                      rec( 
                                                          content := " where\n\
    ", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 138653, 
                                                          root := ~, 
                                                          start := 138645, 
                                                          stop := 138652 ), 
                                                      rec( 
                                                          content := " is the \
number of edges (counting multiple edges as one) and\n    ", 
                                                          count := 
                                                            [ 5, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 1, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 138726, 
                                                          root := ~, 
                                                          start := 138718, 
                                                          stop := 138725 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in the digraph. ", count := [ 5, 1, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 138773, 
                                                          root := ~, 
                                                          start := 138769, 
                                                          stop := 138772 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 1, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\n> [2, 3], [], [4, 6], [5], [], [7, 8, 9], [], [], []]);\
\n<immutable digraph with 9 vertices, 8 edges>\ngap> DigraphTopologicalSort(D)\
;\n[ 2, 5, 4, 7, 8, 9, 6, 3, 1 ]\ngap> D := Digraph(IsMutableDigraph, [[2, 3],\
 [3], [4], []]);\n<mutable digraph with 4 vertices, 4 edges>\ngap> DigraphTopo\
logicalSort(D);\n[ 4, 3, 2, 1 ]\n", count := [ 5, 1, 8, 7 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 139144, 
                                                          root := ~, 
                                                          start := 138778, 
                                                          stop := 139143 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 139161, root := ~, 
                                                  start := 138022, 
                                                  stop := 139160 ) ], 
                                          count := [ 5, 1, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 139175, root := ~, 
                                          start := 137887, stop := 139174 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 8, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, i", 
                                                      Name := "DigraphVertexLa\
bel" ), content := 0, count := [ 5, 1, 9, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 139248, root := ~, 
                                                  start := 139196, 
                                                  stop := 139247 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, i, obj"
                                                        , 
                                                      Name := "SetDigraphVerte\
xLabel" ), content := 0, count := [ 5, 1, 9, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 139310, root := ~, 
                                                  start := 139251, 
                                                  stop := 139309 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 139348, 
                                                          root := ~, 
                                                          start := 139334, 
                                                          stop := 139347 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then the first operation returns the label\n    of the vertex ", 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 139432, 
                                                          root := ~, 
                                                          start := 139424, 
                                                          stop := 139431 ), 
                                                      rec( 
                                                          content := ". The se\
cond operation can be used to set the label\n    of the vertex ", 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 139510, 
                                                          root := ~, 
                                                          start := 139502, 
                                                          stop := 139509 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 139528, 
                                                          root := ~, 
                                                          start := 139514, 
                                                          stop := 139527 ), 
                                                      rec( 
                                                          content := " to the \
arbitrary ", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " object\\
n    ", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
bj", count := [ 5, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 139573, 
                                                          root := ~, 
                                                          start := 139563, 
                                                          stop := 139572 ), 
                                                      rec( content := ".  ", 
                                                          count := 
                                                            [ 5, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 139580, 
                                                          root := ~, 
                                                          start := 139576, 
                                                          stop := 139579 ), 
                                                      rec( 
                                                          content := "\n\n    \
The label of a vertex can be changed an arbitrary number of times. If no\n    \
label has been set for the vertex ", count := [ 5, 1, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 139705, 
                                                          root := ~, 
                                                          start := 139697, 
                                                          stop := 139704 ), 
                                                      rec( 
                                                          content := ", then t\
he default value is\n    ", count := [ 5, 1, 9, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 139745, 
                                                          root := ~, 
                                                          start := 139737, 
                                                          stop := 139744 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 139751, 
                                                          root := ~, 
                                                          start := 139747, 
                                                          stop := 139750 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 139774, 
                                                          root := ~, 
                                                          start := 139760, 
                                                          stop := 139773 ), 
                                                      rec( 
                                                          content := " is a di\
graph created from a record with a component\n    ", count := [ 5, 1, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertices", count := [ 5, 1, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 139846, 
                                                          root := ~, 
                                                          start := 139831, 
                                                          stop := 139845 ), 
                                                      rec( 
                                                          content := ", then t\
he labels of the vertices are set to the value of\n    this component.", 
                                                          count := 
                                                            [ 5, 1, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 139927, 
                                                          root := ~, 
                                                          start := 139923, 
                                                          stop := 139926 ), 
                                                      rec( 
                                                          content := "\n\n    \
Induced subdigraphs, and some other operations which create new digraphs from\
\n    old ones, inherit their labels from their parents.\n\n    ", 
                                                          count := 
                                                            [ 5, 1, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDigraph6String(\"&DHUEe_\");\n<immutable digraph with 5 \
vertices, 11 edges>\ngap> DigraphVertexLabel(D, 3);\n3\ngap> D := Digraph([\"a\
\", \"b\", \"c\"], [], []);\n<immutable empty digraph with 3 vertices>\ngap> D\
igraphVertexLabel(D, 2);\n\"b\"\ngap> SetDigraphVertexLabel(D, 2, \"d\");\ngap\
> DigraphVertexLabel(D, 2);\n\"d\"\ngap> D := InducedSubdigraph(D, [1, 2]);\n<\
immutable empty digraph with 2 vertices>\ngap> DigraphVertexLabel(D, 2);\n\"d\
\"\ngap> D := Digraph(IsMutableDigraph, [\"e\", \"f\", \"g\"], [], []);\n<muta\
ble empty digraph with 3 vertices>\ngap> DigraphVertexLabel(D, 1);\n\"e\"\ngap\
> SetDigraphVertexLabel(D, 1, \"h\");\ngap> DigraphVertexLabel(D, 1);\n\"h\"\n\
gap> InducedSubdigraph(D, [1, 2]);\n<mutable empty digraph with 2 vertices>\ng\
ap> DigraphVertexLabel(D, 1);\n\"h\"\n", count := [ 5, 1, 9, 9 ], name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 9, 9 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 140863, 
                                                          root := ~, 
                                                          start := 140071, 
                                                          stop := 140862 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 9, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 140880, root := ~, 
                                                  start := 139313, 
                                                  stop := 140879 ) ], 
                                          count := [ 5, 1, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 140894, root := ~, 
                                          start := 139181, stop := 140893 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 9, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphVertexLa\
bels" ), content := 0, count := [ 5, 1, 10, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 140963, root := ~, 
                                                  start := 140915, 
                                                  stop := 140962 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list", 
                                                      Name := "SetDigraphVerte\
xLabels" ), content := 0, count := [ 5, 1, 10, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 141023, root := ~, 
                                                  start := 140966, 
                                                  stop := 141022 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 141061, 
                                                          root := ~, 
                                                          start := 141047, 
                                                          stop := 141060 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphVertexLabels", count := [ 5, 1, 10, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 141107, 
                                                          root := ~, 
                                                          start := 141081, 
                                                          stop := 141106 ), 
                                                      rec( 
                                                          content := " returns\
 a\n    copy of the labels of the vertices in ", count := [ 5, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 141174, 
                                                          root := ~, 
                                                          start := 141160, 
                                                          stop := 141173 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
etDigraphVertexLabels", count := [ 5, 1, 10, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 10, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 141209, 
                                                          root := ~, 
                                                          start := 141180, 
                                                          stop := 141208 ), 
                                                      rec( 
                                                          content := " can be \
used to set the labels of the vertices\n    in ", count := [ 5, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 141277, 
                                                          root := ~, 
                                                          start := 141263, 
                                                          stop := 141276 ), 
                                                      rec( 
                                                          content := " to the \
list of\n    arbitrary ", count := [ 5, 1, 10, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " objects\
 ", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 141332, 
                                                          root := ~, 
                                                          start := 141321, 
                                                          stop := 141331 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 141338, 
                                                          root := ~, 
                                                          start := 141334, 
                                                          stop := 141337 ), 
                                                      rec( 
                                                          content := "\n\n    \
The label of a vertex can be changed an arbitrary number of times. If no\n    \
label has been set for the vertex ", count := [ 5, 1, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 141463, 
                                                          root := ~, 
                                                          start := 141455, 
                                                          stop := 141462 ), 
                                                      rec( 
                                                          content := ", then t\
he default value is\n    ", count := [ 5, 1, 10, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 10, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 141503, 
                                                          root := ~, 
                                                          start := 141495, 
                                                          stop := 141502 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 10, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 141509, 
                                                          root := ~, 
                                                          start := 141505, 
                                                          stop := 141508 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 1, 10, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 10, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 10, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 141532, 
                                                          root := ~, 
                                                          start := 141518, 
                                                          stop := 141531 ), 
                                                      rec( 
                                                          content := " is a di\
graph created from a record with a component\n    ", count := [ 5, 1, 10, 7 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertices", count := [ 5, 1, 10, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 10, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 141604, 
                                                          root := ~, 
                                                          start := 141589, 
                                                          stop := 141603 ), 
                                                      rec( 
                                                          content := ", then t\
he labels of the vertices are set to the value of\n    this component.", 
                                                          count := 
                                                            [ 5, 1, 10, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 10, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 141685, 
                                                          root := ~, 
                                                          start := 141681, 
                                                          stop := 141684 ), 
                                                      rec( 
                                                          content := "\n\n    \
Induced subdigraphs, and other operations which create new digraphs from\n    \
old ones, inherit their labels from their parents.\n\n    ", 
                                                          count := 
                                                            [ 5, 1, 10, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDigraph6String(\"&DHUEe_\");\n<immutable digraph with 5 \
vertices, 11 edges>\ngap> DigraphVertexLabels(D);\n[ 1 .. 5 ]\ngap> D := Digra\
ph([\"a\", \"b\", \"c\"], [], []);\n<immutable empty digraph with 3 vertices>\
\ngap> DigraphVertexLabels(D);\n[ \"a\", \"b\", \"c\" ]\ngap> SetDigraphVertex\
Label(D, 2, \"d\");\ngap> DigraphVertexLabels(D);\n[ \"a\", \"d\", \"c\" ]\nga\
p> D := InducedSubdigraph(D, [1, 3]);\n<immutable empty digraph with 2 vertice\
s>\ngap> DigraphVertexLabels(D);\n[ \"a\", \"c\" ]\ngap> D := Digraph(IsMutabl\
eDigraph, [\"e\", \"f\", \"g\"], [], []);\n<mutable empty digraph with 3 verti\
ces>\ngap> SetDigraphVertexLabels(D, [\"h\", \"i\", \"j\"]);\ngap> DigraphVert\
exLabels(D);\n[ \"h\", \"i\", \"j\" ]\ngap> InducedSubdigraph(D, [1, 3]);\n<mu\
table empty digraph with 2 vertices>\ngap> DigraphVertexLabels(D);\n[ \"h\", \
\"j\" ]\n", count := [ 5, 1, 10, 9 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 1, 10, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 142648, 
                                                          root := ~, 
                                                          start := 141824, 
                                                          stop := 142647 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 10, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 10, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 142665, root := ~, 
                                                  start := 141026, 
                                                  stop := 142664 ) ], 
                                          count := [ 5, 1, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 142679, root := ~, 
                                          start := 140900, stop := 142678 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 10, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, i, j", 
                                                      Name := "DigraphEdgeLabe\
l" ), content := 0, count := [ 5, 1, 11, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 142753, root := ~, 
                                                  start := 142700, 
                                                  stop := 142752 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, i, j, o\
bj", Name := "SetDigraphEdgeLabel" ), content := 0, count := [ 5, 1, 11, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 142817, root := ~, 
                                                  start := 142756, 
                                                  stop := 142816 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 142855, 
                                                          root := ~, 
                                                          start := 142841, 
                                                          stop := 142854 ), 
                                                      rec( 
                                                          content := " is a di\
graph without multiple edges, then the first\n    operation returns the label \
of the edge from vertex ", count := [ 5, 1, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 142972, 
                                                          root := ~, 
                                                          start := 142964, 
                                                          stop := 142971 ), 
                                                      rec( 
                                                          content := " to vert\
ex\n    ", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 142995, 
                                                          root := ~, 
                                                          start := 142987, 
                                                          stop := 142994 ), 
                                                      rec( 
                                                          content := ".  The s\
econd operation can be used to set the label of the edge\n    between vertex "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 143087, 
                                                          root := ~, 
                                                          start := 143079, 
                                                          stop := 143086 ), 
                                                      rec( 
                                                          content := " and ver\
tex ", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 143107, 
                                                          root := ~, 
                                                          start := 143099, 
                                                          stop := 143106 ), 
                                                      rec( 
                                                          content := " to the \
arbitrary ", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " object\\
n    ", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
bj", count := [ 5, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 143152, 
                                                          root := ~, 
                                                          start := 143142, 
                                                          stop := 143151 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 143158, 
                                                          root := ~, 
                                                          start := 143154, 
                                                          stop := 143157 ), 
                                                      rec( 
                                                          content := "\n\n    \
The label of an edge can be changed an arbitrary number of times. If no\n    l\
abel has been set for the edge, then the default value is ", 
                                                          count := 
                                                            [ 5, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 5, 1, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 143307, 
                                                          root := ~, 
                                                          start := 143299, 
                                                          stop := 143306 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 143313, 
                                                          root := ~, 
                                                          start := 143309, 
                                                          stop := 143312 ), 
                                                      rec( 
                                                          content := "\n\n    \
Induced subdigraphs, and some other operations which create new digraphs from\
\n    old ones, inherit their edge labels from their parents.\n\n    See also \
", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
EdgeLabels" ), content := 0, count := [ 5, 1, 11, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 143502, 
                                                          root := ~, 
                                                          start := 143471, 
                                                          stop := 143501 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 5, 1, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDigraph6String(\"&DHUEe_\");\n<immutable digraph with 5 \
vertices, 11 edges>\ngap> DigraphEdgeLabel(D, 3, 1);\n1\ngap> SetDigraphEdgeLa\
bel(D, 2, 5, [42]);\ngap> DigraphEdgeLabel(D, 2, 5);\n[ 42 ]\ngap> D := Induce\
dSubdigraph(D, [2, 5]);\n<immutable digraph with 2 vertices, 3 edges>\ngap> Di\
graphEdgeLabel(D, 1, 2);\n[ 42 ]\ngap> D := ChainDigraph(IsMutableDigraph, 5);\
\n<mutable digraph with 5 vertices, 4 edges>\ngap> DigraphEdgeLabel(D, 2, 3);\
\n1\ngap> SetDigraphEdgeLabel(D, 4, 5, [1729]);\ngap> DigraphEdgeLabel(D, 4, 5\
);\n[ 1729 ]\ngap> InducedSubdigraph(D, [4, 5]);\n<mutable digraph with 2 vert\
ices, 1 edge>\ngap> DigraphEdgeLabel(D, 1, 2);\n[ 1729 ]\n", count := 
                                                                    [ 5, 1, 
                                                                      11, 8 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 11, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 144197, 
                                                          root := ~, 
                                                          start := 143509, 
                                                          stop := 144196 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 11, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 144214, root := ~, 
                                                  start := 142820, 
                                                  stop := 144213 ) ], 
                                          count := [ 5, 1, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 144228, root := ~, 
                                          start := 142685, stop := 144227 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 11, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphEdgeLabe\
ls" ), content := 0, count := [ 5, 1, 12, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 144295, root := ~, 
                                                  start := 144249, 
                                                  stop := 144294 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, labels"
                                                        , 
                                                      Label := "for a digraph \
and a list of lists", Name := "SetDigraphEdgeLabels" ), content := 0, 
                                                  count := [ 5, 1, 12, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 144401, root := ~, 
                                                  start := 144298, 
                                                  stop := 144400 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, func", 
                                                      Label := "for a digraph \
and a function", Name := "SetDigraphEdgeLabels" ), content := 0, 
                                                  count := [ 5, 1, 12, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 144500, root := ~, 
                                                  start := 144404, 
                                                  stop := 144499 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 144538, 
                                                          root := ~, 
                                                          start := 144524, 
                                                          stop := 144537 ), 
                                                      rec( 
                                                          content := " is a di\
graph without multiple edges, then\n    ", count := [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEdgeLabels", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 144609, 
                                                          root := ~, 
                                                          start := 144585, 
                                                          stop := 144608 ), 
                                                      rec( 
                                                          content := " returns\
 a copy of the labels of the edges\n    in ", count := [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 144673, 
                                                          root := ~, 
                                                          start := 144659, 
                                                          stop := 144672 ), 
                                                      rec( 
                                                          content := " as a li\
st of lists ", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
abels", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 144706, 
                                                          root := ~, 
                                                          start := 144693, 
                                                          stop := 144705 ), 
                                                      rec( 
                                                          content := " such th\
at\n    ", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
abels[i][j]", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 144740, 
                                                          root := ~, 
                                                          start := 144721, 
                                                          stop := 144739 ), 
                                                      rec( 
                                                          content := " is the \
label on the edge from vertex ", count := [ 5, 1, 12, 7 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 144786, 
                                                          root := ~, 
                                                          start := 144778, 
                                                          stop := 144785 ), 
                                                      rec( 
                                                          content := "\n    to\
 vertex ", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
utNeighbours(digraph)[i][j]", count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 144836, 
                                                          root := ~, 
                                                          start := 144801, 
                                                          stop := 144835 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
etDigraphEdgeLabels", count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 144870, 
                                                          root := ~, 
                                                          start := 144843, 
                                                          stop := 144869 ), 
                                                      rec( 
                                                          content := " can be \
used to set the labels of the edges in\n    ", count := [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 144935, 
                                                          root := ~, 
                                                          start := 144921, 
                                                          stop := 144934 ), 
                                                      rec( 
                                                          content := " without\
 multiple edges to the list ", count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
abels", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 144984, 
                                                          root := ~, 
                                                          start := 144971, 
                                                          stop := 144983 ), 
                                                      rec( 
                                                          content := " of list\
s of\n    arbitrary ", count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " objects\
 such that ", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist[i][j]", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 145052, 
                                                          root := ~, 
                                                          start := 145035, 
                                                          stop := 145051 ), 
                                                      rec( 
                                                          content := " is the \
label on the edge\n    from vertex ", count := [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 145102, 
                                                          root := ~, 
                                                          start := 145094, 
                                                          stop := 145101 ), 
                                                      rec( 
                                                          content := " to the \
vertex ", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
utNeighbours(digraph>[i][j]", count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 145152, 
                                                          root := ~, 
                                                          start := 145117, 
                                                          stop := 145151 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 Alternatively ", count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
etDigraphEdgeLabels", count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 12, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 145200, 
                                                          root := ~, 
                                                          start := 145173, 
                                                          stop := 145199 ), 
                                                      rec( 
                                                          content := " can be \
called with binary function\n    ", count := [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
unc", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 145251, 
                                                          root := ~, 
                                                          start := 145240, 
                                                          stop := 145250 ), 
                                                      rec( 
                                                          content := " that as\
 its second argument that when passed two vertices ", count := [ 5, 1, 12, 7 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 145318, 
                                                          root := ~, 
                                                          start := 145310, 
                                                          stop := 145317 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 145335, 
                                                          root := ~, 
                                                          start := 145327, 
                                                          stop := 145334 ), 
                                                      rec( 
                                                          content := " returns\
 the label for the edge between vertex ", count := [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 145390, 
                                                          root := ~, 
                                                          start := 145382, 
                                                          stop := 145389 ), 
                                                      rec( 
                                                          content := " and ver\
tex\n    ", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 1, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 145414, 
                                                          root := ~, 
                                                          start := 145406, 
                                                          stop := 145413 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 12, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 145420, 
                                                          root := ~, 
                                                          start := 145416, 
                                                          stop := 145419 ), 
                                                      rec( 
                                                          content := "\n\n    \
The label of an edge can be changed an arbitrary number of times. If no\n    l\
abel has been set for an edge, then the default value is ", 
                                                          count := 
                                                            [ 5, 1, 12, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 5, 1, 12, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 12, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 145568, 
                                                          root := ~, 
                                                          start := 145560, 
                                                          stop := 145567 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 1, 12, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 12, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 145574, 
                                                          root := ~, 
                                                          start := 145570, 
                                                          stop := 145573 ), 
                                                      rec( 
                                                          content := "\n\n    \
Induced subdigraphs, and some other operations which create new digraphs\n    \
from old ones, inherit their labels from their parents.\n\n    ", 
                                                          count := 
                                                            [ 5, 1, 12, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDigraph6String(\"&DHUEe_\");\n<immutable digraph with 5 \
vertices, 11 edges>\ngap> DigraphEdgeLabels(D);\n[ [ 1 ], [ 1, 1, 1 ], [ 1 ], \
[ 1, 1, 1 ], [ 1, 1, 1 ] ]\ngap> SetDigraphEdgeLabel(D, 2, 1, \"d\");\ngap> Di\
graphEdgeLabels(D);\n[ [ 1 ], [ \"d\", 1, 1 ], [ 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ]\
 ]\ngap> D := InducedSubdigraph(D, [1, 2, 3]);\n<immutable digraph with 3 vert\
ices, 4 edges>\ngap> DigraphEdgeLabels(D);\n[ [ 1 ], [ \"d\", 1 ], [ 1 ] ]\nga\
p> OutNeighbours(D);\n[ [ 3 ], [ 1, 3 ], [ 1 ] ]\ngap> D := CompleteBipartiteD\
igraph(IsMutableDigraph, 2, 3);\n<mutable digraph with 5 vertices, 12 edges>\n\
gap> DigraphEdgeLabels(D);\n[ [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1 ], [ 1, 1 ], [ \
1, 1 ] ]\ngap> SetDigraphEdgeLabel(D, 2, 4, \"a\");\ngap> DigraphEdgeLabels(D)\
;\n[ [ 1, 1, 1 ], [ 1, \"a\", 1 ], [ 1, 1 ], [ 1, 1 ], [ 1, 1 ] ]\ngap> Induce\
dSubdigraph(D, [1, 2, 3, 4]);\n<mutable digraph with 4 vertices, 8 edges>\ngap\
> DigraphEdgeLabels(D);\n[ [ 1, 1 ], [ 1, \"a\" ], [ 1, 1 ], [ 1, 1 ] ]\ngap> \
OutNeighbors(D);\n[ [ 3, 4 ], [ 3, 4 ], [ 1, 2 ], [ 1, 2 ] ]\n", count := 
                                                                    [ 5, 1, 
                                                                      12, 10 ]
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 12, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 146785, 
                                                          root := ~, 
                                                          start := 145718, 
                                                          stop := 146784 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 12, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 12, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 146802, root := ~, 
                                                  start := 144503, 
                                                  stop := 146801 ) ], 
                                          count := [ 5, 1, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 146816, root := ~, 
                                          start := 144234, stop := 146815 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 12, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "DigraphInEdges"\
 ), content := 0, count := [ 5, 1, 13, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 146888, root := ~, 
                                                  start := 146837, 
                                                  stop := 146887 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 edges.", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 13, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 146926, root := ~, 
                                                  start := 146891, 
                                                  stop := 146925 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 5, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphInEdges", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 146968, 
                                                          root := ~, 
                                                          start := 146947, 
                                                          stop := 146967 ), 
                                                      rec( 
                                                          content := " returns\
 the list of all edges of ", count := [ 5, 1, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 147016, 
                                                          root := ~, 
                                                          start := 147002, 
                                                          stop := 147015 ), 
                                                      rec( 
                                                          content := "\n    wh\
ich have ", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 147045, 
                                                          root := ~, 
                                                          start := 147032, 
                                                          stop := 147044 ), 
                                                      rec( 
                                                          content := " as thei\
r range.\n    ", count := [ 5, 1, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 2], [3, 3], [4, 4], [1, 1]]);\n<immutable multidigraph\
 with 4 vertices, 8 edges>\ngap> DigraphInEdges(D, 2);\n[ [ 1, 2 ], [ 1, 2 ] ]\
\n", count := [ 5, 1, 13, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 1, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 147251, 
                                                          root := ~, 
                                                          start := 147066, 
                                                          stop := 147250 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 13, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 147268, root := ~, 
                                                  start := 146929, 
                                                  stop := 147267 ) ], 
                                          count := [ 5, 1, 13, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 147282, root := ~, 
                                          start := 146822, stop := 147281 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 13, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "DigraphOutEdges\
" ), content := 0, count := [ 5, 1, 14, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 147355, root := ~, 
                                                  start := 147303, 
                                                  stop := 147354 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 edges.", count := [ 5, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 147393, root := ~, 
                                                  start := 147358, 
                                                  stop := 147392 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 5, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphOutEdges", count := [ 5, 1, 14, 3 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 5, 1, 14, 3 ], mathmode := "Text", name := "C", 
                                                          next := 147436, 
                                                          root := ~, 
                                                          start := 147414, 
                                                          stop := 147435 ), 
                                                      rec( 
                                                          content := " returns\
 the list of all edges of ", count := [ 5, 1, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 147484, 
                                                          root := ~, 
                                                          start := 147470, 
                                                          stop := 147483 ), 
                                                      rec( 
                                                          content := "\n    wh\
ich have ", count := [ 5, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 147513, 
                                                          root := ~, 
                                                          start := 147500, 
                                                          stop := 147512 ), 
                                                      rec( 
                                                          content := " as thei\
r source.\n    ", count := [ 5, 1, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 2], [3, 3], [4, 4], [1, 1]]);\n<immutable multidigraph\
 with 4 vertices, 8 edges>\ngap> DigraphOutEdges(D, 2);\n[ [ 2, 3 ], [ 2, 3 ] \
]\n", count := [ 5, 1, 14, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 1, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 147721, 
                                                          root := ~, 
                                                          start := 147535, 
                                                          stop := 147720 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 147738, root := ~, 
                                                  start := 147396, 
                                                  stop := 147737 ) ], 
                                          count := [ 5, 1, 14, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 147752, root := ~, 
                                          start := 147288, stop := 147751 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 14, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list", 
                                                      Label := "for digraph an\
d list", Name := "IsDigraphEdge" ), content := 0, count := [ 5, 1, 15, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 147858, root := ~, 
                                                  start := 147773, 
                                                  stop := 147857 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, u, v", 
                                                      Label := "for digraph an\
d two pos ints", Name := "IsDigraphEdge" ), content := 0, 
                                                  count := [ 5, 1, 15, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 147954, root := ~, 
                                                  start := 147861, 
                                                  stop := 147953 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 147977, 
                                                          root := ~, 
                                                          start := 147966, 
                                                          stop := 147976 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 147993, 
                                                          root := ~, 
                                                          start := 147981, 
                                                          stop := 147992 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 15, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 148004, root := ~, 
                                                  start := 147957, 
                                                  stop := 148003 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    In \
the first form, this function returns ", count := [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 148077, 
                                                          root := ~, 
                                                          start := 148066, 
                                                          stop := 148076 ), 
                                                      rec( 
                                                          content := " if and \
only if the list\n    ", count := [ 5, 1, 15, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 148117, 
                                                          root := ~, 
                                                          start := 148106, 
                                                          stop := 148116 ), 
                                                      rec( 
                                                          content := " specifi\
es an edge in the digraph ", count := [ 5, 1, 15, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 148165, 
                                                          root := ~, 
                                                          start := 148151, 
                                                          stop := 148164 ), 
                                                      rec( 
                                                          content := ".  Speci\
fically,\n    this operation returns ", count := [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 148220, 
                                                          root := ~, 
                                                          start := 148209, 
                                                          stop := 148219 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 148235, 
                                                          root := ~, 
                                                          start := 148224, 
                                                          stop := 148234 ), 
                                                      rec( 
                                                          content := " is a pa\
ir of positive\n    integers where ", count := [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 148288, 
                                                          root := ~, 
                                                          start := 148277, 
                                                          stop := 148287 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1]", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 148298, 
                                                          root := ~, 
                                                          start := 148288, 
                                                          stop := 148297 ), 
                                                      rec( 
                                                          content := " is the \
source and ", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 148328, 
                                                          root := ~, 
                                                          start := 148317, 
                                                          stop := 148327 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
2]", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 148338, 
                                                          root := ~, 
                                                          start := 148328, 
                                                          stop := 148337 ), 
                                                      rec( 
                                                          content := "\n    is\
 the range of an edge in ", count := [ 5, 1, 15, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 148384, 
                                                          root := ~, 
                                                          start := 148370, 
                                                          stop := 148383 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 148402, 
                                                          root := ~, 
                                                          start := 148390, 
                                                          stop := 148401 ), 
                                                      rec( 
                                                          content := " otherwi\
se. ", count := [ 5, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 148418, 
                                                          root := ~, 
                                                          start := 148414, 
                                                          stop := 148417 ), 
                                                      rec( 
                                                          content := "\n\n    \
The second form simply returns ", count := [ 5, 1, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 148466, 
                                                          root := ~, 
                                                          start := 148455, 
                                                          stop := 148465 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 5, 1, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
", count := [ 5, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                                , 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "u", count := [ 5, 1, 15, 6 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 15, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 148482, root := ~, start := 148474, stop := 14848\
1 ), rec( content := ", ", count := [ 5, 1, 15, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "v\
", count := [ 5, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 5, 1, 
                                                                      15, 6 ],
                                                                  mathmode := \
"Text", name := "A", next := 148492, root := ~, start := 148484, stop := 14849\
1 ), rec( content := "]", count := [ 5, 1, 15, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 15, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 148497, 
                                                          root := ~, 
                                                          start := 148470, 
                                                          stop := 148496 ), 
                                                      rec( 
                                                          content := " is\n   \
 an edge in ", count := [ 5, 1, 15, 6 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 148530, 
                                                          root := ~, 
                                                          start := 148516, 
                                                          stop := 148529 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 5, 1, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 5, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 148548, 
                                                          root := ~, 
                                                          start := 148536, 
                                                          stop := 148547 ), 
                                                      rec( 
                                                          content := " otherwi\
se.\n\n", count := [ 5, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 2], [6], [], [3], [], [1]]);\n<immutable multidigraph \
with 6 vertices, 5 edges>\ngap> IsDigraphEdge(D, [1, 1]);\nfalse\ngap> IsDigra\
phEdge(D, [1, 2]);\ntrue\ngap> IsDigraphEdge(D, [1, 8]);\nfalse\n", 
                                                                  count := 
                                                                    [ 5, 1, 
                                                                      15, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 15, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 148805, 
                                                          root := ~, 
                                                          start := 148561, 
                                                          stop := 148804 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 15, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 148822, root := ~, 
                                                  start := 148007, 
                                                  stop := 148821 ) ], 
                                          count := [ 5, 1, 15, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 148836, root := ~, 
                                          start := 147758, stop := 148835 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 15, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list", 
                                                      Name := "IsMatching" ), 
                                                  content := 0, 
                                                  count := [ 5, 1, 16, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 148902, root := ~, 
                                                  start := 148857, 
                                                  stop := 148901 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list", 
                                                      Name := "IsMaximalMatchi\
ng" ), content := 0, count := [ 5, 1, 16, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 148957, root := ~, 
                                                  start := 148905, 
                                                  stop := 148956 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list", 
                                                      Name := "IsMaximumMatchi\
ng" ), content := 0, count := [ 5, 1, 16, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 149012, root := ~, 
                                                  start := 148960, 
                                                  stop := 149011 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list", 
                                                      Name := "IsPerfectMatchi\
ng" ), content := 0, count := [ 5, 1, 16, 8 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 149067, root := ~, 
                                                  start := 149015, 
                                                  stop := 149066 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 149090, 
                                                          root := ~, 
                                                          start := 149079, 
                                                          stop := 149089 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 149106, 
                                                          root := ~, 
                                                          start := 149094, 
                                                          stop := 149105 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 16, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 149117, root := ~, 
                                                  start := 149070, 
                                                  stop := 149116 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149155, 
                                                          root := ~, 
                                                          start := 149141, 
                                                          stop := 149154 ), 
                                                      rec( 
                                                          content := " is a di\
graph and ", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149184, 
                                                          root := ~, 
                                                          start := 149173, 
                                                          stop := 149183 ), 
                                                      rec( 
                                                          content := " is a li\
st of pairs of\n    vertices of ", count := [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149237, 
                                                          root := ~, 
                                                          start := 149223, 
                                                          stop := 149236 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sMatching", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 149261, 
                                                          root := ~, 
                                                          start := 149244, 
                                                          stop := 149260 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 149281, 
                                                          root := ~, 
                                                          start := 149270, 
                                                          stop := 149280 ), 
                                                      rec( 
                                                          content := " if\n   \
 ", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149300, 
                                                          root := ~, 
                                                          start := 149289, 
                                                          stop := 149299 ), 
                                                      rec( 
                                                          content := " is a ma\
tching of ", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149332, 
                                                          root := ~, 
                                                          start := 149318, 
                                                          stop := 149331 ), 
                                                      rec( 
                                                          content := ".  The o\
peration\n    ", count := [ 5, 1, 16, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sMaximalMatching", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 5, 1, 16, 9 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 149377, 
                                                          root := ~, 
                                                          start := 149353, 
                                                          stop := 149376 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 149397, 
                                                          root := ~, 
                                                          start := 149386, 
                                                          stop := 149396 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149412, 
                                                          root := ~, 
                                                          start := 149401, 
                                                          stop := 149411 ), 
                                                      rec( 
                                                          content := " is a ma\
ximal \n    matching, ", count := [ 5, 1, 16, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sMaximumMatching", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 5, 1, 16, 9 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 149465, 
                                                          root := ~, 
                                                          start := 149441, 
                                                          stop := 149464 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 149485, 
                                                          root := ~, 
                                                          start := 149474, 
                                                          stop := 149484 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149500, 
                                                          root := ~, 
                                                          start := 149489, 
                                                          stop := 149499 ), 
                                                      rec( 
                                                          content := " is a\n \
   maximum matching and ", count := [ 5, 1, 16, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sPerfectMatching", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 5, 1, 16, 9 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 149555, 
                                                          root := ~, 
                                                          start := 149531, 
                                                          stop := 149554 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 149575, 
                                                          root := ~, 
                                                          start := 149564, 
                                                          stop := 149574 ), 
                                                      rec( 
                                                          content := " if \n  \
  ", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149595, 
                                                          root := ~, 
                                                          start := 149584, 
                                                          stop := 149594 ), 
                                                      rec( 
                                                          content := " is a pe\
rfect, matching of ", count := [ 5, 1, 16, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149636, 
                                                          root := ~, 
                                                          start := 149622, 
                                                          stop := 149635 ), 
                                                      rec( 
                                                          content := ", respec\
tively.  \n    Otherwise, each of these operations return ", 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 5, 1, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 149713, 
                                                          root := ~, 
                                                          start := 149701, 
                                                          stop := 149712 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 149723, 
                                                          root := ~, 
                                                          start := 149719, 
                                                          stop := 149722 ), 
                                                      rec( 
                                                          content := "\n\n    \
A ", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
atching", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 149746, 
                                                          root := ~, 
                                                          start := 149731, 
                                                          stop := 149745 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "M\
", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 149755, 
                                                          root := ~, 
                                                          start := 149747, 
                                                          stop := 149754 ), 
                                                      rec( 
                                                          content := " of a di\
graph ", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149783, 
                                                          root := ~, 
                                                          start := 149769, 
                                                          stop := 149782 ), 
                                                      rec( 
                                                          content := " is a su\
bset of the\n    edges of ", count := [ 5, 1, 16, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149830, 
                                                          root := ~, 
                                                          start := 149816, 
                                                          stop := 149829 ), 
                                                      rec( 
                                                          content := ", i.e. "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEdges(", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "digraph", count := [ 5, 1, 16, 10 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 1, 16, 10 ], 
                                                                  mathmode := \
"Text", name := "A", next := 149867, root := ~, start := 149853, stop := 14986\
6 ), rec( content := ")", count := [ 5, 1, 16, 10 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 16, 10 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 149872, 
                                                          root := ~, 
                                                          start := 149837, 
                                                          stop := 149871 ), 
                                                      rec( 
                                                          content := ", such\n\
    that no pair of distinct edges in ", count := [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "M\
", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 149925, 
                                                          root := ~, 
                                                          start := 149917, 
                                                          stop := 149924 ), 
                                                      rec( 
                                                          content := " are inc\
ident to the same vertex\n    of ", count := [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 149979, 
                                                          root := ~, 
                                                          start := 149965, 
                                                          stop := 149978 ), 
                                                      rec( 
                                                          content := ".  Note \
that this definition allows a matching to contain\n    loops.  See ", 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ 5, 1, 16, 10 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 150083, 
                                                          root := ~, 
                                                          start := 150053, 
                                                          stop := 150082 ), 
                                                      rec( 
                                                          content := ".  The m\
atching ", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "M\
", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 150107, 
                                                          root := ~, 
                                                          start := 150099, 
                                                          stop := 150106 ), 
                                                      rec( 
                                                          content := " is\n   \
 ", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
aximal", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 150129, 
                                                          root := ~, 
                                                          start := 150115, 
                                                          stop := 150128 ), 
                                                      rec( 
                                                          content := " if it i\
s contained in no larger matching of the digraph,\n    is ", 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
aximum", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 150208, 
                                                          root := ~, 
                                                          start := 150194, 
                                                          stop := 150207 ), 
                                                      rec( 
                                                          content := " if it h\
as the greatest cardinality among all matchings and\n    is ", 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
erfect", count := [ 5, 1, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 150289, 
                                                          root := ~, 
                                                          start := 150275, 
                                                          stop := 150288 ), 
                                                      rec( 
                                                          content := " if ever\
y vertex of the digraph is incident to an edge in\n    the matching.  Every ma\
ximum or perfect matching is maximal. Note, however,\n    that not every perfe\
ct matching of digraphs with loops is maximum.\n\n    ", count := 
                                                            [ 5, 1, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2], [1, 2], [2, 3, 4], [3, 5], [1]]);\n<immutable digr\
aph with 5 vertices, 10 edges>\ngap> IsMatching(D, [[2, 1], [3, 2]]);\nfalse\n\
gap> edges := [[3, 2]];;\ngap> IsMatching(D, edges);\ntrue\ngap> IsMaximalMatc\
hing(D, edges);\nfalse\ngap> edges := [[2, 1], [3, 4]];;\ngap> IsMaximalMatchi\
ng(D, edges);\ntrue\ngap> IsPerfectMatching(D, edges);\nfalse\ngap> edges := [\
[1, 2], [3, 3], [4, 5]];;\ngap> IsPerfectMatching(D, edges);\ntrue\ngap> IsMax\
imumMatching(D, edges);\nfalse\ngap> edges := [[1, 1], [2, 2], [3, 3], [4, 5]]\
;;\ngap> IsMaximumMatching(D, edges);\ntrue\n", count := [ 5, 1, 16, 11 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 16, 11 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 151103, 
                                                          root := ~, 
                                                          start := 150503, 
                                                          stop := 151102 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 16, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 16, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 151120, root := ~, 
                                                  start := 149120, 
                                                  stop := 151119 ) ], 
                                          count := [ 5, 1, 16, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 151134, root := ~, 
                                          start := 148842, stop := 151133 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 16, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMaximalM\
atching" ), content := 0, count := [ 5, 1, 17, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 151206, root := ~, 
                                                  start := 151155, 
                                                  stop := 151205 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 pairs of vertices.", count := [ 5, 1, 17, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 151256, root := ~, 
                                                  start := 151209, 
                                                  stop := 151255 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns a maximal matching of the digraph ", count := 
                                                            [ 5, 1, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 151347, 
                                                          root := ~, 
                                                          start := 151333, 
                                                          stop := 151346 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 151357, 
                                                          root := ~, 
                                                          start := 151353, 
                                                          stop := 151356 ), 
                                                      rec( 
                                                          content := "\n\n    \
For the definition of a maximal matching, see ", count := [ 5, 1, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsMaxim\
alMatching" ), content := 0, count := [ 5, 1, 17, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 151440, 
                                                          root := ~, 
                                                          start := 151409, 
                                                          stop := 151439 ), 
                                                      rec( 
                                                          content := ". \n\n  \
  ", count := [ 5, 1, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDiSparse6String(\".IeAoXCJU@|SHAe?d\");\n<immutable digr\
aph with 10 vertices, 13 edges>\ngap> M := DigraphMaximalMatching(D);; IsMaxim\
alMatching(D, M);\ntrue\ngap> D := RandomDigraph(100);;\ngap> IsMaximalMatchin\
g(D, DigraphMaximalMatching(D));\ntrue\ngap> D := GeneralisedPetersenGraph(IsM\
utableDigraph, 9, 2);\n<mutable digraph with 18 vertices, 54 edges>\ngap> IsMa\
ximalMatching(D, DigraphMaximalMatching(D));\ntrue\n", count := [ 5, 1, 17, 5 
                                                                     ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 17, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 151908, 
                                                          root := ~, 
                                                          start := 151448, 
                                                          stop := 151907 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 151925, root := ~, 
                                                  start := 151259, 
                                                  stop := 151924 ) ], 
                                          count := [ 5, 1, 17, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 151939, root := ~, 
                                          start := 151140, stop := 151938 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 1, 17, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMaximumM\
atching" ), content := 0, count := [ 5, 1, 18, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 152011, root := ~, 
                                                  start := 151960, 
                                                  stop := 152010 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 pairs of vertices.", count := [ 5, 1, 18, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 152061, root := ~, 
                                                  start := 152014, 
                                                  stop := 152060 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns a maximum matching of the digraph ", count := 
                                                            [ 5, 1, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 152152, 
                                                          root := ~, 
                                                          start := 152138, 
                                                          stop := 152151 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 152162, 
                                                          root := ~, 
                                                          start := 152158, 
                                                          stop := 152161 ), 
                                                      rec( 
                                                          content := "\n\n    \
For the definition of a maximum matching, see ", count := [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsMaxim\
umMatching" ), content := 0, count := [ 5, 1, 18, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 152245, 
                                                          root := ~, 
                                                          start := 152214, 
                                                          stop := 152244 ), 
                                                      rec( 
                                                          content := ".\n    I\
f ", count := [ 5, 1, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 1, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 152268, 
                                                          root := ~, 
                                                          start := 152254, 
                                                          stop := 152267 ), 
                                                      rec( 
                                                          content := " is bipa\
rtite (see ", count := [ 5, 1, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsBipar\
titeDigraph" ), content := 0, count := [ 5, 1, 18, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 152319, 
                                                          root := ~, 
                                                          start := 152287, 
                                                          stop := 152318 ), 
                                                      rec( 
                                                          content := "), then \
\n    the algorithm used has complexity ", count := [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m*sqrt(n))", count := [ 5, 1, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 152385, 
                                                          root := ~, 
                                                          start := 152366, 
                                                          stop := 152384 ), 
                                                      rec( 
                                                          content := ". Otherw\
ise for general \n    graphs the complexity is ", count := [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m*n*log(n))", count := [ 5, 1, 18, 4 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 152459, 
                                                          root := ~, 
                                                          start := 152439, 
                                                          stop := 152458 ), 
                                                      rec( 
                                                          content := ". Here "
                                                            , 
                                                          count := 
                                                            [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 1, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 152474, 
                                                          root := ~, 
                                                          start := 152466, 
                                                          stop := 152473 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices \n    and ", count := [ 5, 1, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 1, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 1, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 152518, 
                                                          root := ~, 
                                                          start := 152510, 
                                                          stop := 152517 ), 
                                                      rec( 
                                                          content := " is the \
number of edges.\n\n    ", count := [ 5, 1, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDigraph6String(\"&I@EA_A?AdDp[_c??OO\");\n<immutable dig\
raph with 10 vertices, 23 edges>\ngap> M := DigraphMaximumMatching(D);; IsMaxi\
malMatching(D, M);\ntrue\ngap> Length(M);\n5\ngap> D := Digraph([[5, 6, 7, 8],\
 [6, 7, 8], [7, 8], [8], \n>                  [], [], [], []]);;\ngap> M := Di\
graphMaximumMatching(D);\n[ [ 1, 5 ], [ 2, 6 ], [ 3, 7 ], [ 4, 8 ] ]\ngap> D :\
= GeneralisedPetersenGraph(IsMutableDigraph, 9, 2);\n<mutable digraph with 18 \
vertices, 54 edges>\ngap> M := DigraphMaximumMatching(D);;\ngap> IsMaximalMatc\
hing(D, M);\ntrue\ngap> Length(M);\n9\n", count := [ 5, 1, 18, 5 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 1, 18, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 153145, 
                                                          root := ~, 
                                                          start := 152548, 
                                                          stop := 153144 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 1, 18, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 1, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 153162, root := ~, 
                                                  start := 152064, 
                                                  stop := 153161 ) ], 
                                          count := [ 5, 1, 18, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 153176, root := ~, 
                                          start := 151945, stop := 153175 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 5, 1, 18, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 5, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 153190, 
                                  root := ~, start := 132169, stop := 153189 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 5, 1, 18, 6 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Neighbours and de\
gree", count := [ 5, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 5, 2, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 153243, 
                                          root := ~, start := 153203, 
                                          stop := 153242 ), 
                                      rec( content := "\n    ", 
                                          count := [ 5, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "AdjacencyMatrix\
" ), content := 0, count := [ 5, 2, 1, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 153307, root := ~, 
                                                  start := 153263, 
                                                  stop := 153306 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "AdjacencyMatrix\
MutableCopy" ), content := 0, count := [ 5, 2, 1, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 153365, root := ~, 
                                                  start := 153310, 
                                                  stop := 153364 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A square \
matrix of non-negative integers.", count := [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 153428, root := ~, 
                                                  start := 153368, 
                                                  stop := 153427 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the adjacency matrix ", count := [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 153502, 
                                                          root := ~, 
                                                          start := 153492, 
                                                          stop := 153501 ), 
                                                      rec( 
                                                          content := " of the \
digraph\n    ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 153536, 
                                                          root := ~, 
                                                          start := 153522, 
                                                          stop := 153535 ), 
                                                      rec( 
                                                          content := ".\n    T\
he value of the matrix entry ", count := [ 5, 2, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at[i][j]", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 153588, 
                                                          root := ~, 
                                                          start := 153572, 
                                                          stop := 153587 ), 
                                                      rec( 
                                                          content := " is the \
number of edges\n    in ", count := [ 5, 2, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 153633, 
                                                          root := ~, 
                                                          start := 153619, 
                                                          stop := 153632 ), 
                                                      rec( 
                                                          content := " with so\
urce ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 153654, 
                                                          root := ~, 
                                                          start := 153646, 
                                                          stop := 153653 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 153673, 
                                                          root := ~, 
                                                          start := 153665, 
                                                          stop := 153672 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 153692, 
                                                          root := ~, 
                                                          start := 153678, 
                                                          stop := 153691 ), 
                                                      rec( 
                                                          content := "\n    ha\
s no vertices, then the empty list is returned. ", count := [ 5, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 153751, 
                                                          root := ~, 
                                                          start := 153747, 
                                                          stop := 153750 ), 
                                                      rec( 
                                                          content := "\n\n    \
The function ", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
djacencyMatrix", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 153792, 
                                                          root := ~, 
                                                          start := 153770, 
                                                          stop := 153791 ), 
                                                      rec( 
                                                          content := " returns\
 an immutable list of\n    lists, whereas the function ", count := 
                                                            [ 5, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
djacencyMatrixMutableCopy", count := [ 5, 2, 1, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 1, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 153887, 
                                                          root := ~, 
                                                          start := 153854, 
                                                          stop := 153886 ), 
                                                      rec( 
                                                          content := " returns\
 a copy\n    of ", count := [ 5, 2, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
djacencyMatrix", count := [ 5, 2, 1, 6 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 153932, 
                                                          root := ~, 
                                                          start := 153910, 
                                                          stop := 153931 ), 
                                                      rec( 
                                                          content := " that is\
 a mutable list of mutable lists. ", count := [ 5, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 153978, 
                                                          root := ~, 
                                                          start := 153974, 
                                                          stop := 153977 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([\n> [2, 2, 2], [1, 3, 6, 8, 9, 10], [4, 6, 8],\n> [1, 2, \
3, 9], [3, 3], [3, 5, 6, 10], [1, 2, 7],\n> [1, 2, 3, 10, 5, 6, 10], [1, 3, 4,\
 5, 8, 10],\n> [2, 3, 4, 6, 7, 10]]);\n<immutable multidigraph with 10 vertice\
s, 44 edges>\ngap> mat := AdjacencyMatrix(gr);;\ngap> Display(mat);\n[ [  0,  \
3,  0,  0,  0,  0,  0,  0,  0,  0 ],\n  [  1,  0,  1,  0,  0,  1,  0,  1,  1, \
 1 ],\n  [  0,  0,  0,  1,  0,  1,  0,  1,  0,  0 ],\n  [  1,  1,  1,  0,  0, \
 0,  0,  0,  1,  0 ],\n  [  0,  0,  2,  0,  0,  0,  0,  0,  0,  0 ],\n  [  0, \
 0,  1,  0,  1,  1,  0,  0,  0,  1 ],\n  [  1,  1,  0,  0,  0,  0,  1,  0,  0,\
  0 ],\n  [  1,  1,  1,  0,  1,  1,  0,  0,  0,  2 ],\n  [  1,  0,  1,  1,  1,\
  0,  0,  1,  0,  1 ],\n  [  0,  1,  1,  1,  0,  1,  1,  0,  0,  1 ] ]\ngap> D\
 := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 ed\
ges>\ngap> Display(AdjacencyMatrix(D));\n[ [  0,  1,  0 ],\n  [  0,  0,  1 ],\
\n  [  1,  0,  0 ] ]\n", count := [ 5, 2, 1, 8 ], name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 154948, 
                                                          root := ~, 
                                                          start := 153984, 
                                                          stop := 154947 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 154965, root := ~, 
                                                  start := 153431, 
                                                  stop := 154964 ) ], 
                                          count := [ 5, 2, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 154979, root := ~, 
                                          start := 153248, stop := 154978 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 1, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "CharacteristicP\
olynomial" ), content := 0, count := [ 5, 2, 2, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 155053, root := ~, 
                                                  start := 155000, 
                                                  stop := 155052 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A polynom\
ial with integer coefficients.", count := [ 5, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 155114, root := ~, 
                                                  start := 155056, 
                                                  stop := 155113 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the characteristic polynomial of the digraph\n     ", 
                                                          count := 
                                                            [ 5, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 155221, 
                                                          root := ~, 
                                                          start := 155207, 
                                                          stop := 155220 ), 
                                                      rec( 
                                                          content := ". That i\
s it returns the characteristic polynomial\n      of the adjacency matrix of t\
he digraph ", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 155331, 
                                                          root := ~, 
                                                          start := 155317, 
                                                          stop := 155330 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\n> [2, 2, 2], [1, 3, 6, 8, 9, 10], [4, 6, 8],\n> [1, 2, 3\
, 9], [3, 3], [3, 5, 6, 10], [1, 2, 7],\n> [1, 2, 3, 10, 5, 6, 10], [1, 3, 4, \
5, 8, 10],\n> [2, 3, 4, 6, 7, 10]]);\n<immutable multidigraph with 10 vertices\
, 44 edges>\ngap> CharacteristicPolynomial(D);\nx_1^10-3*x_1^9-7*x_1^8-x_1^7+1\
4*x_1^6+x_1^5-26*x_1^4+51*x_1^3-10*x_1^2\\\n+18*x_1-30\ngap> D := CompleteDigr\
aph(5);\n<immutable complete digraph with 5 vertices>\ngap> CharacteristicPoly\
nomial(D);\nx_1^5-10*x_1^3-20*x_1^2-15*x_1-4\ngap> D := CycleDigraph(IsMutable\
Digraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> CharacteristicP\
olynomial(D);\nx_1^3-1\n", count := [ 5, 2, 2, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 155997, 
                                                          root := ~, 
                                                          start := 155336, 
                                                          stop := 155996 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 156014, root := ~, 
                                                  start := 155117, 
                                                  stop := 156013 ) ], 
                                          count := [ 5, 2, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 156028, root := ~, 
                                          start := 154985, stop := 156027 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "BooleanAdjacenc\
yMatrix" ), content := 0, count := [ 5, 2, 3, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 156100, root := ~, 
                                                  start := 156049, 
                                                  stop := 156099 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "BooleanAdjacenc\
yMatrixMutableCopy" ), content := 0, count := [ 5, 2, 3, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 156165, root := ~, 
                                                  start := 156103, 
                                                  stop := 156164 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A square \
matrix of booleans.", count := [ 5, 2, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 3, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 156215, root := ~, 
                                                  start := 156168, 
                                                  stop := 156214 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 156253, 
                                                          root := ~, 
                                                          start := 156239, 
                                                          stop := 156252 ), 
                                                      rec( 
                                                          content := " is a di\
graph with a positive number of vertices\n    ", count := [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 156314, 
                                                          root := ~, 
                                                          start := 156306, 
                                                          stop := 156313 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
ooleanAdjacencyMatrix(", count := [ 5, 2, 3, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 3, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 156351, 
                                                          root := ~, 
                                                          start := 156321, 
                                                          stop := 156350 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 156365, 
                                                          root := ~, 
                                                          start := 156351, 
                                                          stop := 156364 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 156373, 
                                                          root := ~, 
                                                          start := 156365, 
                                                          stop := 156372 ), 
                                                      rec( 
                                                          content := "\n    re\
turns the boolean adjacency matrix ", count := [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 156425, 
                                                          root := ~, 
                                                          start := 156415, 
                                                          stop := 156424 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 156443, 
                                                          root := ~, 
                                                          start := 156429, 
                                                          stop := 156442 ), 
                                                      rec( 
                                                          content := ".  The\n\
    value of the matrix entry ", count := [ 5, 2, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at[j][i]", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 156496, 
                                                          root := ~, 
                                                          start := 156480, 
                                                          stop := 156495 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 156511, 
                                                          root := ~, 
                                                          start := 156500, 
                                                          stop := 156510 ), 
                                                      rec( 
                                                          content := " if and \
only if\n    there exists an edge in ", count := [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 156569, 
                                                          root := ~, 
                                                          start := 156555, 
                                                          stop := 156568 ), 
                                                      rec( 
                                                          content := " with so\
urce ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 156590, 
                                                          root := ~, 
                                                          start := 156582, 
                                                          stop := 156589 ), 
                                                      rec( 
                                                          content := " and ran\
ge\n    ", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 156613, 
                                                          root := ~, 
                                                          start := 156605, 
                                                          stop := 156612 ), 
                                                      rec( 
                                                          content := ".  If ",
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 156633, 
                                                          root := ~, 
                                                          start := 156619, 
                                                          stop := 156632 ), 
                                                      rec( 
                                                          content := " has no \
vertices, then the empty list is\n    returned. ", count := [ 5, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 156692, 
                                                          root := ~, 
                                                          start := 156688, 
                                                          stop := 156691 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that the boolean adjacency matrix loses information about multiple\n    e\
dges.  ", count := [ 5, 2, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 156786, 
                                                          root := ~, 
                                                          start := 156782, 
                                                          stop := 156785 ), 
                                                      rec( 
                                                          content := "\n\n    \
The attribute ", count := [ 5, 2, 3, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
ooleanAdjacencyMatrix", count := [ 5, 2, 3, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 3, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 156835, 
                                                          root := ~, 
                                                          start := 156806, 
                                                          stop := 156834 ), 
                                                      rec( 
                                                          content := " returns\
 an immutable list of\n    immutable lists, whereas the function\n    ", 
                                                          count := 
                                                            [ 5, 2, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
ooleanAdjacencyMatrixMutableCopy", count := [ 5, 2, 3, 7 ], mathmode := "Text"
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 3, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 156951, 
                                                          root := ~, 
                                                          start := 156911, 
                                                          stop := 156950 ), 
                                                      rec( 
                                                          content := " returns\
 a copy of the\n    ", count := [ 5, 2, 3, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
ooleanAdjacencyMatrix", count := [ 5, 2, 3, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 3, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 157007, 
                                                          root := ~, 
                                                          start := 156978, 
                                                          stop := 157006 ), 
                                                      rec( 
                                                          content := " that is\
 a mutable list of mutable lists. ", count := [ 5, 2, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 3, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 157053, 
                                                          root := ~, 
                                                          start := 157049, 
                                                          stop := 157052 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 2, 3, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[3, 4], [2, 3], [1, 2, 4], [4]]);\n<immutable digraph wit\
h 4 vertices, 8 edges>\ngap> PrintArray(BooleanAdjacencyMatrix(gr));\n[ [  fal\
se,  false,   true,   true ],\n  [  false,   true,   true,  false ],\n  [   tr\
ue,   true,  false,   true ],\n  [  false,  false,  false,   true ] ]\ngap> gr\
 := CycleDigraph(4);;\ngap> PrintArray(BooleanAdjacencyMatrix(gr));\n[ [  fals\
e,   true,  false,  false ],\n  [  false,  false,   true,  false ],\n  [  fals\
e,  false,  false,   true ],\n  [   true,  false,  false,  false ] ]\ngap> Boo\
leanAdjacencyMatrix(EmptyDigraph(0));\n[  ]\ngap> D := CycleDigraph(IsMutableD\
igraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> PrintArray(Boole\
anAdjacencyMatrix(D));\n[ [  false,   true,  false ],\n  [  false,  false,   t\
rue ],\n  [   true,  false,  false ] ]\n", count := [ 5, 2, 3, 9 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 3, 9 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 157888, 
                                                          root := ~, 
                                                          start := 157058, 
                                                          stop := 157887 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 3, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 157905, root := ~, 
                                                  start := 156218, 
                                                  stop := 157904 ) ], 
                                          count := [ 5, 2, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 157919, root := ~, 
                                          start := 156034, stop := 157918 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 3, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphAdjacenc\
yFunction" ), content := 0, count := [ 5, 2, 4, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 157993, root := ~, 
                                                  start := 157940, 
                                                  stop := 157992 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A functio\
n.", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 5, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 158026, root := ~, 
                                                  start := 157996, 
                                                  stop := 158025 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 158064, 
                                                          root := ~, 
                                                          start := 158050, 
                                                          stop := 158063 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphAdjacencyFunction", count := [ 5, 2, 4, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 158115, 
                                                          root := ~, 
                                                          start := 158084, 
                                                          stop := 158114 ), 
                                                      rec( 
                                                          content := " returns\
\n    a function which takes two integer parameters ", count := [ 5, 2, 4, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
, y", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 158185, 
                                                          root := ~, 
                                                          start := 158174, 
                                                          stop := 158184 ), 
                                                      rec( 
                                                          content := " and ret\
urns\n    ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 158213, 
                                                          root := ~, 
                                                          start := 158202, 
                                                          stop := 158212 ), 
                                                      rec( 
                                                          content := " if ther\
e exists an edge from vertex ", count := [ 5, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 158258, 
                                                          root := ~, 
                                                          start := 158250, 
                                                          stop := 158257 ), 
                                                      rec( 
                                                          content := " to vert\
ex ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "y\
", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 158277, 
                                                          root := ~, 
                                                          start := 158269, 
                                                          stop := 158276 ), 
                                                      rec( 
                                                          content := "\n    in\
 ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 158299, 
                                                          root := ~, 
                                                          start := 158285, 
                                                          stop := 158298 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 158316, 
                                                          root := ~, 
                                                          start := 158304, 
                                                          stop := 158315 ), 
                                                      rec( 
                                                          content := " if not.\
\n\n    ", count := [ 5, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph := Digraph([[1, 2], [3], []]);\n<immutable digraph with 3 vertic\
es, 3 edges>\ngap> foo := DigraphAdjacencyFunction(digraph);\nfunction( u, v )\
 ... end\ngap> foo(1, 1);\ntrue\ngap> foo(1, 2);\ntrue\ngap> foo(1, 3);\nfalse\
\ngap> foo(3, 1);\nfalse\ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n>        \
          [\"a\", \"b\", \"b\"],\n>                  [\"b\", \"a\", \"a\"]);\n\
<immutable multidigraph with 3 vertices, 3 edges>\ngap> foo := DigraphAdjacenc\
yFunction(gr);\nfunction( u, v ) ... end\ngap> foo(1, 2);\ntrue\ngap> foo(3, 2\
);\nfalse\ngap> foo(3, 1);\nfalse\ngap> D := CycleDigraph(IsMutableDigraph, 3)\
;\n<mutable digraph with 3 vertices, 3 edges>\ngap> foo := DigraphAdjacencyFun\
ction(D);\nfunction( u, v ) ... end\ngap> foo(1, 2);\ntrue\ngap> foo(2, 1);\nf\
alse\n", count := [ 5, 2, 4, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 159097, 
                                                          root := ~, 
                                                          start := 158330, 
                                                          stop := 159096 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 159114, root := ~, 
                                                  start := 158029, 
                                                  stop := 159113 ) ], 
                                          count := [ 5, 2, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 159128, root := ~, 
                                          start := 157925, stop := 159127 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphRange" )
                                                    , content := 0, 
                                                  count := [ 5, 2, 5, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 159190, root := ~, 
                                                  start := 159149, 
                                                  stop := 159189 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphSource" 
                                                     ), content := 0, 
                                                  count := [ 5, 2, 5, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 159235, root := ~, 
                                                  start := 159193, 
                                                  stop := 159234 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 positive integers.", count := [ 5, 2, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 159285, root := ~, 
                                                  start := 159238, 
                                                  stop := 159284 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphRange", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 159325, 
                                                          root := ~, 
                                                          start := 159306, 
                                                          stop := 159324 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphSource", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 159350, 
                                                          root := ~, 
                                                          start := 159330, 
                                                          stop := 159349 ), 
                                                      rec( 
                                                          content := " return \
the range and source of\n    the digraph ", count := [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 159412, 
                                                          root := ~, 
                                                          start := 159398, 
                                                          stop := 159411 ), 
                                                      rec( 
                                                          content := ". More p\
recisely, position ", count := [ 5, 2, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 159447, 
                                                          root := ~, 
                                                          start := 159439, 
                                                          stop := 159446 ), 
                                                      rec( 
                                                          content := " in\n   \
 ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphRange(", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "digraph", count := [ 5, 2, 5, 5 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 159485, root := ~, start := 159471, stop := 15948\
4 ), rec( content := ")", count := [ 5, 2, 5, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 5, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 159490, 
                                                          root := ~, 
                                                          start := 159455, 
                                                          stop := 159489 ), 
                                                      rec( 
                                                          content := " is the \
range of the ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 159519, 
                                                          root := ~, 
                                                          start := 159511, 
                                                          stop := 159518 ), 
                                                      rec( 
                                                          content := "th edge \
of\n    ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 159548, 
                                                          root := ~, 
                                                          start := 159534, 
                                                          stop := 159547 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 5, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([\n> [2, 1, 3, 5], [1, 3, 4], [2, 3], [2], [1, 2, 3, 4]]);\
\n<immutable digraph with 5 vertices, 14 edges>\ngap> DigraphRange(gr);\n[ 2, \
1, 3, 5, 1, 3, 4, 2, 3, 2, 1, 2, 3, 4 ]\ngap> DigraphSource(gr);\n[ 1, 1, 1, 1\
, 2, 2, 2, 3, 3, 4, 5, 5, 5, 5 ]\ngap> DigraphEdges(gr);\n[ [ 1, 2 ], [ 1, 1 ]\
, [ 1, 3 ], [ 1, 5 ], [ 2, 1 ], [ 2, 3 ], \n  [ 2, 4 ], [ 3, 2 ], [ 3, 3 ], [ \
4, 2 ], [ 5, 1 ], [ 5, 2 ], \n  [ 5, 3 ], [ 5, 4 ] ]\ngap> D := CycleDigraph(I\
sMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> Digraph\
Range(D);\n[ 2, 3, 1 ]\ngap> DigraphSource(D);\n[ 1, 2, 3 ]\n", count := 
                                                                    [ 5, 2, 
                                                                      5, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 5, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 160176, 
                                                          root := ~, 
                                                          start := 159555, 
                                                          stop := 160175 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 160193, root := ~, 
                                                  start := 159288, 
                                                  stop := 160192 ) ], 
                                          count := [ 5, 2, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 160207, root := ~, 
                                          start := 159134, stop := 160206 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 5, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "OutNeighbours" 
                                                     ), content := 0, 
                                                  count := [ 5, 2, 6, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 160270, root := ~, 
                                                  start := 160228, 
                                                  stop := 160269 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "OutNeighbors" )
                                                    , content := 0, 
                                                  count := [ 5, 2, 6, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 160314, root := ~, 
                                                  start := 160273, 
                                                  stop := 160313 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "OutNeighboursMu\
tableCopy" ), content := 0, count := [ 5, 2, 6, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 160370, root := ~, 
                                                  start := 160317, 
                                                  stop := 160369 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "OutNeighborsMut\
ableCopy" ), content := 0, count := [ 5, 2, 6, 8 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 160425, root := ~, 
                                                  start := 160373, 
                                                  stop := 160424 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "The adjac\
encies of a digraph.", count := [ 5, 2, 6, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 6, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 160476, root := ~, 
                                                  start := 160428, 
                                                  stop := 160475 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the list ", count := [ 5, 2, 6, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 160538, 
                                                          root := ~, 
                                                          start := 160528, 
                                                          stop := 160537 ), 
                                                      rec( 
                                                          content := " of out-\
neighbours of each vertex\n    of the digraph ", count := [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 160605, 
                                                          root := ~, 
                                                          start := 160591, 
                                                          stop := 160604 ), 
                                                      rec( 
                                                          content := ".\n    M\
ore specifically, a vertex ", count := [ 5, 2, 6, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 160647, 
                                                          root := ~, 
                                                          start := 160639, 
                                                          stop := 160646 ), 
                                                      rec( 
                                                          content := " appears\
 in ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut[i]", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 160672, 
                                                          root := ~, 
                                                          start := 160659, 
                                                          stop := 160671 ), 
                                                      rec( 
                                                          content := " each ti\
me\n    there exists an edge with source ", count := [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 160728, 
                                                          root := ~, 
                                                          start := 160720, 
                                                          stop := 160727 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 160747, 
                                                          root := ~, 
                                                          start := 160739, 
                                                          stop := 160746 ), 
                                                      rec( 
                                                          content := " in\n   \
 ", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 160769, 
                                                          root := ~, 
                                                          start := 160755, 
                                                          stop := 160768 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 160775, 
                                                          root := ~, 
                                                          start := 160771, 
                                                          stop := 160774 ), 
                                                      rec( 
                                                          content := "\n\n    \
The function ", count := [ 5, 2, 6, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
utNeighbours", count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 160814, 
                                                          root := ~, 
                                                          start := 160794, 
                                                          stop := 160813 ), 
                                                      rec( 
                                                          content := " returns\
 an immutable list of\n    lists, whereas the function ", count := 
                                                            [ 5, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
utNeighboursMutableCopy", count := [ 5, 2, 6, 10 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 6, 10 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 160907, 
                                                          root := ~, 
                                                          start := 160876, 
                                                          stop := 160906 ), 
                                                      rec( 
                                                          content := " returns\
 a copy\n    of ", count := [ 5, 2, 6, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
utNeighbours", count := [ 5, 2, 6, 10 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 160950, 
                                                          root := ~, 
                                                          start := 160930, 
                                                          stop := 160949 ), 
                                                      rec( 
                                                          content := " which i\
s a mutable list of mutable lists. ", count := [ 5, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 6, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 160997, 
                                                          root := ~, 
                                                          start := 160993, 
                                                          stop := 160996 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n>                  [\"a\", \"b\", \
\"b\"],\n>                  [\"b\", \"a\", \"c\"]);\n<immutable digraph with 3\
 vertices, 3 edges>\ngap> OutNeighbours(gr);\n[ [ 2 ], [ 1, 3 ], [  ] ]\ngap> \
gr := Digraph([[1, 2, 3], [2, 1], [3]]);\n<immutable digraph with 3 vertices, \
6 edges>\ngap> OutNeighbours(gr);\n[ [ 1, 2, 3 ], [ 2, 1 ], [ 3 ] ]\ngap> gr :\
= DigraphByAdjacencyMatrix([\n>  [1, 2, 1],\n>  [1, 1, 0],\n>  [0, 0, 1]]);\n<\
immutable multidigraph with 3 vertices, 7 edges>\ngap> OutNeighbours(gr);\n[ [\
 1, 2, 2, 3 ], [ 1, 2 ], [ 3 ] ]\ngap> OutNeighboursMutableCopy(gr);\n[ [ 1, 2\
, 2, 3 ], [ 1, 2 ], [ 3 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mu\
table digraph with 3 vertices, 3 edges>\ngap> OutNeighbours(D);\n[ [ 2 ], [ 3 \
], [ 1 ] ]\n", count := [ 5, 2, 6, 12 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 2, 6, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 161785, 
                                                          root := ~, 
                                                          start := 161003, 
                                                          stop := 161784 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 6, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 161802, root := ~, 
                                                  start := 160479, 
                                                  stop := 161801 ) ], 
                                          count := [ 5, 2, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 161816, root := ~, 
                                          start := 160213, stop := 161815 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 6, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "InNeighbours" )
                                                    , content := 0, 
                                                  count := [ 5, 2, 7, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 161878, root := ~, 
                                                  start := 161837, 
                                                  stop := 161877 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "InNeighbors" ),
                                                  content := 0, 
                                                  count := [ 5, 2, 7, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 161921, root := ~, 
                                                  start := 161881, 
                                                  stop := 161920 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "InNeighboursMut\
ableCopy" ), content := 0, count := [ 5, 2, 7, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 161976, root := ~, 
                                                  start := 161924, 
                                                  stop := 161975 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "InNeighborsMuta\
bleCopy" ), content := 0, count := [ 5, 2, 7, 8 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 162030, root := ~, 
                                                  start := 161979, 
                                                  stop := 162029 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 lists of vertices.", count := [ 5, 2, 7, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 7, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 162080, root := ~, 
                                                  start := 162033, 
                                                  stop := 162079 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the list ", count := [ 5, 2, 7, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nn", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 162142, 
                                                          root := ~, 
                                                          start := 162132, 
                                                          stop := 162141 ), 
                                                      rec( 
                                                          content := " of in-n\
eighbours of each vertex\n    of the digraph ", count := [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 162208, 
                                                          root := ~, 
                                                          start := 162194, 
                                                          stop := 162207 ), 
                                                      rec( 
                                                          content := ".\n    M\
ore specifically, a vertex ", count := [ 5, 2, 7, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 162250, 
                                                          root := ~, 
                                                          start := 162242, 
                                                          stop := 162249 ), 
                                                      rec( 
                                                          content := " appears\
 in ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nn[i]", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 162275, 
                                                          root := ~, 
                                                          start := 162262, 
                                                          stop := 162274 ), 
                                                      rec( 
                                                          content := " each ti\
me\n    there exists an edge with source ", count := [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 162331, 
                                                          root := ~, 
                                                          start := 162323, 
                                                          stop := 162330 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 162350, 
                                                          root := ~, 
                                                          start := 162342, 
                                                          stop := 162349 ), 
                                                      rec( 
                                                          content := " in\n   \
 ", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 7, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 162372, 
                                                          root := ~, 
                                                          start := 162358, 
                                                          stop := 162371 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 2, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 162378, 
                                                          root := ~, 
                                                          start := 162374, 
                                                          stop := 162377 ), 
                                                      rec( 
                                                          content := "\n\n    \
The function ", count := [ 5, 2, 7, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
nNeighbours", count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 162416, 
                                                          root := ~, 
                                                          start := 162397, 
                                                          stop := 162415 ), 
                                                      rec( 
                                                          content := " returns\
 an immutable list of\n    lists, whereas the function ", count := 
                                                            [ 5, 2, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
nNeighboursMutableCopy", count := [ 5, 2, 7, 10 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 7, 10 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 162508, 
                                                          root := ~, 
                                                          start := 162478, 
                                                          stop := 162507 ), 
                                                      rec( 
                                                          content := " returns\
 a copy\n    of ", count := [ 5, 2, 7, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
nNeighbours", count := [ 5, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 162550, 
                                                          root := ~, 
                                                          start := 162531, 
                                                          stop := 162549 ), 
                                                      rec( 
                                                          content := " which i\
s a mutable list of mutable lists. ", count := [ 5, 2, 7, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 7, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 162597, 
                                                          root := ~, 
                                                          start := 162593, 
                                                          stop := 162596 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that each entry of ", count := [ 5, 2, 7, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nn", count := [ 5, 2, 7, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 7, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 162637, 
                                                          root := ~, 
                                                          start := 162627, 
                                                          stop := 162636 ), 
                                                      rec( 
                                                          content := " is sort\
ed into ascending order. ", count := [ 5, 2, 7, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 162674, 
                                                          root := ~, 
                                                          start := 162670, 
                                                          stop := 162673 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n>                  [\"a\", \"b\", \
\"b\"],\n>                  [\"b\", \"a\", \"c\"]);\n<immutable digraph with 3\
 vertices, 3 edges>\ngap> InNeighbours(gr);\n[ [ 2 ], [ 1 ], [ 2 ] ]\ngap> gr \
:= Digraph([[1, 2, 3], [2, 1], [3]]);\n<immutable digraph with 3 vertices, 6 e\
dges>\ngap> InNeighbours(gr);\n[ [ 1, 2 ], [ 1, 2 ], [ 1, 3 ] ]\ngap> gr := Di\
graphByAdjacencyMatrix([\n>  [1, 2, 1],\n>  [1, 1, 0],\n>  [0, 0, 1]]);\n<immu\
table multidigraph with 3 vertices, 7 edges>\ngap> InNeighbours(gr);\n[ [ 1, 2\
 ], [ 1, 1, 2 ], [ 1, 3 ] ]\ngap> InNeighboursMutableCopy(gr);\n[ [ 1, 2 ], [ \
1, 1, 2 ], [ 1, 3 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable \
digraph with 3 vertices, 3 edges>\ngap> InNeighbours(D);\n[ [ 3 ], [ 1 ], [ 2 \
] ]\n", count := [ 5, 2, 7, 13 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 163455, 
                                                          root := ~, 
                                                          start := 162680, 
                                                          stop := 163454 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 7, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 7, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 163472, root := ~, 
                                                  start := 162083, 
                                                  stop := 163471 ) ], 
                                          count := [ 5, 2, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 163486, root := ~, 
                                          start := 161822, stop := 163485 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 7, 14 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "OutDegrees" ), 
                                                  content := 0, 
                                                  count := [ 5, 2, 8, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 163546, root := ~, 
                                                  start := 163507, 
                                                  stop := 163545 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "OutDegreeSequen\
ce" ), content := 0, count := [ 5, 2, 8, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 163595, root := ~, 
                                                  start := 163549, 
                                                  stop := 163594 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "OutDegreeSet" )
                                                    , content := 0, 
                                                  count := [ 5, 2, 8, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 163639, root := ~, 
                                                  start := 163598, 
                                                  stop := 163638 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 non-negative integers.", count := [ 5, 2, 8, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 8, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 163693, root := ~, 
                                                  start := 163642, 
                                                  stop := 163692 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\n    G\
iven a digraph ", count := [ 5, 2, 8, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 163745, 
                                                          root := ~, 
                                                          start := 163731, 
                                                          stop := 163744 ), 
                                                      rec( 
                                                          content := " with ",
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 163759, 
                                                          root := ~, 
                                                          start := 163751, 
                                                          stop := 163758 ), 
                                                      rec( 
                                                          content := " vertice\
s, the function\n    ", count := [ 5, 2, 8, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
utDegrees", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 163804, 
                                                          root := ~, 
                                                          start := 163787, 
                                                          stop := 163803 ), 
                                                      rec( 
                                                          content := " returns\
 an immutable list ", count := [ 5, 2, 8, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 163841, 
                                                          root := ~, 
                                                          start := 163831, 
                                                          stop := 163840 ), 
                                                      rec( 
                                                          content := " of leng\
th ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 163860, 
                                                          root := ~, 
                                                          start := 163852, 
                                                          stop := 163859 ), 
                                                      rec( 
                                                          content := ", such t\
hat\n    for a vertex ", count := [ 5, 2, 8, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 163897, 
                                                          root := ~, 
                                                          start := 163889, 
                                                          stop := 163896 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 163915, 
                                                          root := ~, 
                                                          start := 163901, 
                                                          stop := 163914 ), 
                                                      rec( 
                                                          content := ", the va\
lue of ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut[i]", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 163943, 
                                                          root := ~, 
                                                          start := 163930, 
                                                          stop := 163942 ), 
                                                      rec( 
                                                          content := " is the\\
n    out-degree of vertex ", count := [ 5, 2, 8, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 163984, 
                                                          root := ~, 
                                                          start := 163976, 
                                                          stop := 163983 ), 
                                                      rec( 
                                                          content := ".\n    S\
ee ", count := [ 5, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "OutDegr\
eeOfVertex" ), content := 0, count := [ 5, 2, 8, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 164025, 
                                                          root := ~, 
                                                          start := 163994, 
                                                          stop := 164024 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 164031, 
                                                          root := ~, 
                                                          start := 164027, 
                                                          stop := 164030 ), 
                                                      rec( 
                                                          content := "\n\n    \
The function ", count := [ 5, 2, 8, 8 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
utDegreeSequence", count := [ 5, 2, 8, 8 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 5, 2, 8, 8 ], mathmode := "Text", name := "C", 
                                                          next := 164074, 
                                                          root := ~, 
                                                          start := 164050, 
                                                          stop := 164073 ), 
                                                      rec( 
                                                          content := " returns\
 the same list,\n    after it has been sorted into non-increasing order. ", 
                                                          count := 
                                                            [ 5, 2, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 8, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 164158, 
                                                          root := ~, 
                                                          start := 164154, 
                                                          stop := 164157 ), 
                                                      rec( 
                                                          content := "\n\n    \
The function ", count := [ 5, 2, 8, 9 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
utDegreeSet", count := [ 5, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 164196, 
                                                          root := ~, 
                                                          start := 164177, 
                                                          stop := 164195 ), 
                                                      rec( 
                                                          content := " returns\
 the same list, sorted into\n    increasing order with duplicate entries remov\
ed. ", count := [ 5, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 8, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 164289, 
                                                          root := ~, 
                                                          start := 164285, 
                                                          stop := 164288 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 2, 8, 10 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 3, 2, 2], [], [2, 1], []]);\n<immutable multidigraph w\
ith 4 vertices, 6 edges>\ngap> OutDegrees(D);\n[ 4, 0, 2, 0 ]\ngap> OutDegreeS\
equence(D);\n[ 4, 2, 0, 0 ]\ngap> OutDegreeSet(D);\n[ 0, 2, 4 ]\ngap> D := Cyc\
leDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ng\
ap> OutDegrees(D);\n[ 1, 1, 1 ]\n", count := [ 5, 2, 8, 11 ], name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 164659, 
                                                          root := ~, 
                                                          start := 164295, 
                                                          stop := 164658 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 8, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 164676, root := ~, 
                                                  start := 163696, 
                                                  stop := 164675 ) ], 
                                          count := [ 5, 2, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 164690, root := ~, 
                                          start := 163492, stop := 164689 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 8, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "InDegrees" ), 
                                                  content := 0, 
                                                  count := [ 5, 2, 9, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 164749, root := ~, 
                                                  start := 164711, 
                                                  stop := 164748 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "InDegreeSequenc\
e" ), content := 0, count := [ 5, 2, 9, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 164797, root := ~, 
                                                  start := 164752, 
                                                  stop := 164796 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "InDegreeSet" ),
                                                  content := 0, 
                                                  count := [ 5, 2, 9, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 164840, root := ~, 
                                                  start := 164800, 
                                                  stop := 164839 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 non-negative integers.", count := [ 5, 2, 9, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 9, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 164894, root := ~, 
                                                  start := 164843, 
                                                  stop := 164893 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\n    G\
iven a digraph ", count := [ 5, 2, 9, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 164946, 
                                                          root := ~, 
                                                          start := 164932, 
                                                          stop := 164945 ), 
                                                      rec( 
                                                          content := " with ",
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 164960, 
                                                          root := ~, 
                                                          start := 164952, 
                                                          stop := 164959 ), 
                                                      rec( 
                                                          content := " vertice\
s, the function\n    ", count := [ 5, 2, 9, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
nDegrees", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 165004, 
                                                          root := ~, 
                                                          start := 164988, 
                                                          stop := 165003 ), 
                                                      rec( 
                                                          content := " returns\
 an immutable list ", count := [ 5, 2, 9, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nn", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 165041, 
                                                          root := ~, 
                                                          start := 165031, 
                                                          stop := 165040 ), 
                                                      rec( 
                                                          content := " of leng\
th ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 165060, 
                                                          root := ~, 
                                                          start := 165052, 
                                                          stop := 165059 ), 
                                                      rec( 
                                                          content := ", such t\
hat\n    for a vertex ", count := [ 5, 2, 9, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 165097, 
                                                          root := ~, 
                                                          start := 165089, 
                                                          stop := 165096 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 165115, 
                                                          root := ~, 
                                                          start := 165101, 
                                                          stop := 165114 ), 
                                                      rec( 
                                                          content := ", the va\
lue of ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nn[i]", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 165143, 
                                                          root := ~, 
                                                          start := 165130, 
                                                          stop := 165142 ), 
                                                      rec( 
                                                          content := " is\n   \
 the in-degree of vertex ", count := [ 5, 2, 9, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 165183, 
                                                          root := ~, 
                                                          start := 165175, 
                                                          stop := 165182 ), 
                                                      rec( 
                                                          content := ".\n    S\
ee ", count := [ 5, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "InDegre\
eOfVertex" ), content := 0, count := [ 5, 2, 9, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 165223, 
                                                          root := ~, 
                                                          start := 165193, 
                                                          stop := 165222 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 165229, 
                                                          root := ~, 
                                                          start := 165225, 
                                                          stop := 165228 ), 
                                                      rec( 
                                                          content := "\n\n    \
The function ", count := [ 5, 2, 9, 8 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
nDegreeSequence", count := [ 5, 2, 9, 8 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 5, 2, 9, 8 ], mathmode := "Text", name := "C", 
                                                          next := 165271, 
                                                          root := ~, 
                                                          start := 165248, 
                                                          stop := 165270 ), 
                                                      rec( 
                                                          content := " returns\
 the same list,\n    after it has been sorted into non-increasing order. ", 
                                                          count := 
                                                            [ 5, 2, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 9, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 165355, 
                                                          root := ~, 
                                                          start := 165351, 
                                                          stop := 165354 ), 
                                                      rec( 
                                                          content := "\n\n    \
The function ", count := [ 5, 2, 9, 9 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
nDegreeSet", count := [ 5, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 9, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 165392, 
                                                          root := ~, 
                                                          start := 165374, 
                                                          stop := 165391 ), 
                                                      rec( 
                                                          content := " returns\
 the same list, sorted into\n    increasing order with duplicate entries remov\
ed. ", count := [ 5, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 9, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 165485, 
                                                          root := ~, 
                                                          start := 165481, 
                                                          stop := 165484 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 2, 9, 10 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 3, 2, 2, 4], [], [2, 1, 4], []]);\n<immutable multidig\
raph with 4 vertices, 8 edges>\ngap> InDegrees(D);\n[ 2, 3, 1, 2 ]\ngap> InDeg\
reeSequence(D);\n[ 3, 2, 2, 1 ]\ngap> InDegreeSet(D);\n[ 1, 2, 3 ]\ngap> D := \
CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\
\ngap> InDegrees(D);\n[ 1, 1, 1 ]\n", count := [ 5, 2, 9, 11 ], name := "PCDAT\
A", root := ~ ) ], count := [ 5, 2, 9, 11 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 165857, 
                                                          root := ~, 
                                                          start := 165491, 
                                                          stop := 165856 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 9, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 9, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 165874, root := ~, 
                                                  start := 164897, 
                                                  stop := 165873 ) ], 
                                          count := [ 5, 2, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 165888, root := ~, 
                                          start := 164696, stop := 165887 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 9, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "OutDegreeOfVert\
ex" ), content := 0, count := [ 5, 2, 10, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 165963, root := ~, 
                                                  start := 165909, 
                                                  stop := 165962 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "The non-n\
egative integer.", count := [ 5, 2, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 166010, root := ~, 
                                                  start := 165966, 
                                                  stop := 166009 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns the out-degree of the vertex ", count := [ 5, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 166096, 
                                                          root := ~, 
                                                          start := 166083, 
                                                          stop := 166095 ), 
                                                      rec( 
                                                          content := " in the\\
n    digraph ", count := [ 5, 2, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 166130, 
                                                          root := ~, 
                                                          start := 166116, 
                                                          stop := 166129 ), 
                                                      rec( 
                                                          content := ".\n    T\
he out-degree of ", count := [ 5, 2, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 166167, 
                                                          root := ~, 
                                                          start := 166154, 
                                                          stop := 166166 ), 
                                                      rec( 
                                                          content := " is the \
number of edges in ", count := [ 5, 2, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 166208, 
                                                          root := ~, 
                                                          start := 166194, 
                                                          stop := 166207 ), 
                                                      rec( 
                                                          content := "\n    wh\
ose source is ", count := [ 5, 2, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 166242, 
                                                          root := ~, 
                                                          start := 166229, 
                                                          stop := 166241 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 166252, 
                                                          root := ~, 
                                                          start := 166248, 
                                                          stop := 166251 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\n> [2, 2, 1], [1, 4], [2, 2, 4, 2], [1, 1, 2, 2, 1, 2, 2]\
]);\n<immutable multidigraph with 4 vertices, 16 edges>\ngap> OutDegreeOfVerte\
x(D, 1);\n3\ngap> OutDegreeOfVertex(D, 2);\n2\ngap> OutDegreeOfVertex(D, 3);\n\
4\ngap> OutDegreeOfVertex(D, 4);\n7\n", count := [ 5, 2, 10, 5 ], name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 10, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 166548, 
                                                          root := ~, 
                                                          start := 166257, 
                                                          stop := 166547 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 166565, root := ~, 
                                                  start := 166013, 
                                                  stop := 166564 ) ], 
                                          count := [ 5, 2, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 166579, root := ~, 
                                          start := 165894, stop := 166578 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 10, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "OutNeighboursOf\
Vertex" ), content := 0, count := [ 5, 2, 11, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 166658, root := ~, 
                                                  start := 166600, 
                                                  stop := 166657 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "OutNeighborsOfV\
ertex" ), content := 0, count := [ 5, 2, 11, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 166718, root := ~, 
                                                  start := 166661, 
                                                  stop := 166717 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 vertices.", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 166759, root := ~, 
                                                  start := 166721, 
                                                  stop := 166758 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\n    T\
his operation returns the list ", count := [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 166823, 
                                                          root := ~, 
                                                          start := 166813, 
                                                          stop := 166822 ), 
                                                      rec( 
                                                          content := " of vert\
ices of the digraph\n    ", count := [ 5, 2, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 166869, 
                                                          root := ~, 
                                                          start := 166855, 
                                                          stop := 166868 ), 
                                                      rec( 
                                                          content := ".\n    A\
 vertex ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 166892, 
                                                          root := ~, 
                                                          start := 166884, 
                                                          stop := 166891 ), 
                                                      rec( 
                                                          content := " appears\
 in the list ", count := [ 5, 2, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 166923, 
                                                          root := ~, 
                                                          start := 166913, 
                                                          stop := 166922 ), 
                                                      rec( 
                                                          content := " each ti\
me there exists an\n    edge  with source ", count := [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 166985, 
                                                          root := ~, 
                                                          start := 166972, 
                                                          stop := 166984 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 167004, 
                                                          root := ~, 
                                                          start := 166996, 
                                                          stop := 167003 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 167022, 
                                                          root := ~, 
                                                          start := 167008, 
                                                          stop := 167021 ), 
                                                      rec( 
                                                          content := "; in\n  \
  particular, this means that ", count := [ 5, 2, 11, 5 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut", count := [ 5, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 167069, 
                                                          root := ~, 
                                                          start := 167059, 
                                                          stop := 167068 ), 
                                                      rec( 
                                                          content := " may con\
tain duplicates.", count := [ 5, 2, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 167097, 
                                                          root := ~, 
                                                          start := 167093, 
                                                          stop := 167096 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 2, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\n> [2, 2, 3], [1, 3, 4], [2, 2, 3], [1, 1, 2, 2, 1, 2, 2]\
]);\n<immutable multidigraph with 4 vertices, 16 edges>\ngap> OutNeighboursOfV\
ertex(D, 1);\n[ 2, 2, 3 ]\ngap> OutNeighboursOfVertex(D, 3);\n[ 2, 2, 3 ]\n", 
                                                                  count := 
                                                                    [ 5, 2, 
                                                                      11, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 2, 11, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 167357, 
                                                          root := ~, 
                                                          start := 167102, 
                                                          stop := 167356 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 11, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 167374, root := ~, 
                                                  start := 166762, 
                                                  stop := 167373 ) ], 
                                          count := [ 5, 2, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 167388, root := ~, 
                                          start := 166585, stop := 167387 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 11, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "InDegreeOfVerte\
x" ), content := 0, count := [ 5, 2, 12, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 167462, root := ~, 
                                                  start := 167409, 
                                                  stop := 167461 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A non-neg\
ative integer.", count := [ 5, 2, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 167507, root := ~, 
                                                  start := 167465, 
                                                  stop := 167506 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns the in-degree of the vertex ", count := [ 5, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 167592, 
                                                          root := ~, 
                                                          start := 167579, 
                                                          stop := 167591 ), 
                                                      rec( 
                                                          content := " in the\\
n    digraph ", count := [ 5, 2, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 167626, 
                                                          root := ~, 
                                                          start := 167612, 
                                                          stop := 167625 ), 
                                                      rec( 
                                                          content := ".\n    T\
he in-degree of ", count := [ 5, 2, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 167662, 
                                                          root := ~, 
                                                          start := 167649, 
                                                          stop := 167661 ), 
                                                      rec( 
                                                          content := " is the \
number of edges in ", count := [ 5, 2, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 167703, 
                                                          root := ~, 
                                                          start := 167689, 
                                                          stop := 167702 ), 
                                                      rec( 
                                                          content := "\n    wh\
ose range is ", count := [ 5, 2, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 167736, 
                                                          root := ~, 
                                                          start := 167723, 
                                                          stop := 167735 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\n> [2, 2, 1], [1, 4], [2, 2, 4, 2], [1, 1, 2, 2, 1, 2, 2]\
]);\n<immutable multidigraph with 4 vertices, 16 edges>\ngap> InDegreeOfVertex\
(D, 1);\n5\ngap> InDegreeOfVertex(D, 2);\n9\ngap> InDegreeOfVertex(D, 3);\n0\n\
gap> InDegreeOfVertex(D, 4);\n2\n", count := [ 5, 2, 12, 4 ], name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 168029, 
                                                          root := ~, 
                                                          start := 167742, 
                                                          stop := 168028 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 168046, root := ~, 
                                                  start := 167510, 
                                                  stop := 168045 ) ], 
                                          count := [ 5, 2, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 168060, root := ~, 
                                          start := 167394, stop := 168059 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 12, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "InNeighboursOfV\
ertex" ), content := 0, count := [ 5, 2, 13, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 168138, root := ~, 
                                                  start := 168081, 
                                                  stop := 168137 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "InNeighborsOfVe\
rtex" ), content := 0, count := [ 5, 2, 13, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 168197, root := ~, 
                                                  start := 168141, 
                                                  stop := 168196 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 postitive vertices.", count := [ 5, 2, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 13, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 168248, root := ~, 
                                                  start := 168200, 
                                                  stop := 168247 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\n    T\
his operation returns the list ", count := [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nn", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 168312, 
                                                          root := ~, 
                                                          start := 168302, 
                                                          stop := 168311 ), 
                                                      rec( 
                                                          content := " of vert\
ices of the digraph\n    ", count := [ 5, 2, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 168358, 
                                                          root := ~, 
                                                          start := 168344, 
                                                          stop := 168357 ), 
                                                      rec( 
                                                          content := ".\n    A\
 vertex ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 168381, 
                                                          root := ~, 
                                                          start := 168373, 
                                                          stop := 168380 ), 
                                                      rec( 
                                                          content := " appears\
 in the list ", count := [ 5, 2, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nn", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 168412, 
                                                          root := ~, 
                                                          start := 168402, 
                                                          stop := 168411 ), 
                                                      rec( 
                                                          content := " each ti\
me there exists an\n    edge  with source ", count := [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 168469, 
                                                          root := ~, 
                                                          start := 168461, 
                                                          stop := 168468 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 168493, 
                                                          root := ~, 
                                                          start := 168480, 
                                                          stop := 168492 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 168511, 
                                                          root := ~, 
                                                          start := 168497, 
                                                          stop := 168510 ), 
                                                      rec( 
                                                          content := "; in\n  \
  particular, this means that ", count := [ 5, 2, 13, 5 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nn", count := [ 5, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 168558, 
                                                          root := ~, 
                                                          start := 168548, 
                                                          stop := 168557 ), 
                                                      rec( 
                                                          content := " may con\
tain duplicates. ", count := [ 5, 2, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 168587, 
                                                          root := ~, 
                                                          start := 168583, 
                                                          stop := 168586 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\n> [2, 2, 3], [1, 3, 4], [2, 2, 3], [1, 1, 2, 2, 1, 2, 2]\
]);\n<immutable multidigraph with 4 vertices, 16 edges>\ngap> InNeighboursOfVe\
rtex(D, 1);\n[ 2, 4, 4, 4 ]\ngap> InNeighboursOfVertex(D, 2);\n[ 1, 1, 3, 3, 4\
, 4, 4, 4 ]\n", count := [ 5, 2, 13, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 2, 13, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 168864, 
                                                          root := ~, 
                                                          start := 168593, 
                                                          stop := 168863 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 13, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 13, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 168881, root := ~, 
                                                  start := 168251, 
                                                  stop := 168880 ) ], 
                                          count := [ 5, 2, 13, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 168895, root := ~, 
                                          start := 168066, stop := 168894 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 13, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphLoops" )
                                                    , content := 0, 
                                                  count := [ 5, 2, 14, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 168957, root := ~, 
                                                  start := 168916, 
                                                  stop := 168956 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 vertices.", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 168998, root := ~, 
                                                  start := 168960, 
                                                  stop := 168997 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 169036, 
                                                          root := ~, 
                                                          start := 169022, 
                                                          stop := 169035 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphLoops", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 169075, 
                                                          root := ~, 
                                                          start := 169056, 
                                                          stop := 169074 ), 
                                                      rec( 
                                                          content := " returns\
 the list\n    consisting of the ", count := [ 5, 2, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Vertices" ), content := 0, count := [ 5, 2, 14, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 169144, 
                                                          root := ~, 
                                                          start := 169115, 
                                                          stop := 169143 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 5, 2, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 169162, 
                                                          root := ~, 
                                                          start := 169148, 
                                                          stop := 169161 ), 
                                                      rec( 
                                                          content := "\n    at\
 which there is a loop. See ", count := [ 5, 2, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ 5, 2, 14, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 169226, 
                                                          root := ~, 
                                                          start := 169197, 
                                                          stop := 169225 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 2, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 169232, 
                                                          root := ~, 
                                                          start := 169228, 
                                                          stop := 169231 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 2, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2], [3], []]);\n<immutable digraph with 3 vertices, 2 edg\
es>\ngap> DigraphHasLoops(D);\nfalse\ngap> DigraphLoops(D);\n[  ]\ngap> D := D\
igraph([[3, 5], [1], [2, 4, 3], [4], [2, 1]]);\n<immutable digraph with 5 vert\
ices, 9 edges>\ngap> DigraphLoops(D);\n[ 3, 4 ]\ngap> D := Digraph(IsMutableDi\
graph, [[1], [1]]);\n<mutable digraph with 2 vertices, 2 edges>\ngap> DigraphL\
oops(D);\n[ 1 ]\n", count := [ 5, 2, 14, 5 ], name := "PCDATA", root := ~ ) ],
                                                          count := 
                                                            [ 5, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 169662, 
                                                          root := ~, 
                                                          start := 169238, 
                                                          stop := 169661 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 169679, root := ~, 
                                                  start := 169001, 
                                                  stop := 169678 ) ], 
                                          count := [ 5, 2, 14, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 169693, root := ~, 
                                          start := 168901, stop := 169692 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 14, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, u, v", 
                                                      Name := "PartialOrderDig\
raphMeetOfVertices" ), content := 0, count := [ 5, 2, 15, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 169786, root := ~, 
                                                  start := 169714, 
                                                  stop := 169785 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, u, v", 
                                                      Name := "PartialOrderDig\
raphJoinOfVertices" ), content := 0, count := [ 5, 2, 15, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 169861, root := ~, 
                                                  start := 169789, 
                                                  stop := 169860 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A positiv\
e integer or ", count := [ 5, 2, 15, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 169906, 
                                                          root := ~, 
                                                          start := 169895, 
                                                          stop := 169905 ) ], 
                                                  count := [ 5, 2, 15, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 169916, root := ~, 
                                                  start := 169864, 
                                                  stop := 169915 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
the first argument is a partial order digraph ", count := [ 5, 2, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsParti\
alOrderDigraph" ), content := 0, count := [ 5, 2, 15, 5 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 170027, 
                                                          root := ~, 
                                                          start := 169988, 
                                                          stop := 170026 ), 
                                                      rec( 
                                                          content := " then th\
ese operations return the meet, or\n    the join, of the two input vertices. I\
f the meet (or join) is does not\n    exist then ", count := [ 5, 2, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 170171, 
                                                          root := ~, 
                                                          start := 170160, 
                                                          stop := 170170 ), 
                                                      rec( 
                                                          content := " is retu\
rned. The meet (or join) is guaranteed to\n    exist when the first argument s\
atisfies\n    ", count := [ 5, 2, 15, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsMeetS\
emilatticeDigraph" ), content := 0, count := [ 5, 2, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 170307, 
                                                          root := ~, 
                                                          start := 170269, 
                                                          stop := 170306 ), 
                                                      rec( 
                                                          content := "  (or\n \
   ", count := [ 5, 2, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsJoinS\
emilatticeDigraph" ), content := 0, count := [ 5, 2, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 170355, 
                                                          root := ~, 
                                                          start := 170317, 
                                                          stop := 170354 ), 
                                                      rec( 
                                                          content := ") - see \
the documentation for these\n    properties for the definition of the meet (or\
 the join).\n\n    ", count := [ 5, 2, 15, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1], [1, 2], [1, 3], [1, 2, 3, 4]]);\n<immutable digraph w\
ith 4 vertices, 9 edges>\ngap> PartialOrderDigraphMeetOfVertices(D, 2, 3);\n4\
\ngap> PartialOrderDigraphJoinOfVertices(D, 2, 3);\n1\ngap> PartialOrderDigrap\
hMeetOfVertices(D, 1, 2);\n2\ngap> PartialOrderDigraphJoinOfVertices(D, 3, 4);\
\n3\ngap> D := Digraph([[1], [2], [1, 2, 3], [1, 2, 4]]);\n<immutable digraph \
with 4 vertices, 8 edges>\ngap> PartialOrderDigraphMeetOfVertices(D, 3, 4);\nf\
ail\ngap> PartialOrderDigraphJoinOfVertices(D, 3, 4);\nfail\ngap> PartialOrder\
DigraphMeetOfVertices(D, 1, 2);\nfail\ngap> PartialOrderDigraphJoinOfVertices(\
D, 1, 2);\nfail\n", count := [ 5, 2, 15, 6 ], name := "PCDATA", root := ~ ) ],
                                                          count := 
                                                            [ 5, 2, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 171108, 
                                                          root := ~, 
                                                          start := 170457, 
                                                          stop := 171107 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 15, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 171125, root := ~, 
                                                  start := 169921, 
                                                  stop := 171124 ) ], 
                                          count := [ 5, 2, 15, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 171139, root := ~, 
                                          start := 169699, stop := 171138 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 15, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DegreeMatrix" )
                                                    , content := 0, 
                                                  count := [ 5, 2, 16, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 171201, root := ~, 
                                                  start := 171160, 
                                                  stop := 171200 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A square \
matrix of non-negative integers.", count := [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 16, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 171264, root := ~, 
                                                  start := 171204, 
                                                  stop := 171263 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the outdegree matrix ", count := [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 171338, 
                                                          root := ~, 
                                                          start := 171328, 
                                                          stop := 171337 ), 
                                                      rec( 
                                                          content := " of the \
digraph\n    ", count := [ 5, 2, 16, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 171372, 
                                                          root := ~, 
                                                          start := 171358, 
                                                          stop := 171371 ), 
                                                      rec( 
                                                          content := ". The va\
lue of the ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 171399, 
                                                          root := ~, 
                                                          start := 171391, 
                                                          stop := 171398 ), 
                                                      rec( 
                                                          content := "th diago\
nal matrix entry is the\n    outdegree of the vertex ", count := 
                                                            [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 171467, 
                                                          root := ~, 
                                                          start := 171459, 
                                                          stop := 171466 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 171485, 
                                                          root := ~, 
                                                          start := 171471, 
                                                          stop := 171484 ), 
                                                      rec( 
                                                          content := ". All of\
f-diagonal entries \n    are ", count := [ 5, 2, 16, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 171529, 
                                                          root := ~, 
                                                          start := 171521, 
                                                          stop := 171528 ), 
                                                      rec( 
                                                          content := ".\n    I\
f ", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 171552, 
                                                          root := ~, 
                                                          start := 171538, 
                                                          stop := 171551 ), 
                                                      rec( 
                                                          content := " has no \
vertices, then the empty list is returned. ", count := [ 5, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 16, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 171607, 
                                                          root := ~, 
                                                          start := 171603, 
                                                          stop := 171606 ), 
                                                      rec( 
                                                          content := "\n\n    \
See ", count := [ 5, 2, 16, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "OutDegr\
ees" ), content := 0, count := [ 5, 2, 16, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 171641, 
                                                          root := ~, 
                                                          start := 171617, 
                                                          stop := 171640 ), 
                                                      rec( 
                                                          content := " for mor\
e information.\n    ", count := [ 5, 2, 16, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2, 3], [4], [1, 3, 4], []]);\n<immutable digraph with \
4 vertices, 7 edges>\ngap> PrintArray(DegreeMatrix(D));\n[ [  3,  0,  0,  0 ],\
\n  [  0,  1,  0,  0 ],\n  [  0,  0,  3,  0 ],\n  [  0,  0,  0,  0 ] ]\ngap> D\
 := CycleDigraph(5);;\ngap> PrintArray(DegreeMatrix(D));\n[ [  1,  0,  0,  0, \
 0 ],\n  [  0,  1,  0,  0,  0 ],\n  [  0,  0,  1,  0,  0 ],\n  [  0,  0,  0,  \
1,  0 ],\n  [  0,  0,  0,  0,  1 ] ]\ngap> DegreeMatrix(EmptyDigraph(0));\n[  \
]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 verti\
ces, 3 edges>\ngap> Display(DegreeMatrix(D));\n[ [  1,  0,  0 ],\n  [  0,  1, \
 0 ],\n  [  0,  0,  1 ] ]\n", count := [ 5, 2, 16, 5 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 172328, 
                                                          root := ~, 
                                                          start := 171668, 
                                                          stop := 172327 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 16, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 172345, root := ~, 
                                                  start := 171267, 
                                                  stop := 172344 ) ], 
                                          count := [ 5, 2, 16, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 172359, root := ~, 
                                          start := 171145, stop := 172358 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 2, 16, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "LaplacianMatrix\
" ), content := 0, count := [ 5, 2, 17, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 172424, root := ~, 
                                                  start := 172380, 
                                                  stop := 172423 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A square \
matrix of integers.", count := [ 5, 2, 17, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 172474, root := ~, 
                                                  start := 172427, 
                                                  stop := 172473 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the outdegree Laplacian matrix ", count := [ 5, 2, 17, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 172558, 
                                                          root := ~, 
                                                          start := 172548, 
                                                          stop := 172557 ), 
                                                      rec( 
                                                          content := " of the\\
n    digraph ", count := [ 5, 2, 17, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 172592, 
                                                          root := ~, 
                                                          start := 172578, 
                                                          stop := 172591 ), 
                                                      rec( 
                                                          content := ". The ou\
tdegree Laplacian matrix is defined as\n    ", count := [ 5, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
egreeMatrix(digraph) - AdjacencyMatrix(digraph)", count := [ 5, 2, 17, 3 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 5, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 172698, 
                                                          root := ~, 
                                                          start := 172643, 
                                                          stop := 172697 ), 
                                                      rec( 
                                                          content := ".  If\n \
   ", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 172722, 
                                                          root := ~, 
                                                          start := 172708, 
                                                          stop := 172721 ), 
                                                      rec( 
                                                          content := " has no \
vertices, then the empty list is returned. ", count := [ 5, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 172777, 
                                                          root := ~, 
                                                          start := 172773, 
                                                          stop := 172776 ), 
                                                      rec( 
                                                          content := "\n\n    \
See ", count := [ 5, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "DegreeM\
atrix" ), content := 0, count := [ 5, 2, 17, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 172813, 
                                                          root := ~, 
                                                          start := 172787, 
                                                          stop := 172812 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Adjacen\
cyMatrix" ), content := 0, count := [ 5, 2, 17, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 172847, 
                                                          root := ~, 
                                                          start := 172818, 
                                                          stop := 172846 ), 
                                                      rec( 
                                                          content := " for mor\
e\n    information.\n    ", count := [ 5, 2, 17, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[1, 2, 3], [4], [1, 3, 4], []]);\n<immutable digraph with\
 4 vertices, 7 edges>\ngap> PrintArray(LaplacianMatrix(gr));\n[ [   2,  -1,  -\
1,   0 ],\n  [   0,   1,   0,  -1 ],\n  [  -1,   0,   2,  -1 ],\n  [   0,   0,\
   0,   0 ] ]\ngap> LaplacianMatrix(EmptyDigraph(0));\n[  ]\ngap> D := CycleDi\
graph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> \
Display(LaplacianMatrix(D));\n[ [   1,  -1,   0 ],\n  [   0,   1,  -1 ],\n  [ \
 -1,   0,   1 ] ]\n", count := [ 5, 2, 17, 5 ], name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 2, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 173381, 
                                                          root := ~, 
                                                          start := 172878, 
                                                          stop := 173380 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 2, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 2, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 173398, root := ~, 
                                                  start := 172477, 
                                                  stop := 173397 ) ], 
                                          count := [ 5, 2, 17, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 173412, root := ~, 
                                          start := 172365, stop := 173411 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 5, 2, 17, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 5, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 173426, 
                                  root := ~, start := 153194, stop := 173425 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 5, 2, 17, 6 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Reachability and \
connectivity", count := [ 5, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 5, 3, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 173487, 
                                          root := ~, start := 173439, 
                                          stop := 173486 ), 
                                      rec( content := "\n    ", 
                                          count := [ 5, 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphDiameter\
" ), content := 0, count := [ 5, 3, 1, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 173551, root := ~, 
                                                  start := 173507, 
                                                  stop := 173550 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r or ", count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 173588, 
                                                          root := ~, 
                                                          start := 173577, 
                                                          stop := 173587 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 173599, root := ~, 
                                                  start := 173554, 
                                                  stop := 173598 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the diameter of the digraph ", count := [ 5, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 173684, 
                                                          root := ~, 
                                                          start := 173670, 
                                                          stop := 173683 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 173694, 
                                                          root := ~, 
                                                          start := 173690, 
                                                          stop := 173693 ), 
                                                      rec( 
                                                          content := "\n\n    \
If a digraph ", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 173727, 
                                                          root := ~, 
                                                          start := 173713, 
                                                          stop := 173726 ), 
                                                      rec( 
                                                          content := " is stro\
ngly connected and has at least 1\n    vertex, then the ", 
                                                          count := 
                                                            [ 5, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
iameter", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 173805, 
                                                          root := ~, 
                                                          start := 173790, 
                                                          stop := 173804 ), 
                                                      rec( 
                                                          content := " is the \
maximum shortest distance between\n    any pair of distinct vertices. Otherwis\
e then the diameter of\n    ", count := [ 5, 3, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 173931, 
                                                          root := ~, 
                                                          start := 173917, 
                                                          stop := 173930 ), 
                                                      rec( 
                                                          content := " is unde\
fined, and this function returns the value\n    ", count := [ 5, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 173997, 
                                                          root := ~, 
                                                          start := 173986, 
                                                          stop := 173996 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 174003, 
                                                          root := ~, 
                                                          start := 173999, 
                                                          stop := 174002 ), 
                                                      rec( 
                                                          content := "\n\n    \
See ", count := [ 5, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
ShortestDistances" ), content := 0, count := [ 5, 3, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 174051, 
                                                          root := ~, 
                                                          start := 174013, 
                                                          stop := 174050 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 174057, 
                                                          root := ~, 
                                                          start := 174053, 
                                                          stop := 174056 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 3, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2], [3], [4, 5], [5], [1, 2, 3, 4, 5]]);\n<immutable digr\
aph with 5 vertices, 10 edges>\ngap> DigraphDiameter(D);\n3\ngap> D := ChainDi\
graph(2);\n<immutable chain digraph with 2 vertices>\ngap> DigraphDiameter(D);\
\nfail\ngap> IsStronglyConnectedDigraph(D);\nfalse\ngap> D := GeneralisedPeter\
senGraph(IsMutableDigraph, 6, 2);\n<mutable digraph with 12 vertices, 36 edges\
>\ngap> DigraphDiameter(D);\n4\n", count := [ 5, 3, 1, 7 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 174501, 
                                                          root := ~, 
                                                          start := 174062, 
                                                          stop := 174500 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 174518, root := ~, 
                                                  start := 173602, 
                                                  stop := 174517 ) ], 
                                          count := [ 5, 3, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 174532, root := ~, 
                                          start := 173492, stop := 174531 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 1, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, u, v", 
                                                      Label := "for a digraph \
and two vertices", Name := "DigraphShortestDistance" ), content := 0, 
                                                  count := [ 5, 3, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 174658, root := ~, 
                                                  start := 174553, 
                                                  stop := 174657 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list", 
                                                      Label := "for a digraph \
and a list", Name := "DigraphShortestDistance" ), content := 0, 
                                                  count := [ 5, 3, 2, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 174760, root := ~, 
                                                  start := 174661, 
                                                  stop := 174759 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list1, \
list2", Label := "for a digraph, a list, and a list", Name := "DigraphShortest\
Distance" ), content := 0, count := [ 5, 3, 2, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 174879, root := ~, 
                                                  start := 174763, 
                                                  stop := 174878 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r or ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 174916, 
                                                          root := ~, 
                                                          start := 174905, 
                                                          stop := 174915 ) ], 
                                                  count := [ 5, 3, 2, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 174926, root := ~, 
                                                  start := 174882, 
                                                  stop := 174925 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
there is a directed path in the digraph ", count := [ 5, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175004, 
                                                          root := ~, 
                                                          start := 174990, 
                                                          stop := 175003 ), 
                                                      rec( 
                                                          content := " between\
 vertex\n    ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175032, 
                                                          root := ~, 
                                                          start := 175024, 
                                                          stop := 175031 ), 
                                                      rec( 
                                                          content := " and ver\
tex ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175052, 
                                                          root := ~, 
                                                          start := 175044, 
                                                          stop := 175051 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns the length of the\n    shortest such directed path.  If \
no such directed path exists, then this\n    operation returns ", 
                                                          count := 
                                                            [ 5, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 175210, 
                                                          root := ~, 
                                                          start := 175199, 
                                                          stop := 175209 ), 
                                                      rec( 
                                                          content := ". See Se\
ction ", count := [ 5, 3, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 175274, 
                                                          root := ~, 
                                                          start := 175224, 
                                                          stop := 175273 ), 
                                                      rec( 
                                                          content := " for the\
 definition of a directed path. ", count := [ 5, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 175318, 
                                                          root := ~, 
                                                          start := 175314, 
                                                          stop := 175317 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the second form is used, then ", count := [ 5, 3, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175368, 
                                                          root := ~, 
                                                          start := 175357, 
                                                          stop := 175367 ), 
                                                      rec( 
                                                          content := " should \
be a list of length two,\n    containing two positive integers which correspon\
d to the vertices ", count := [ 5, 3, 2, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175479, 
                                                          root := ~, 
                                                          start := 175471, 
                                                          stop := 175478 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175496, 
                                                          root := ~, 
                                                          start := 175488, 
                                                          stop := 175495 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 175502, 
                                                          root := ~, 
                                                          start := 175498, 
                                                          stop := 175501 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that as usual, a vertex is considered to be at distance 0 from\n    itsel\
f .", count := [ 5, 3, 2, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 175592, 
                                                          root := ~, 
                                                          start := 175588, 
                                                          stop := 175591 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the third form is used, then ", count := [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist1", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175642, 
                                                          root := ~, 
                                                          start := 175630, 
                                                          stop := 175641 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist2", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175659, 
                                                          root := ~, 
                                                          start := 175647, 
                                                          stop := 175658 ), 
                                                      rec( 
                                                          content := " are bot\
h lists\n    of vertices. The shortest directed path between ", 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist1", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175739, 
                                                          root := ~, 
                                                          start := 175727, 
                                                          stop := 175738 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist2", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175760, 
                                                          root := ~, 
                                                          start := 175748, 
                                                          stop := 175759 ), 
                                                      rec( 
                                                          content := " is then\
 the length of the shortest directed path which starts\n    with a vertex in "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist1", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175856, 
                                                          root := ~, 
                                                          start := 175844, 
                                                          stop := 175855 ), 
                                                      rec( 
                                                          content := " and ter\
minates at a vertex in ", count := [ 5, 3, 2, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist2", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175899, 
                                                          root := ~, 
                                                          start := 175887, 
                                                          stop := 175898 ), 
                                                      rec( 
                                                          content := ", if\n  \
  such directed path exists. If ", count := [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist1", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175950, 
                                                          root := ~, 
                                                          start := 175938, 
                                                          stop := 175949 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist2", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 175967, 
                                                          root := ~, 
                                                          start := 175955, 
                                                          stop := 175966 ), 
                                                      rec( 
                                                          content := " have no\
n-empty\n    intersection, the operation returns ", count := [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
", count := [ 5, 3, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 176031, 
                                                          root := ~, 
                                                          start := 176023, 
                                                          stop := 176030 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 2, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 176036, 
                                                          root := ~, 
                                                          start := 176032, 
                                                          stop := 176035 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 3, 2, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2], [3], [1, 4], [1, 3], [5]]);\n<immutable digraph with \
5 vertices, 7 edges>\ngap> DigraphShortestDistance(D, 1, 3);\n2\ngap> DigraphS\
hortestDistance(D, [3, 3]);\n0\ngap> DigraphShortestDistance(D, 5, 2);\nfail\n\
gap> DigraphShortestDistance(D, [1, 2], [4, 5]);\n2\ngap> DigraphShortestDista\
nce(D, [1, 3], [3, 5]);\n0\n", count := [ 5, 3, 2, 12 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 2, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 176400, 
                                                          root := ~, 
                                                          start := 176041, 
                                                          stop := 176399 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 2, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 2, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 176417, root := ~, 
                                                  start := 174929, 
                                                  stop := 176416 ) ], 
                                          count := [ 5, 3, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 176431, root := ~, 
                                          start := 174538, stop := 176430 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 2, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphShortest\
Distances" ), content := 0, count := [ 5, 3, 3, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 176505, root := ~, 
                                                  start := 176452, 
                                                  stop := 176504 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A square \
matrix.", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 176543, root := ~, 
                                                  start := 176508, 
                                                  stop := 176542 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 176581, 
                                                          root := ~, 
                                                          start := 176567, 
                                                          stop := 176580 ), 
                                                      rec( 
                                                          content := " is a di\
graph with ", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 176608, 
                                                          root := ~, 
                                                          start := 176600, 
                                                          stop := 176607 ), 
                                                      rec( 
                                                          content := " vertice\
s, then this\n    function returns an ", count := [ 5, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
 \\times n", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 176670, 
                                                          root := ~, 
                                                          start := 176653, 
                                                          stop := 176669 ), 
                                                      rec( 
                                                          content := " matrix \
", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 176688, 
                                                          root := ~, 
                                                          start := 176678, 
                                                          stop := 176687 ), 
                                                      rec( 
                                                          content := ", where \
each entry is\n    either a non-negative integer, or ", count := 
                                                            [ 5, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 176759, 
                                                          root := ~, 
                                                          start := 176748, 
                                                          stop := 176758 ), 
                                                      rec( 
                                                          content := ".  If ",
                                                          count := 
                                                            [ 5, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
 = 0", count := [ 5, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 176777, 
                                                          root := ~, 
                                                          start := 176765, 
                                                          stop := 176776 ), 
                                                      rec( 
                                                          content := ", then a\
n\n    empty list is returned. ", count := [ 5, 3, 3, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 176819, 
                                                          root := ~, 
                                                          start := 176815, 
                                                          stop := 176818 ), 
                                                      rec( 
                                                          content := "\n\n    \
If there is a directed path from vertex ", count := [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 176873, 
                                                          root := ~, 
                                                          start := 176865, 
                                                          stop := 176872 ), 
                                                      rec( 
                                                          content := " to vert\
ex ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 176892, 
                                                          root := ~, 
                                                          start := 176884, 
                                                          stop := 176891 ), 
                                                      rec( 
                                                          content := ", then\n\
    the value of ", count := [ 5, 3, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at[i][j]", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 176932, 
                                                          root := ~, 
                                                          start := 176916, 
                                                          stop := 176931 ), 
                                                      rec( 
                                                          content := " is the \
length of the shortest such directed\n    path. If no such directed path exist\
s, then the value of ", count := [ 5, 3, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at[i][j]", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 177054, 
                                                          root := ~, 
                                                          start := 177038, 
                                                          stop := 177053 ), 
                                                      rec( 
                                                          content := " is\n   \
 ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 177073, 
                                                          root := ~, 
                                                          start := 177062, 
                                                          stop := 177072 ), 
                                                      rec( 
                                                          content := ".  We us\
e the convention that the distance from every vertex to\n    itself is ", 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 177159, 
                                                          root := ~, 
                                                          start := 177151, 
                                                          stop := 177158 ), 
                                                      rec( 
                                                          content := ", i.e. "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at[i][i] = 0", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 177186, 
                                                          root := ~, 
                                                          start := 177166, 
                                                          stop := 177185 ), 
                                                      rec( 
                                                          content := " for all\
 vertices ", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 177212, 
                                                          root := ~, 
                                                          start := 177204, 
                                                          stop := 177211 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 177222, 
                                                          root := ~, 
                                                          start := 177218, 
                                                          stop := 177221 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this function is a version of the Floyd-Warshall\n    algor\
ithm, and has complexity ", count := [ 5, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(n^3)", count := [ 5, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 177343, 
                                                          root := ~, 
                                                          start := 177330, 
                                                          stop := 177342 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 5, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2], [3], [1, 2], [4]]);\n<immutable digraph with 4 ver\
tices, 6 edges>\ngap> mat := DigraphShortestDistances(D);;\ngap> PrintArray(ma\
t);\n[ [     0,     1,     2,  fail ],\n  [     2,     0,     1,  fail ],\n  [\
     1,     1,     0,  fail ],\n  [  fail,  fail,  fail,     0 ] ]\ngap> D := \
CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\
\ngap> DigraphShortestDistances(D);\n[ [ 0, 1, 2 ], [ 2, 0, 1 ], [ 1, 2, 0 ] ]\
\n", count := [ 5, 3, 3, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 177839, 
                                                          root := ~, 
                                                          start := 177350, 
                                                          stop := 177838 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 177856, root := ~, 
                                                  start := 176546, 
                                                  stop := 177855 ) ], 
                                          count := [ 5, 3, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 177870, root := ~, 
                                          start := 176437, stop := 177869 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 3, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, v", 
                                                      Name := "DigraphLongestD\
istanceFromVertex" ), content := 0, count := [ 5, 3, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 177955, root := ~, 
                                                  start := 177891, 
                                                  stop := 177954 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r, or ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 177997, 
                                                          root := ~, 
                                                          start := 177982, 
                                                          stop := 177996 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 178008, root := ~, 
                                                  start := 177958, 
                                                  stop := 178007 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 178046, 
                                                          root := ~, 
                                                          start := 178032, 
                                                          stop := 178045 ), 
                                                      rec( 
                                                          content := " is a di\
graph and ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 178072, 
                                                          root := ~, 
                                                          start := 178064, 
                                                          stop := 178071 ), 
                                                      rec( 
                                                          content := " is a ve\
rtex in ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 178102, 
                                                          root := ~, 
                                                          start := 178088, 
                                                          stop := 178101 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen this operation returns the length of the longest directed walk in\n    ", 
                                                          count := 
                                                            [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 178197, 
                                                          root := ~, 
                                                          start := 178183, 
                                                          stop := 178196 ), 
                                                      rec( 
                                                          content := " which b\
egins at vertex ", count := [ 5, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 178229, 
                                                          root := ~, 
                                                          start := 178221, 
                                                          stop := 178228 ), 
                                                      rec( 
                                                          content := ".  See S\
ection ", count := [ 5, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 178294, 
                                                          root := ~, 
                                                          start := 178244, 
                                                          stop := 178293 ), 
                                                      rec( 
                                                          content := " for the\
 definitions of directed\n    walk, directed cycle, and loop.\n    ", 
                                                          count := 
                                                            [ 5, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 178371, 
                                                          root := ~, 
                                                          start := 178367, 
                                                          stop := 178370 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        If there exists a directed w\
alk starting at vertex ", count := [ 5, 3, 4, 6 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "v", count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", root :=\
 ~ ) ], count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "A", next := 1784\
64, root := ~, start := 178456, stop := 178463 ), rec( content := "\n        w\
hich traverses a loop or a directed cycle,\n        then we consider there to \
be a walk of infinite length from ", count := [ 5, 3, 4, 6 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ re\
c( content := "v", count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 178593, root := ~, start := 178585, stop := 178592 ), rec( content := "\n \
       (realised by repeatedly traversing the loop/directed cycle),\n        a\
nd so the result is ", count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "P\
CDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := \
"infinity", count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 5, 3, 4, 6 ], mathmode := "Text", name := "K", next := \
178707, root := ~, start := 178692, stop := 178706 ), rec( content := ".\n    \
    To disallow walks using loops, try using\n        ", count := [ 5, 3, 4, 6\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
 Oper := "DigraphRemoveLoops" ), content := 0, count := [ 5, 3, 4, 6 ], mathmo\
de := "Text", name := "Ref", next := 178798, root := ~, start := 178766, stop \
:= 178797 ), rec( content := ":", count := [ 5, 3, 4, 6 ], mathmode := "Text",
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 0, count := 
                                                                            [ \
5, 3, 4, 7 ], mathmode := "Text", name := "P", next := 178803, root := ~, star\
t := 178799, stop := 178802 ), rec( content := "\n\n        ", count := [ 5, 3\
, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( content := "DigraphLongestDistanceFromVertex(Digr\
aphRemoveLoops(", count := [ 5, 3, 4, 7 ], mathmode := "Text", name := "PCDATA\
", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "digr\
aph", count := [ 5, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~\
 ) ], count := [ 5, 3, 4, 7 ], mathmode := "Text", name := "A", next := 178882\
, root := ~, start := 178868, stop := 178881 ), rec( content := ",", count := \
[ 5, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\
utes := rec(  ), content := [ rec( content := "v", count := [ 5, 3, 4, 7 ], ma\
thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 7 ], ma\
thmode := "Text", name := "A", next := 178891, root := ~, start := 178883, sto\
p := 178890 ), rec( content := "))", count := [ 5, 3, 4, 7 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 7 ], mathmode := "Tex\
t", name := "C", next := 178897, root := ~, start := 178813, stop := 178896 ),
                                                                      rec( 
                                                                          cont\
ent := ".\n      ", count := [ 5, 3, 4, 7 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 5, 3, 4, 6 ], name := "Item", next := 178912, 
                                                                  root := ~, 
                                                                  start := 178\
390, stop := 178911 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        Otherwise, if all directed walks\n        starting at vertex ", 
                                                                          coun\
t := [ 5, 3, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "v", count := [ 5, 3, 4, 9 ], \
mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 9 ], 
                                                                          math\
mode := "Text", name := "A", next := 179003, root := ~, start := 178995, stop \
:= 179002 ), rec( content := " have finite length,\n        then the length of\
 the longest such walk is returned.\n      ", count := [ 5, 3, 4, 9 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 4, 9 ], 
                                                                  name := "Ite\
m", next := 179099, root := ~, start := 178920, stop := 179098 ) ], 
                                                          count := 
                                                            [ 5, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 179111, 
                                                          root := ~, 
                                                          start := 178377, 
                                                          stop := 179110 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that the result is ", count := [ 5, 3, 4, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 4, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 179149, 
                                                          root := ~, 
                                                          start := 179141, 
                                                          stop := 179148 ), 
                                                      rec( 
                                                          content := " if and \
only if ", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 4, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 179173, 
                                                          root := ~, 
                                                          start := 179165, 
                                                          stop := 179172 ), 
                                                      rec( 
                                                          content := " is a si\
nk of\n    ", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 4, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 4, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 179205, 
                                                          root := ~, 
                                                          start := 179191, 
                                                          stop := 179204 ), 
                                                      rec( 
                                                          content := ".  See "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 4, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Sinks" ), content := 0, count := [ 5, 3, 4, 11 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 179238, 
                                                          root := ~, 
                                                          start := 179212, 
                                                          stop := 179237 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 3, 4, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2], [3, 4], [], [5], [], [6]]);\n<immutable digraph with \
6 vertices, 5 edges>\ngap> DigraphLongestDistanceFromVertex(D, 1);\n3\ngap> Di\
graphLongestDistanceFromVertex(D, 3);\n0\ngap> 3 in DigraphSinks(D);\ntrue\nga\
p> DigraphLongestDistanceFromVertex(D, 6);\ninfinity\n", count := [ 5, 3, 4, 
                                                                      12 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 4, 12 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 179550, 
                                                          root := ~, 
                                                          start := 179241, 
                                                          stop := 179549 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 4, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 179567, root := ~, 
                                                  start := 178011, 
                                                  stop := 179566 ) ], 
                                          count := [ 5, 3, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 179581, root := ~, 
                                          start := 177876, stop := 179580 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 4, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex,\
 distance", Label := "for a digraph, a pos int, and an int", 
                                                      Name := "DigraphDistance\
Set" ), content := 0, count := [ 5, 3, 5, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 179712, root := ~, 
                                                  start := 179602, 
                                                  stop := 179711 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex,\
 distances", Label := "for a digraph, a pos int, and a list", 
                                                      Name := "DigraphDistance\
Set" ), content := 0, count := [ 5, 3, 5, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 179826, root := ~, 
                                                  start := 179715, 
                                                  stop := 179825 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 vertices", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 179866, root := ~, 
                                                  start := 179829, 
                                                  stop := 179865 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns the list of all vertices in digraph ", 
                                                          count := 
                                                            [ 5, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 179960, 
                                                          root := ~, 
                                                          start := 179946, 
                                                          stop := 179959 ), 
                                                      rec( 
                                                          content := "\n    su\
ch that the shortest distance to a vertex ", count := [ 5, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 180022, 
                                                          root := ~, 
                                                          start := 180009, 
                                                          stop := 180021 ), 
                                                      rec( 
                                                          content := " is\n   \
 ", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
istance", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 180045, 
                                                          root := ~, 
                                                          start := 180030, 
                                                          stop := 180044 ), 
                                                      rec( 
                                                          content := " or is i\
n the list ", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
istances", count := [ 5, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 180080, 
                                                          root := ~, 
                                                          start := 180064, 
                                                          stop := 180079 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 180086, 
                                                          root := ~, 
                                                          start := 180082, 
                                                          stop := 180085 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 180106, 
                                                          root := ~, 
                                                          start := 180092, 
                                                          stop := 180105 ), 
                                                      rec( 
                                                          content := " should \
be a digraph, ", count := [ 5, 3, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 180141, 
                                                          root := ~, 
                                                          start := 180128, 
                                                          stop := 180140 ), 
                                                      rec( 
                                                          content := " should \
be a positive\n    integer, ", count := [ 5, 3, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
istance", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 180191, 
                                                          root := ~, 
                                                          start := 180176, 
                                                          stop := 180190 ), 
                                                      rec( 
                                                          content := " should \
be a non-negative integer, and\n    ", count := [ 5, 3, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
istances", count := [ 5, 3, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 180250, 
                                                          root := ~, 
                                                          start := 180234, 
                                                          stop := 180249 ), 
                                                      rec( 
                                                          content := " should \
be a list of non-negative integers.\n\n    ", count := [ 5, 3, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2], [3], [1, 4], [1, 3]]);\n<immutable digraph with 4 ver\
tices, 6 edges>\ngap> DigraphDistanceSet(D, 2, [1, 2]);\n[ 3, 1, 4 ]\ngap> Dig\
raphDistanceSet(D, 3, 1);\n[ 1, 4 ]\ngap> DigraphDistanceSet(D, 2, 0);\n[ 2 ]\
\n", count := [ 5, 3, 5, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 180557, 
                                                          root := ~, 
                                                          start := 180299, 
                                                          stop := 180556 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 180574, root := ~, 
                                                  start := 179869, 
                                                  stop := 180573 ) ], 
                                          count := [ 5, 3, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 180588, root := ~, 
                                          start := 179587, stop := 180587 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 5, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphGirth" )
                                                    , content := 0, 
                                                  count := [ 5, 3, 6, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 180650, root := ~, 
                                                  start := 180609, 
                                                  stop := 180649 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r, or ", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 180692, 
                                                          root := ~, 
                                                          start := 180677, 
                                                          stop := 180691 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 180703, root := ~, 
                                                  start := 180653, 
                                                  stop := 180702 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s attribute returns the ", count := [ 5, 3, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
irth", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 180763, 
                                                          root := ~, 
                                                          start := 180751, 
                                                          stop := 180762 ), 
                                                      rec( 
                                                          content := " of the \
digraph ", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 180793, 
                                                          root := ~, 
                                                          start := 180779, 
                                                          stop := 180792 ), 
                                                      rec( 
                                                          content := ".\n    T\
he ", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
irth", count := [ 5, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 180815, 
                                                          root := ~, 
                                                          start := 180803, 
                                                          stop := 180814 ), 
                                                      rec( 
                                                          content := " of a di\
graph is the length of its shortest simple circuit.\n    See Section ", 
                                                          count := 
                                                            [ 5, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 180935, 
                                                          root := ~, 
                                                          start := 180891, 
                                                          stop := 180934 ), 
                                                      rec( 
                                                          content := " for the\
 definitions\n    of simple circuit, directed cycle, and loop.\n    ", 
                                                          count := 
                                                            [ 5, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 181013, 
                                                          root := ~, 
                                                          start := 181009, 
                                                          stop := 181012 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 181036, 
                                                          root := ~, 
                                                          start := 181022, 
                                                          stop := 181035 ), 
                                                      rec( 
                                                          content := " has no \
directed cycles, then this function will return\n    ", count := 
                                                            [ 5, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 181111, 
                                                          root := ~, 
                                                          start := 181096, 
                                                          stop := 181110 ), 
                                                      rec( 
                                                          content := ".  If ",
                                                          count := 
                                                            [ 5, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 181131, 
                                                          root := ~, 
                                                          start := 181117, 
                                                          stop := 181130 ), 
                                                      rec( 
                                                          content := " contain\
s a loop, then this function will\n    return ", count := [ 5, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 5, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 181192, 
                                                          root := ~, 
                                                          start := 181184, 
                                                          stop := 181191 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 181202, 
                                                          root := ~, 
                                                          start := 181198, 
                                                          stop := 181201 ), 
                                                      rec( 
                                                          content := "\n\n    \
In the worst case, the method used in this function is a version of the\n    F\
loyd-Warshall algorithm, and has complexity ", count := [ 5, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                                , 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 5, 3, 6, 5 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 6, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 181342, root := ~, start := 181334, stop := 18134\
1 ), rec( content := " ^ 3)", count := [ 5, 3, 6, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 6, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 181351, 
                                                          root := ~, 
                                                          start := 181329, 
                                                          stop := 181350 ), 
                                                      rec( 
                                                          content := ", where\\
n    ", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 181371, 
                                                          root := ~, 
                                                          start := 181363, 
                                                          stop := 181370 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in ", count := [ 5, 3, 6, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 181415, 
                                                          root := ~, 
                                                          start := 181401, 
                                                          stop := 181414 ), 
                                                      rec( 
                                                          content := ".  If th\
e digraph has\n    known automorphisms [see ", count := [ 5, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Group" ), content := 0, count := [ 5, 3, 6, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 181492, 
                                                          root := ~, 
                                                          start := 181466, 
                                                          stop := 181491 ), 
                                                      rec( 
                                                          content := "], then \
the performance\n    is likely to be better.\n    ", count := [ 5, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 181552, 
                                                          root := ~, 
                                                          start := 181548, 
                                                          stop := 181551 ), 
                                                      rec( 
                                                          content := "\n\n    \
For symmetric digraphs, see also ", count := [ 5, 3, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
UndirectedGirth" ), content := 0, count := [ 5, 3, 6, 6 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 181627, 
                                                          root := ~, 
                                                          start := 181591, 
                                                          stop := 181626 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 181633, 
                                                          root := ~, 
                                                          start := 181629, 
                                                          stop := 181632 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 3, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1], [1]]);\n<immutable digraph with 2 vertices, 2 edges>\
\ngap> DigraphGirth(D);\n1\ngap> D := Digraph([[2, 3], [3], [4], []]);\n<immut\
able digraph with 4 vertices, 4 edges>\ngap> DigraphGirth(D);\ninfinity\ngap> \
D := Digraph([[2, 3], [3], [4], [1]]);\n<immutable digraph with 4 vertices, 5 \
edges>\ngap> DigraphGirth(D);\n3\ngap> D := GeneralisedPetersenGraph(IsMutable\
Digraph, 6, 2);\n<mutable digraph with 12 vertices, 36 edges>\ngap> DigraphGir\
th(D);\n2\n", count := [ 5, 3, 6, 8 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 6, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 182131, 
                                                          root := ~, 
                                                          start := 181638, 
                                                          stop := 182130 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 182148, root := ~, 
                                                  start := 180706, 
                                                  stop := 182147 ) ], 
                                          count := [ 5, 3, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 182162, root := ~, 
                                          start := 180594, stop := 182161 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 6, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphOddGirth\
" ), content := 0, count := [ 5, 3, 7, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 182227, root := ~, 
                                                  start := 182183, 
                                                  stop := 182226 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r, or ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 182269, 
                                                          root := ~, 
                                                          start := 182254, 
                                                          stop := 182268 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 182280, root := ~, 
                                                  start := 182230, 
                                                  stop := 182279 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s attribute returns the ", count := [ 5, 3, 7, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
dd girth", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 182344, 
                                                          root := ~, 
                                                          start := 182328, 
                                                          stop := 182343 ), 
                                                      rec( 
                                                          content := " of the \
digraph ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 182374, 
                                                          root := ~, 
                                                          start := 182360, 
                                                          stop := 182373 ), 
                                                      rec( 
                                                          content := ".\n    T\
he ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
dd girth", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 182400, 
                                                          root := ~, 
                                                          start := 182384, 
                                                          stop := 182399 ), 
                                                      rec( 
                                                          content := " of a di\
graph is the length of its shortest simple\n    circuit of odd length.  See Se\
ction ", count := [ 5, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 182539, 
                                                          root := ~, 
                                                          start := 182491, 
                                                          stop := 182538 ), 
                                                      rec( 
                                                          content := " for the\
 definitions of simple circuit, directed\n    cycle, and loop.\n    ", 
                                                          count := 
                                                            [ 5, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 182617, 
                                                          root := ~, 
                                                          start := 182613, 
                                                          stop := 182616 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 182640, 
                                                          root := ~, 
                                                          start := 182626, 
                                                          stop := 182639 ), 
                                                      rec( 
                                                          content := " has no \
directed cycles of odd length, then this function\n    will return ", 
                                                          count := 
                                                            [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 182729, 
                                                          root := ~, 
                                                          start := 182714, 
                                                          stop := 182728 ), 
                                                      rec( 
                                                          content := ", even i\
f ", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 182753, 
                                                          root := ~, 
                                                          start := 182739, 
                                                          stop := 182752 ), 
                                                      rec( 
                                                          content := " has a d\
irected cycle\n    of even length.  If ", count := [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 182813, 
                                                          root := ~, 
                                                          start := 182799, 
                                                          stop := 182812 ), 
                                                      rec( 
                                                          content := " contain\
s a loop, then this function\n    will return ", count := [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 5, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 182874, 
                                                          root := ~, 
                                                          start := 182866, 
                                                          stop := 182873 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 182884, 
                                                          root := ~, 
                                                          start := 182880, 
                                                          stop := 182883 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 5, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Girth" ), content := 0, count := [ 5, 3, 7, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 182925, 
                                                          root := ~, 
                                                          start := 182899, 
                                                          stop := 182924 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 182931, 
                                                          root := ~, 
                                                          start := 182927, 
                                                          stop := 182930 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 3, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2], [3, 1], [1]]);\n<immutable digraph with 3 vertices, 4\
 edges>\ngap> DigraphOddGirth(D);\n3\ngap> D := CycleDigraph(4);\n<immutable c\
ycle digraph with 4 vertices>\ngap> DigraphOddGirth(D);\ninfinity\ngap> D := D\
igraph([[2], [3], [], [3], [4]]);\n<immutable digraph with 5 vertices, 4 edges\
>\ngap> DigraphOddGirth(D);\ninfinity\ngap> D := CycleDigraph(IsMutableDigraph\
, 4);\n<mutable digraph with 4 vertices, 4 edges>\ngap> DigraphDisjointUnion(D\
, CycleDigraph(5));\n<mutable digraph with 9 vertices, 9 edges>\ngap> DigraphO\
ddGirth(D);\n5\n", count := [ 5, 3, 7, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 183511, 
                                                          root := ~, 
                                                          start := 182936, 
                                                          stop := 183510 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 7, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 183528, root := ~, 
                                                  start := 182283, 
                                                  stop := 183527 ) ], 
                                          count := [ 5, 3, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 183542, root := ~, 
                                          start := 182168, stop := 183541 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 7, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphUndirect\
edGirth" ), content := 0, count := [ 5, 3, 8, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 183614, root := ~, 
                                                  start := 183563, 
                                                  stop := 183613 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r or ", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 183655, 
                                                          root := ~, 
                                                          start := 183640, 
                                                          stop := 183654 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 183666, root := ~, 
                                                  start := 183617, 
                                                  stop := 183665 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 183704, 
                                                          root := ~, 
                                                          start := 183690, 
                                                          stop := 183703 ), 
                                                      rec( 
                                                          content := " is a sy\
mmetric digraph, then this function returns the\n    girth of ", 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 183787, 
                                                          root := ~, 
                                                          start := 183773, 
                                                          stop := 183786 ), 
                                                      rec( 
                                                          content := " when tr\
eated as an undirected graph (i.e. each pair\n    of edges ", 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i, j]", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 183866, 
                                                          root := ~, 
                                                          start := 183853, 
                                                          stop := 183865 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
j, i]", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 183884, 
                                                          root := ~, 
                                                          start := 183871, 
                                                          stop := 183883 ), 
                                                      rec( 
                                                          content := " is trea\
ted as a single edge between\n    ", count := [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 183933, 
                                                          root := ~, 
                                                          start := 183925, 
                                                          stop := 183932 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 183946, 
                                                          root := ~, 
                                                          start := 183938, 
                                                          stop := 183945 ), 
                                                      rec( content := "). ", 
                                                          count := 
                                                            [ 5, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 183953, 
                                                          root := ~, 
                                                          start := 183949, 
                                                          stop := 183952 ), 
                                                      rec( 
                                                          content := "\n\n    \
The ", count := [ 5, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
irth", count := [ 5, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 183975, 
                                                          root := ~, 
                                                          start := 183963, 
                                                          stop := 183974 ), 
                                                      rec( 
                                                          content := " of an u\
ndirected graph is the length of its shortest simple\n    cycle, i.e. the shor\
test non-trivial path starting and ending at the same\n    vertex and passing \
through no vertex or edge more than once. ", count := [ 5, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 184183, 
                                                          root := ~, 
                                                          start := 184179, 
                                                          stop := 184182 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 184206, 
                                                          root := ~, 
                                                          start := 184192, 
                                                          stop := 184205 ), 
                                                      rec( 
                                                          content := " has no \
cycles, then this function will return\n    ", count := [ 5, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 5, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 184272, 
                                                          root := ~, 
                                                          start := 184257, 
                                                          stop := 184271 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 184278, 
                                                          root := ~, 
                                                          start := 184274, 
                                                          stop := 184277 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 3, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 4], [1, 3], [2, 4], [1, 3]]);\n<immutable digraph with\
 4 vertices, 8 edges>\ngap> DigraphUndirectedGirth(D);\n4\ngap> D := Digraph([\
[2], [1, 3], [2]]);\n<immutable digraph with 3 vertices, 4 edges>\ngap> Digrap\
hUndirectedGirth(D);\ninfinity\ngap> D := Digraph([[1], [], [4], [3]]);\n<immu\
table digraph with 4 vertices, 3 edges>\ngap> DigraphUndirectedGirth(D);\n1\ng\
ap> D := GeneralisedPetersenGraph(IsMutableDigraph, 9, 2);\n<mutable digraph w\
ith 18 vertices, 54 edges>\ngap> DigraphUndirectedGirth(D);\n5\n", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      8, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 8, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 184830, 
                                                          root := ~, 
                                                          start := 184283, 
                                                          stop := 184829 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 184847, root := ~, 
                                                  start := 183669, 
                                                  stop := 184846 ) ], 
                                          count := [ 5, 3, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 184861, root := ~, 
                                          start := 183548, stop := 184860 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 8, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphConnecte\
dComponents" ), content := 0, count := [ 5, 3, 9, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 184937, root := ~, 
                                                  start := 184882, 
                                                  stop := 184936 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphNrConnec\
tedComponents" ), content := 0, count := [ 5, 3, 9, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 184997, root := ~, 
                                                  start := 184940, 
                                                  stop := 184996 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A record.\
", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 5, 3, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 185028, root := ~, 
                                                  start := 185000, 
                                                  stop := 185027 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the record ", count := [ 5, 3, 9, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "w\
cc", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 185092, 
                                                          root := ~, 
                                                          start := 185082, 
                                                          stop := 185091 ), 
                                                      rec( 
                                                          content := " corresp\
onding to the weakly\n    connected components of the digraph ", 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 185175, 
                                                          root := ~, 
                                                          start := 185161, 
                                                          stop := 185174 ), 
                                                      rec( 
                                                          content := ".  Two v\
ertices of\n    ", count := [ 5, 3, 9, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 185212, 
                                                          root := ~, 
                                                          start := 185198, 
                                                          stop := 185211 ), 
                                                      rec( 
                                                          content := " are in \
the same weakly connected component whenever they are\n    equal, or there exi\
sts a directed path (ignoring the orientation of edges)\n    between them.  Mo\
re formally, two vertices are in the same weakly connected\n    component of "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 185464, 
                                                          root := ~, 
                                                          start := 185450, 
                                                          stop := 185463 ), 
                                                      rec( 
                                                          content := " if and \
only if they are in the same strongly\n    connected component (see ", 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
StronglyConnectedComponents" ), content := 0, count := [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 185587, 
                                                          root := ~, 
                                                          start := 185539, 
                                                          stop := 185586 ), 
                                                      rec( 
                                                          content := ")\n    o\
f the ", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
SymmetricClosure" ), content := 0, count := [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 185637, 
                                                          root := ~, 
                                                          start := 185600, 
                                                          stop := 185636 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 185655, 
                                                          root := ~, 
                                                          start := 185641, 
                                                          stop := 185654 ), 
                                                      rec( content := ".  ", 
                                                          count := 
                                                            [ 5, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 185662, 
                                                          root := ~, 
                                                          start := 185658, 
                                                          stop := 185661 ), 
                                                      rec( 
                                                          content := "\n\n    \
The set of weakly connected components is a partition of\n    the vertex set o\
f ", count := [ 5, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 185761, 
                                                          root := ~, 
                                                          start := 185747, 
                                                          stop := 185760 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 185767, 
                                                          root := ~, 
                                                          start := 185763, 
                                                          stop := 185766 ), 
                                                      rec( 
                                                          content := "\n\n    \
The record ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "w\
cc", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 185794, 
                                                          root := ~, 
                                                          start := 185784, 
                                                          stop := 185793 ), 
                                                      rec( 
                                                          content := " has 2 c\
omponents: ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omps", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 185825, 
                                                          root := ~, 
                                                          start := 185813, 
                                                          stop := 185824 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
d", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 185839, 
                                                          root := ~, 
                                                          start := 185830, 
                                                          stop := 185838 ), 
                                                      rec( 
                                                          content := ".\n    T\
he component ", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omps", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 185871, 
                                                          root := ~, 
                                                          start := 185859, 
                                                          stop := 185870 ), 
                                                      rec( 
                                                          content := " is a li\
st of the weakly connected components\n    of  ", count := [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 185939, 
                                                          root := ~, 
                                                          start := 185925, 
                                                          stop := 185938 ), 
                                                      rec( 
                                                          content := " (each o\
f which is a list of vertices).\n    The component ", count := [ 5, 3, 9, 7 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
d", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 186006, 
                                                          root := ~, 
                                                          start := 185997, 
                                                          stop := 186005 ), 
                                                      rec( 
                                                          content := " is a li\
st such that the vertex ", count := [ 5, 3, 9, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 186046, 
                                                          root := ~, 
                                                          start := 186038, 
                                                          stop := 186045 ), 
                                                      rec( 
                                                          content := " is an\n\
    element of the weakly connected component ", count := [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omps[id[i]]", count := [ 5, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 186118, 
                                                          root := ~, 
                                                          start := 186099, 
                                                          stop := 186117 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 186124, 
                                                          root := ~, 
                                                          start := 186120, 
                                                          stop := 186123 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this function has complexity  ", count := [ 5, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 186192, 
                                                          root := ~, 
                                                          start := 186179, 
                                                          stop := 186191 ), 
                                                      rec( 
                                                          content := ", where\\
n    ", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 186212, 
                                                          root := ~, 
                                                          start := 186204, 
                                                          stop := 186211 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and\n    ", count := [ 5, 3, 9, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 9, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 186252, 
                                                          root := ~, 
                                                          start := 186244, 
                                                          stop := 186251 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in the digraph. ", count := [ 5, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 9, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 186299, 
                                                          root := ~, 
                                                          start := 186295, 
                                                          stop := 186298 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphNrConnectedComponents(", count := [ 5, 3, 9, 9 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "d\
igraph", count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ) ], count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "A", 
                                                                  next := 1863\
51, root := ~, start := 186337, stop := 186350 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      9, 9 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 186356, 
                                                          root := ~, 
                                                          start := 186305, 
                                                          stop := 186355 ), 
                                                      rec( 
                                                          content := " is simp\
ly a shortcut\n    for ", count := [ 5, 3, 9, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
ength(DigraphConnectedComponents(", count := [ 5, 3, 9, 9 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          conte\
nt := "digraph", count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 5, 3, 9, 9 ], mathmode := "Text", name := "A", 
                                                                  next := 1864\
37, root := ~, start := 186423, stop := 186436 ), rec( content := ").comps)", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      9, 9 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 9, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 186449, 
                                                          root := ~, 
                                                          start := 186386, 
                                                          stop := 186448 ), 
                                                      rec( 
                                                          content := ",\n    a\
nd is no more efficient.\n\n    ", count := [ 5, 3, 9, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[2], [3, 1], []]);\n<immutable digraph with 3 vertices, 3\
 edges>\ngap> DigraphConnectedComponents(gr);\nrec( comps := [ [ 1, 2, 3 ] ], \
id := [ 1, 1, 1 ] )\ngap> gr := Digraph([[1], [1, 2], []]);\n<immutable digrap\
h with 3 vertices, 3 edges>\ngap> DigraphConnectedComponents(gr);\nrec( comps \
:= [ [ 1, 2 ], [ 3 ] ], id := [ 1, 1, 2 ] )\ngap> DigraphNrConnectedComponents\
(gr);\n2\ngap> gr := EmptyDigraph(0);\n<immutable empty digraph with 0 vertice\
s>\ngap> DigraphConnectedComponents(gr);\nrec( comps := [  ], id := [  ] )\nga\
p> D := CycleDigraph(IsMutableDigraph, 2);\n<mutable digraph with 2 vertices, \
2 edges>\ngap> G := CycleDigraph(3);\n<immutable cycle digraph with 3 vertices\
>\ngap> DigraphDisjointUnion(D, G);\n<mutable digraph with 5 vertices, 5 edges\
>\ngap> DigraphConnectedComponents(D);\nrec( comps := [ [ 1, 2 ], [ 3, 4, 5 ] \
], id := [ 1, 1, 2, 2, 2 ] )\n", count := [ 5, 3, 9, 10 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 9, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 187383, 
                                                          root := ~, 
                                                          start := 186486, 
                                                          stop := 187382 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 9, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 187400, root := ~, 
                                                  start := 185031, 
                                                  stop := 187399 ) ], 
                                          count := [ 5, 3, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 187414, root := ~, 
                                          start := 184867, stop := 187413 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 9, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "DigraphConnecte\
dComponent" ), content := 0, count := [ 5, 3, 10, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 187497, root := ~, 
                                                  start := 187435, 
                                                  stop := 187496 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 vertices.", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 187538, root := ~, 
                                                  start := 187500, 
                                                  stop := 187537 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 187575, 
                                                          root := ~, 
                                                          start := 187562, 
                                                          stop := 187574 ), 
                                                      rec( 
                                                          content := " is a ve\
rtex in the digraph ", count := [ 5, 3, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 187617, 
                                                          root := ~, 
                                                          start := 187603, 
                                                          stop := 187616 ), 
                                                      rec( 
                                                          content := ", then\n\
    this operation returns the connected component of ", count := 
                                                            [ 5, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 187691, 
                                                          root := ~, 
                                                          start := 187678, 
                                                          stop := 187690 ), 
                                                      rec( 
                                                          content := "\n    in\
 ", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 187713, 
                                                          root := ~, 
                                                          start := 187699, 
                                                          stop := 187712 ), 
                                                      rec( 
                                                          content := ".\n    S\
ee ", count := [ 5, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
ConnectedComponents" ), content := 0, count := [ 5, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 187763, 
                                                          root := ~, 
                                                          start := 187723, 
                                                          stop := 187762 ), 
                                                      rec( 
                                                          content := " for mor\
e information.\n    ", count := [ 5, 3, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3], [2], [1, 2], [4]]);\n<immutable digraph with 4 vertic\
es, 5 edges>\ngap> DigraphConnectedComponent(D, 3);\n[ 1, 2, 3 ]\ngap> Digraph\
ConnectedComponent(D, 2);\n[ 1, 2, 3 ]\ngap> DigraphConnectedComponent(D, 4);\
\n[ 4 ]\n", count := [ 5, 3, 10, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 188055, 
                                                          root := ~, 
                                                          start := 187790, 
                                                          stop := 188054 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 188072, root := ~, 
                                                  start := 187541, 
                                                  stop := 188071 ) ], 
                                          count := [ 5, 3, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 188086, root := ~, 
                                          start := 187420, stop := 188085 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 10, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphStrongly\
ConnectedComponents" ), content := 0, count := [ 5, 3, 11, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 188170, root := ~, 
                                                  start := 188107, 
                                                  stop := 188169 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphNrStrong\
lyConnectedComponents" ), content := 0, count := [ 5, 3, 11, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 188238, root := ~, 
                                                  start := 188173, 
                                                  stop := 188237 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A record.\
", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 5, 3, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 188269, root := ~, 
                                                  start := 188241, 
                                                  stop := 188268 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the record ", count := [ 5, 3, 11, 5 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
cc", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 188333, 
                                                          root := ~, 
                                                          start := 188323, 
                                                          stop := 188332 ), 
                                                      rec( 
                                                          content := " corresp\
onding to the strongly\n    connected components of the digraph ", 
                                                          count := 
                                                            [ 5, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 188418, 
                                                          root := ~, 
                                                          start := 188404, 
                                                          stop := 188417 ), 
                                                      rec( 
                                                          content := ".  Two v\
ertices of\n    ", count := [ 5, 3, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 188455, 
                                                          root := ~, 
                                                          start := 188441, 
                                                          stop := 188454 ), 
                                                      rec( 
                                                          content := " are in \
the same strongly connected component whenever they\n    are equal, or there i\
s a directed path from each vertex to the other.  The\n    set of strongly con\
nected components is a partition of the vertex set of\n    ", 
                                                          count := 
                                                            [ 5, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 188689, 
                                                          root := ~, 
                                                          start := 188675, 
                                                          stop := 188688 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 188699, 
                                                          root := ~, 
                                                          start := 188695, 
                                                          stop := 188698 ), 
                                                      rec( 
                                                          content := "\n\n    \
The record ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
cc", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 188726, 
                                                          root := ~, 
                                                          start := 188716, 
                                                          stop := 188725 ), 
                                                      rec( 
                                                          content := " has 2 c\
omponents: ", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omps", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 188757, 
                                                          root := ~, 
                                                          start := 188745, 
                                                          stop := 188756 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
d", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 188771, 
                                                          root := ~, 
                                                          start := 188762, 
                                                          stop := 188770 ), 
                                                      rec( 
                                                          content := ".\n    T\
he component ", count := [ 5, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omps", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 188803, 
                                                          root := ~, 
                                                          start := 188791, 
                                                          stop := 188802 ), 
                                                      rec( 
                                                          content := " is a li\
st of the strongly connected components\n    of ", count := [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 188872, 
                                                          root := ~, 
                                                          start := 188858, 
                                                          stop := 188871 ), 
                                                      rec( 
                                                          content := " (each o\
f which is a list of vertices).\n    The component ", count := [ 5, 3, 11, 6 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
d", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 188939, 
                                                          root := ~, 
                                                          start := 188930, 
                                                          stop := 188938 ), 
                                                      rec( 
                                                          content := " is a li\
st such that the vertex ", count := [ 5, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 188979, 
                                                          root := ~, 
                                                          start := 188971, 
                                                          stop := 188978 ), 
                                                      rec( 
                                                          content := " is an\n\
    element of the strongly connected component ", count := [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omps[id[i]]", count := [ 5, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 189053, 
                                                          root := ~, 
                                                          start := 189034, 
                                                          stop := 189052 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 189059, 
                                                          root := ~, 
                                                          start := 189055, 
                                                          stop := 189058 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this function is a non-recursive version of Gabow's\n    Al\
gorithm ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "Gab00" )
                                                            , content := 0, 
                                                          count := 
                                                            [ 5, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 189169, 
                                                          root := ~, 
                                                          start := 189150, 
                                                          stop := 189168 ), 
                                                      rec( 
                                                          content := " and has\
 complexity ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 189202, 
                                                          root := ~, 
                                                          start := 189189, 
                                                          stop := 189201 ), 
                                                      rec( 
                                                          content := " where\n\
    ", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 189221, 
                                                          root := ~, 
                                                          start := 189213, 
                                                          stop := 189220 ), 
                                                      rec( 
                                                          content := " is the \
number of edges (counting multiple edges as one) and\n    ", 
                                                          count := 
                                                            [ 5, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 189294, 
                                                          root := ~, 
                                                          start := 189286, 
                                                          stop := 189293 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in the digraph. ", count := [ 5, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 11, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 189341, 
                                                          root := ~, 
                                                          start := 189337, 
                                                          stop := 189340 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphNrStronglyConnectedComponents(", count := [ 5, 3, 11, 8 ], mathmode := "\
Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph", count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "A", 
                                                                  next := 1894\
01, root := ~, start := 189387, stop := 189400 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      11, 8 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 189406, 
                                                          root := ~, 
                                                          start := 189347, 
                                                          stop := 189405 ), 
                                                      rec( 
                                                          content := " is simp\
ly a\n    shortcut for\n    ", count := [ 5, 3, 11, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
ength(DigraphStronglyConnectedComponents(", count := [ 5, 3, 11, 8 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph", count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 5, 3, 11, 8 ], mathmode := "Text", name := "A", 
                                                                  next := 1894\
99, root := ~, start := 189485, stop := 189498 ), rec( content := ").comps)", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      11, 8 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 11, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 189511, 
                                                          root := ~, 
                                                          start := 189440, 
                                                          stop := 189510 ), 
                                                      rec( 
                                                          content := ",\n    a\
nd is no more efficient.\n\n    ", count := [ 5, 3, 11, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[2], [3, 1], []]);\n<immutable digraph with 3 vertices, 3\
 edges>\ngap> DigraphStronglyConnectedComponents(gr);\nrec( comps := [ [ 3 ], \
[ 1, 2 ] ], id := [ 2, 2, 1 ] )\ngap> DigraphNrStronglyConnectedComponents(gr)\
;\n2\ngap> D := DigraphDisjointUnion(CycleDigraph(4), CycleDigraph(5));\n<immu\
table digraph with 9 vertices, 9 edges>\ngap> DigraphStronglyConnectedComponen\
ts(D);\nrec( comps := [ [ 1, 2, 3, 4 ], [ 5, 6, 7, 8, 9 ] ], \n  id := [ 1, 1,\
 1, 1, 2, 2, 2, 2, 2 ] )\ngap> DigraphNrStronglyConnectedComponents(D);\n2\nga\
p> D := CycleDigraph(IsMutableDigraph, 2);\n<mutable digraph with 2 vertices, \
2 edges>\ngap> G := CycleDigraph(3);\n<immutable cycle digraph with 3 vertices\
>\ngap> DigraphDisjointUnion(D, G);\n<mutable digraph with 5 vertices, 5 edges\
>\ngap> DigraphStronglyConnectedComponents(D);\nrec( comps := [ [ 1, 2 ], [ 3,\
 4, 5 ] ], id := [ 1, 1, 2, 2, 2 ] )\n", count := [ 5, 3, 11, 9 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 11, 9 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 190454, 
                                                          root := ~, 
                                                          start := 189548, 
                                                          stop := 190453 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 11, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 190471, root := ~, 
                                                  start := 188272, 
                                                  stop := 190470 ) ], 
                                          count := [ 5, 3, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 190485, root := ~, 
                                          start := 188092, stop := 190484 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 11, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "DigraphStrongly\
ConnectedComponent" ), content := 0, count := [ 5, 3, 12, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 190576, root := ~, 
                                                  start := 190506, 
                                                  stop := 190575 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 vertices.", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 190617, root := ~, 
                                                  start := 190579, 
                                                  stop := 190616 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 190654, 
                                                          root := ~, 
                                                          start := 190641, 
                                                          stop := 190653 ), 
                                                      rec( 
                                                          content := " is a ve\
rtex in the digraph ", count := [ 5, 3, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 190696, 
                                                          root := ~, 
                                                          start := 190682, 
                                                          stop := 190695 ), 
                                                      rec( 
                                                          content := ", then\n\
    this operation returns the strongly connected component of ", 
                                                          count := 
                                                            [ 5, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 190779, 
                                                          root := ~, 
                                                          start := 190766, 
                                                          stop := 190778 ), 
                                                      rec( 
                                                          content := "\n    in\
 ", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 190801, 
                                                          root := ~, 
                                                          start := 190787, 
                                                          stop := 190800 ), 
                                                      rec( 
                                                          content := ".\n    S\
ee ", count := [ 5, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
StronglyConnectedComponents" ), content := 0, count := [ 5, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 190859, 
                                                          root := ~, 
                                                          start := 190811, 
                                                          stop := 190858 ), 
                                                      rec( 
                                                          content := " for mor\
e information.\n    ", count := [ 5, 3, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3], [2], [1, 2], [3]]);\n<immutable digraph with 4 vertic\
es, 5 edges>\ngap> DigraphStronglyConnectedComponent(D, 3);\n[ 1, 3 ]\ngap> Di\
graphStronglyConnectedComponent(D, 2);\n[ 2 ]\ngap> DigraphStronglyConnectedCo\
mponent(D, 4);\n[ 4 ]\n", count := [ 5, 3, 12, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 191166, 
                                                          root := ~, 
                                                          start := 190886, 
                                                          stop := 191165 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 191183, root := ~, 
                                                  start := 190620, 
                                                  stop := 191182 ) ], 
                                          count := [ 5, 3, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 191197, root := ~, 
                                          start := 190491, stop := 191196 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 12, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphBicompon\
ents" ), content := 0, count := [ 5, 3, 13, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 191266, root := ~, 
                                                  start := 191218, 
                                                  stop := 191265 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A pair of\
 lists of vertices, or ", count := [ 5, 3, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 191321, 
                                                          root := ~, 
                                                          start := 191310, 
                                                          stop := 191320 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 13, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 191332, root := ~, 
                                                  start := 191269, 
                                                  stop := 191331 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 191370, 
                                                          root := ~, 
                                                          start := 191356, 
                                                          stop := 191369 ), 
                                                      rec( 
                                                          content := " is a bi\
partite digraph, i.e. if it satisfies ", count := [ 5, 3, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBipar\
titeDigraph" ), content := 0, count := [ 5, 3, 13, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 191454, 
                                                          root := ~, 
                                                          start := 191416, 
                                                          stop := 191453 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphBicomponents", count := [ 5, 3, 13, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 191487, 
                                                          root := ~, 
                                                          start := 191461, 
                                                          stop := 191486 ), 
                                                      rec( 
                                                          content := " returns\
 a\n    pair of bicomponents of ", count := [ 5, 3, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 191540, 
                                                          root := ~, 
                                                          start := 191526, 
                                                          stop := 191539 ), 
                                                      rec( 
                                                          content := ". Otherw\
ise,\n    ", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphBicomponents", count := [ 5, 3, 13, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 13, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 191583, 
                                                          root := ~, 
                                                          start := 191557, 
                                                          stop := 191582 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 191603, 
                                                          root := ~, 
                                                          start := 191592, 
                                                          stop := 191602 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 191608, 
                                                          root := ~, 
                                                          start := 191604, 
                                                          stop := 191607 ), 
                                                      rec( 
                                                          content := "\n\n    \
For a bipartite digraph, the vertices can be partitioned into two non-empty\n \
   sets such that the source and range of any edge are in distinct sets. The\n\
    parts of this partition are called ", count := [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "b\
icomponents", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 191826, 
                                                          root := ~, 
                                                          start := 191807, 
                                                          stop := 191825 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 191844, 
                                                          root := ~, 
                                                          start := 191830, 
                                                          stop := 191843 ), 
                                                      rec( 
                                                          content := ".\n    E\
quivalently, a pair of bicomponents of ", count := [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 191904, 
                                                          root := ~, 
                                                          start := 191890, 
                                                          stop := 191903 ), 
                                                      rec( 
                                                          content := " consist\
s of the\n    color-classes of a 2-coloring of ", count := [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 13, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 191972, 
                                                          root := ~, 
                                                          start := 191958, 
                                                          stop := 191971 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 191978, 
                                                          root := ~, 
                                                          start := 191974, 
                                                          stop := 191977 ), 
                                                      rec( 
                                                          content := "\n\n    \
For a bipartite digraph with at least 3 vertices, there is a unique pair of\n \
   bicomponents of bipartite if and only if the digraph is connected. See ", 
                                                          count := 
                                                            [ 5, 3, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsConne\
ctedDigraph" ), content := 0, count := [ 5, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 192173, 
                                                          root := ~, 
                                                          start := 192135, 
                                                          stop := 192172 ), 
                                                      rec( 
                                                          content := " for mor\
e information.\n    ", count := [ 5, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(3);\n<immutable cycle digraph with 3 vertices>\ngap> D\
igraphBicomponents(D);\nfail\ngap> D := ChainDigraph(5);\n<immutable chain dig\
raph with 5 vertices>\ngap> DigraphBicomponents(D);\n[ [ 1, 3, 5 ], [ 2, 4 ] ]\
\ngap> D := Digraph([[5], [1, 4], [5], [5], []]);\n<immutable digraph with 5 v\
ertices, 5 edges>\ngap> DigraphBicomponents(D);\n[ [ 1, 3, 4 ], [ 2, 5 ] ]\nga\
p> D := CompleteBipartiteDigraph(IsMutableDigraph, 2, 3);\n<mutable digraph wi\
th 5 vertices, 12 edges>\ngap> DigraphBicomponents(D);\n[ [ 1, 2 ], [ 3, 4, 5 \
] ]\n", count := [ 5, 3, 13, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 192766, 
                                                          root := ~, 
                                                          start := 192200, 
                                                          stop := 192765 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 13, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 13, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 192783, root := ~, 
                                                  start := 191335, 
                                                  stop := 192782 ) ], 
                                          count := [ 5, 3, 13, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 192797, root := ~, 
                                          start := 191203, stop := 192796 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 13, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "ArticulationPoi\
nts" ), content := 0, count := [ 5, 3, 14, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 192865, root := ~, 
                                                  start := 192818, 
                                                  stop := 192864 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 vertices.", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 192906, root := ~, 
                                                  start := 192868, 
                                                  stop := 192905 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A c\
onnected digraph is ", count := [ 5, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "b\
iconnected", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 192968, 
                                                          root := ~, 
                                                          start := 192950, 
                                                          stop := 192967 ), 
                                                      rec( 
                                                          content := " if it i\
s still connected (in the\n    sense of ", count := [ 5, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsConne\
ctedDigraph" ), content := 0, count := [ 5, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 193047, 
                                                          root := ~, 
                                                          start := 193015, 
                                                          stop := 193046 ), 
                                                      rec( 
                                                          content := ") when a\
ny vertex is removed. \n    If the digraph ", count := [ 5, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 193111, 
                                                          root := ~, 
                                                          start := 193097, 
                                                          stop := 193110 ), 
                                                      rec( 
                                                          content := " is not \
biconnected but is connected, then any\n    vertex ", count := [ 5, 3, 14, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 193177, 
                                                          root := ~, 
                                                          start := 193169, 
                                                          stop := 193176 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 5, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 193195, 
                                                          root := ~, 
                                                          start := 193181, 
                                                          stop := 193194 ), 
                                                      rec( 
                                                          content := " whose r\
emoval makes the resulting digraph\n    disconnected is called an ", 
                                                          count := 
                                                            [ 5, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
rticulation point", count := [ 5, 3, 14, 3 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 193293, 
                                                          root := ~, 
                                                          start := 193268, 
                                                          stop := 193292 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 193298, 
                                                          root := ~, 
                                                          start := 193294, 
                                                          stop := 193297 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
rticulationPoints", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 14, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 193329, 
                                                          root := ~, 
                                                          start := 193304, 
                                                          stop := 193328 ), 
                                                      rec( 
                                                          content := " returns\
 a list of the articulation points of\n    ", count := [ 5, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 193393, 
                                                          root := ~, 
                                                          start := 193379, 
                                                          stop := 193392 ), 
                                                      rec( 
                                                          content := ", if any\
, and, in particular, returns the empty list if\n    ", count := 
                                                            [ 5, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 193467, 
                                                          root := ~, 
                                                          start := 193453, 
                                                          stop := 193466 ), 
                                                      rec( 
                                                          content := " is not \
connected. ", count := [ 5, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 193490, 
                                                          root := ~, 
                                                          start := 193486, 
                                                          stop := 193489 ), 
                                                      rec( 
                                                          content := "\n\n    \
Multiple edges are ignored by this method. ", count := [ 5, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 193543, 
                                                          root := ~, 
                                                          start := 193539, 
                                                          stop := 193542 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this operation has complexity ", count := [ 5, 3, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 193611, 
                                                          root := ~, 
                                                          start := 193598, 
                                                          stop := 193610 ), 
                                                      rec( 
                                                          content := " where\n\
    ", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 193630, 
                                                          root := ~, 
                                                          start := 193622, 
                                                          stop := 193629 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and ", count := [ 5, 3, 14, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 193666, 
                                                          root := ~, 
                                                          start := 193658, 
                                                          stop := 193665 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in\n    the digraph.", count := [ 5, 3, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 14, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 193716, 
                                                          root := ~, 
                                                          start := 193712, 
                                                          stop := 193715 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If ", count := [ 5, 3, 14, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 14, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 14, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 193739, 
                                                          root := ~, 
                                                          start := 193731, 
                                                          stop := 193738 ), 
                                                      rec( 
                                                          content := " has a b\
ridge (see ", count := [ 5, 3, 14, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Bridges\
" ), content := 0, count := [ 5, 3, 14, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 193779, 
                                                          root := ~, 
                                                          start := 193758, 
                                                          stop := 193778 ), 
                                                      rec( 
                                                          content := "), then \
a node incident\n    to the bridge is an articulation point if and only if it \
has degree at\n    least ", count := [ 5, 3, 14, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
", count := [ 5, 3, 14, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 14, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 193896, 
                                                          root := ~, 
                                                          start := 193888, 
                                                          stop := 193895 ), 
                                                      rec( 
                                                          content := ".  It fo\
llows that if ", count := [ 5, 3, 14, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 14, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 14, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 193926, 
                                                          root := ~, 
                                                          start := 193918, 
                                                          stop := 193925 ), 
                                                      rec( 
                                                          content := " has a b\
ridge and at least\n    ", count := [ 5, 3, 14, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 5, 3, 14, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 14, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 193965, 
                                                          root := ~, 
                                                          start := 193957, 
                                                          stop := 193964 ), 
                                                      rec( 
                                                          content := " nodes, \
then at least one of the nodes incident to the bridge is\n    an articulation \
point.  The converse does not hold, there are digraphs\n    with articulation \
points, but no bridges.\n    ", count := [ 5, 3, 14, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 14, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 194159, 
                                                          root := ~, 
                                                          start := 194155, 
                                                          stop := 194158 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 5, 3, 14, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBicon\
nectedDigraph" ), content := 0, count := [ 5, 3, 14, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 194208, 
                                                          root := ~, 
                                                          start := 194174, 
                                                          stop := 194207 ), 
                                                      rec( 
                                                          content := " and \n \
   ", count := [ 5, 3, 14, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBridg\
elessDigraph" ), content := 0, count := [ 5, 3, 14, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 194251, 
                                                          root := ~, 
                                                          start := 194218, 
                                                          stop := 194250 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 5, 3, 14, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> ArticulationPoints(CycleDigraph(5));\n[  ]\ngap> D := Digraph([[2, 7], [\
3, 5], [4], [2], [6], [1], []]);;\ngap> ArticulationPoints(D);\n[ 2, 1 ]\ngap>\
 ArticulationPoints(ChainDigraph(5));\n[ 4, 3, 2 ]\ngap> ArticulationPoints(Nu\
llDigraph(5));\n[  ]\ngap> D := ChainDigraph(IsMutableDigraph, 4);\n<mutable d\
igraph with 4 vertices, 3 edges>\ngap> ArticulationPoints(D);\n[ 3, 2 ]\n", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      14, 9 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 14, 9 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 194656, 
                                                          root := ~, 
                                                          start := 194253, 
                                                          stop := 194655 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 14, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 194673, root := ~, 
                                                  start := 192909, 
                                                  stop := 194672 ) ], 
                                          count := [ 5, 3, 14, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 194687, root := ~, 
                                          start := 192803, stop := 194686 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 14, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D", 
                                                      Name := "Bridges" ), 
                                                  content := 0, 
                                                  count := [ 5, 3, 15, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 194738, root := ~, 
                                                  start := 194708, 
                                                  stop := 194737 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A (possib\
ly empty) list of edges.", count := [ 5, 3, 15, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 15, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 194793, root := ~, 
                                                  start := 194741, 
                                                  stop := 194792 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A c\
onnected digraph is ", count := [ 5, 3, 15, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
-edge-connected", count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "E", 
                                                          next := 194860, 
                                                          root := ~, 
                                                          start := 194837, 
                                                          stop := 194859 ), 
                                                      rec( 
                                                          content := " if it i\
s still connected (in\n    the sense of ", count := [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsConne\
ctedDigraph" ), content := 0, count := [ 5, 3, 15, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 194939, 
                                                          root := ~, 
                                                          start := 194907, 
                                                          stop := 194938 ), 
                                                      rec( 
                                                          content := ") when a\
ny edge is\n    removed.  If the digraph ", count := [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 194995, 
                                                          root := ~, 
                                                          start := 194987, 
                                                          stop := 194994 ), 
                                                      rec( 
                                                          content := " is not \
2-edge-connected but is\n    connected, then any edge ", count := 
                                                            [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u, v]", count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 195069, 
                                                          root := ~, 
                                                          start := 195056, 
                                                          stop := 195068 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 195081, 
                                                          root := ~, 
                                                          start := 195073, 
                                                          stop := 195080 ), 
                                                      rec( 
                                                          content := " whose r\
emoval\n    makes the resulting digraph disconnected is called a ", 
                                                          count := 
                                                            [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "b\
ridge", count := [ 5, 3, 15, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 195166, 
                                                          root := ~, 
                                                          start := 195153, 
                                                          stop := 195165 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 195171, 
                                                          root := ~, 
                                                          start := 195167, 
                                                          stop := 195170 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
ridges", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 195191, 
                                                          root := ~, 
                                                          start := 195177, 
                                                          stop := 195190 ), 
                                                      rec( 
                                                          content := " returns\
 a list of the bridges of ", count := [ 5, 3, 15, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 195233, 
                                                          root := ~, 
                                                          start := 195225, 
                                                          stop := 195232 ), 
                                                      rec( 
                                                          content := ", if any\
, and, in\n    particular, returns the empty list if ", count := 
                                                            [ 5, 3, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 195301, 
                                                          root := ~, 
                                                          start := 195293, 
                                                          stop := 195300 ), 
                                                      rec( 
                                                          content := " is not \
connected. ", count := [ 5, 3, 15, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 195324, 
                                                          root := ~, 
                                                          start := 195320, 
                                                          stop := 195323 ), 
                                                      rec( 
                                                          content := "\n\n    \
Multiple edges are ignored by this method. ", count := [ 5, 3, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 195377, 
                                                          root := ~, 
                                                          start := 195373, 
                                                          stop := 195376 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this operation has complexity ", count := [ 5, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 5, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 195445, 
                                                          root := ~, 
                                                          start := 195432, 
                                                          stop := 195444 ), 
                                                      rec( 
                                                          content := " where\n\
    ", count := [ 5, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 195464, 
                                                          root := ~, 
                                                          start := 195456, 
                                                          stop := 195463 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and ", count := [ 5, 3, 15, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 15, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 195500, 
                                                          root := ~, 
                                                          start := 195492, 
                                                          stop := 195499 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in\n    the digraph.\n    ", count := [ 5, 3, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 195555, 
                                                          root := ~, 
                                                          start := 195551, 
                                                          stop := 195554 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 195572, 
                                                          root := ~, 
                                                          start := 195564, 
                                                          stop := 195571 ), 
                                                      rec( 
                                                          content := " has a b\
ridge, then a node incident to the bridge is an\n    articulation point (see "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Articul\
ationPoints" ), content := 0, count := [ 5, 3, 15, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 195688, 
                                                          root := ~, 
                                                          start := 195656, 
                                                          stop := 195687 ), 
                                                      rec( 
                                                          content := ") if and\
 only if\n    it has degree at least ", count := [ 5, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
", count := [ 5, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 195740, 
                                                          root := ~, 
                                                          start := 195732, 
                                                          stop := 195739 ), 
                                                      rec( 
                                                          content := ".  It fo\
llows that if ", count := [ 5, 3, 15, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 195770, 
                                                          root := ~, 
                                                          start := 195762, 
                                                          stop := 195769 ), 
                                                      rec( 
                                                          content := " has a\n\
    bridge and at least ", count := [ 5, 3, 15, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 5, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 195809, 
                                                          root := ~, 
                                                          start := 195801, 
                                                          stop := 195808 ), 
                                                      rec( 
                                                          content := " nodes, \
then at least one of the nodes\n    incident to the bridge is an articulation \
point. The converse does not\n    hold, there are digraphs with articulation p\
oints, but no bridges.\n    ", count := [ 5, 3, 15, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 196002, 
                                                          root := ~, 
                                                          start := 195998, 
                                                          stop := 196001 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 5, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBicon\
nectedDigraph" ), content := 0, count := [ 5, 3, 15, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 196051, 
                                                          root := ~, 
                                                          start := 196017, 
                                                          stop := 196050 ), 
                                                      rec( 
                                                          content := " and \n \
   ", count := [ 5, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBridg\
elessDigraph" ), content := 0, count := [ 5, 3, 15, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 196094, 
                                                          root := ~, 
                                                          start := 196061, 
                                                          stop := 196093 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 5, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 5], [1, 3, 4, 5], [2, 4], [2, 3], [1, 2]]);\n<immutabl\
e digraph with 5 vertices, 12 edges>\ngap> Bridges(D);\n[  ]\ngap> D := Digrap\
h([[2], [3], [4], [2]]);\n<immutable digraph with 4 vertices, 4 edges>\ngap> B\
ridges(D);\n[ [ 1, 2 ] ]\ngap> Bridges(ChainDigraph(2));\n[ [ 1, 2 ] ]\ngap> A\
rticulationPoints(ChainDigraph(2));\n[  ]\n", count := [ 5, 3, 15, 9 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 15, 9 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 196470, 
                                                          root := ~, 
                                                          start := 196096, 
                                                          stop := 196469 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 15, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 15, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 196487, root := ~, 
                                                  start := 194796, 
                                                  stop := 196486 ) ], 
                                          count := [ 5, 3, 15, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 196501, root := ~, 
                                          start := 194693, stop := 196500 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 15, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D", 
                                                      Name := "StrongOrientati\
on" ), content := 0, count := [ 5, 3, 16, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 196562, root := ~, 
                                                  start := 196522, 
                                                  stop := 196561 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D", 
                                                      Name := "StrongOrientati\
onAttr" ), content := 0, count := [ 5, 3, 16, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 196609, root := ~, 
                                                  start := 196565, 
                                                  stop := 196608 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
 or ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 196645, 
                                                          root := ~, 
                                                          start := 196634, 
                                                          stop := 196644 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 16, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 196656, root := ~, 
                                                  start := 196612, 
                                                  stop := 196655 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
trong orientation", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 16, 5 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 196704, 
                                                          root := ~, 
                                                          start := 196679, 
                                                          stop := 196703 ), 
                                                      rec( 
                                                          content := " of a co\
nnected symmetric digraph ", count := [ 5, 3, 16, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 196746, 
                                                          root := ~, 
                                                          start := 196738, 
                                                          stop := 196745 ), 
                                                      rec( 
                                                          content := " (if\n  \
  it exists) is a strongly connected subdigraph ", count := [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 196809, 
                                                          root := ~, 
                                                          start := 196801, 
                                                          stop := 196808 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 196821, 
                                                          root := ~, 
                                                          start := 196813, 
                                                          stop := 196820 ), 
                                                      rec( 
                                                          content := " such\n \
   that for every edge ", count := [ 5, 3, 16, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u, v]", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 196864, 
                                                          root := ~, 
                                                          start := 196851, 
                                                          stop := 196863 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 196876, 
                                                          root := ~, 
                                                          start := 196868, 
                                                          stop := 196875 ), 
                                                      rec( 
                                                          content := " either \
", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
u, v]", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 196897, 
                                                          root := ~, 
                                                          start := 196884, 
                                                          stop := 196896 ), 
                                                      rec( 
                                                          content := " or\n   \
 ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
v, u]", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 196918, 
                                                          root := ~, 
                                                          start := 196905, 
                                                          stop := 196917 ), 
                                                      rec( 
                                                          content := " is an e\
dge of ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 196941, 
                                                          root := ~, 
                                                          start := 196933, 
                                                          stop := 196940 ), 
                                                      rec( 
                                                          content := " but not\
 both.  Robbin's Theorem states\n    that a digraph admits a strong orientatio\
n if and only if it is\n    bridgeless (see ", count := [ 5, 3, 16, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBridg\
elessDigraph" ), content := 0, count := [ 5, 3, 16, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 197102, 
                                                          root := ~, 
                                                          start := 197069, 
                                                          stop := 197101 ), 
                                                      rec( 
                                                          content := "). \n   \
 ", count := [ 5, 3, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 197114, 
                                                          root := ~, 
                                                          start := 197110, 
                                                          stop := 197113 ), 
                                                      rec( 
                                                          content := "\n\n    \
This operation returns a strong orientation of the digraph ", 
                                                          count := 
                                                            [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 197187, 
                                                          root := ~, 
                                                          start := 197179, 
                                                          stop := 197186 ), 
                                                      rec( 
                                                          content := " if \n  \
  ", count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 197204, 
                                                          root := ~, 
                                                          start := 197196, 
                                                          stop := 197203 ), 
                                                      rec( 
                                                          content := " is symm\
etric and ", count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 197230, 
                                                          root := ~, 
                                                          start := 197222, 
                                                          stop := 197229 ), 
                                                      rec( 
                                                          content := " admits \
a strong orientation. If ", count := [ 5, 3, 16, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 197271, 
                                                          root := ~, 
                                                          start := 197263, 
                                                          stop := 197270 ), 
                                                      rec( 
                                                          content := "\n    is\
 symmetric but does not admit a strong orientation, then ", 
                                                          count := 
                                                            [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 197346, 
                                                          root := ~, 
                                                          start := 197335, 
                                                          stop := 197345 ), 
                                                      rec( 
                                                          content := " is\n   \
 returned. If ", count := [ 5, 3, 16, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 197375, 
                                                          root := ~, 
                                                          start := 197367, 
                                                          stop := 197374 ), 
                                                      rec( 
                                                          content := " is not \
symmetric, then an error is given. \n    ", count := [ 5, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 16, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 197427, 
                                                          root := ~, 
                                                          start := 197423, 
                                                          stop := 197426 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 3, 16, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 197444, 
                                                          root := ~, 
                                                          start := 197436, 
                                                          stop := 197443 ), 
                                                      rec( 
                                                          content := " is immu\
table, ", count := [ 5, 3, 16, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
trongOrientation(", count := [ 5, 3, 16, 7 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "D\
", count := [ 5, 3, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      16, 7 ],
                                                                  mathmode := \
"Text", name := "A", next := 197488, root := ~, start := 197480, stop := 19748\
7 ), rec( content := ")", count := [ 5, 3, 16, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 16, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 197493, 
                                                          root := ~, 
                                                          start := 197459, 
                                                          stop := 197492 ), 
                                                      rec( 
                                                          content := " returns\
 an\n    immutable digraph, and if ", count := [ 5, 3, 16, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 5, 3, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 197543, 
                                                          root := ~, 
                                                          start := 197535, 
                                                          stop := 197542 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then\n    ", count := [ 5, 3, 16, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
trongOrientation(", count := [ 5, 3, 16, 7 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "D\
", count := [ 5, 3, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      16, 7 ],
                                                                  mathmode := \
"Text", name := "A", next := 197594, root := ~, start := 197586, stop := 19759\
3 ), rec( content := ")", count := [ 5, 3, 16, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 16, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 197599, 
                                                          root := ~, 
                                                          start := 197565, 
                                                          stop := 197598 ), 
                                                      rec( 
                                                          content := " returns\
 a mutable digraph. ", count := [ 5, 3, 16, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 16, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 197631, 
                                                          root := ~, 
                                                          start := 197627, 
                                                          stop := 197630 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this operation has complexity ", count := [ 5, 3, 16, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 16, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 197699, 
                                                          root := ~, 
                                                          start := 197686, 
                                                          stop := 197698 ), 
                                                      rec( 
                                                          content := " where\n\
    ", count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 197718, 
                                                          root := ~, 
                                                          start := 197710, 
                                                          stop := 197717 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and ", count := [ 5, 3, 16, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 16, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 197754, 
                                                          root := ~, 
                                                          start := 197746, 
                                                          stop := 197753 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in\n    the digraph.\n", count := [ 5, 3, 16, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> StrongOrientation(DigraphSymmetricClosure(CycleDigraph(5))) \n> = CycleD\
igraph(5);\ntrue\ngap> D := DigraphSymmetricClosure(Digraph(\n> [[2, 7], [3, 5\
], [4], [2], [6], [1], []]));;\ngap> IsBridgelessDigraph(D);\nfalse\ngap> Stro\
ngOrientation(D);\nfail\ngap> StrongOrientation(NullDigraph(0));\n<immutable e\
mpty digraph with 0 vertices>\ngap> StrongOrientation(DigraphDisjointUnion(Com\
pleteDigraph(3), \n>                                           CompleteDigraph\
(3)));\nfail\n", count := [ 5, 3, 16, 9 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 198300, 
                                                          root := ~, 
                                                          start := 197801, 
                                                          stop := 198299 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 16, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 198317, root := ~, 
                                                  start := 196659, 
                                                  stop := 198316 ) ], 
                                          count := [ 5, 3, 16, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 198331, root := ~, 
                                          start := 196507, stop := 198330 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 16, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphPeriod" 
                                                     ), content := 0, 
                                                  count := [ 5, 3, 17, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 198394, root := ~, 
                                                  start := 198352, 
                                                  stop := 198393 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r.", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 198427, root := ~, 
                                                  start := 198397, 
                                                  stop := 198426 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the period of the digraph ", count := [ 5, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 198510, 
                                                          root := ~, 
                                                          start := 198496, 
                                                          stop := 198509 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 198515, 
                                                          root := ~, 
                                                          start := 198511, 
                                                          stop := 198514 ), 
                                                      rec( 
                                                          content := "\n\n    \
If a digraph ", count := [ 5, 3, 17, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 198548, 
                                                          root := ~, 
                                                          start := 198534, 
                                                          stop := 198547 ), 
                                                      rec( 
                                                          content := " has at \
least one directed cycle, then the period\n    is the greatest positive intege\
r which divides the lengths of all directed\n    cycles of ", 
                                                          count := 
                                                            [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 198705, 
                                                          root := ~, 
                                                          start := 198691, 
                                                          stop := 198704 ), 
                                                      rec( 
                                                          content := ".  If ",
                                                          count := 
                                                            [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 198725, 
                                                          root := ~, 
                                                          start := 198711, 
                                                          stop := 198724 ), 
                                                      rec( 
                                                          content := " has no \
directed cycles, then\n    this function returns ", count := [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 198789, 
                                                          root := ~, 
                                                          start := 198781, 
                                                          stop := 198788 ), 
                                                      rec( 
                                                          content := ".  See S\
ection ", count := [ 5, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 198854, 
                                                          root := ~, 
                                                          start := 198804, 
                                                          stop := 198853 ), 
                                                      rec( 
                                                          content := " for the\
 definition of a directed cycle. ", count := [ 5, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 198899, 
                                                          root := ~, 
                                                          start := 198895, 
                                                          stop := 198898 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph with a period of ", count := [ 5, 3, 17, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 5, 3, 17, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 198940, 
                                                          root := ~, 
                                                          start := 198932, 
                                                          stop := 198939 ), 
                                                      rec( 
                                                          content := " is said\
 to be ", count := [ 5, 3, 17, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
periodic", count := [ 5, 3, 17, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 198971, 
                                                          root := ~, 
                                                          start := 198955, 
                                                          stop := 198970 ), 
                                                      rec( 
                                                          content := ".  See\n\
    ", count := [ 5, 3, 17, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsAperi\
odicDigraph" ), content := 0, count := [ 5, 3, 17, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 199014, 
                                                          root := ~, 
                                                          start := 198982, 
                                                          stop := 199013 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 199020, 
                                                          root := ~, 
                                                          start := 199016, 
                                                          stop := 199019 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 3, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[6], [1], [2], [3], [4, 4], [5]]);\n<immutable multidigrap\
h with 6 vertices, 7 edges>\ngap> DigraphPeriod(D);\n6\ngap> D := Digraph([[2]\
, [3, 5], [4], [5], [1, 2]]);\n<immutable digraph with 5 vertices, 7 edges>\ng\
ap> DigraphPeriod(D);\n1\ngap> D := ChainDigraph(2);\n<immutable chain digraph\
 with 2 vertices>\ngap> DigraphPeriod(D);\n0\ngap> IsAcyclicDigraph(D);\ntrue\
\ngap> D := GeneralisedPetersenGraph(IsMutableDigraph, 5, 2);\n<mutable digrap\
h with 10 vertices, 30 edges>\ngap> DigraphPeriod(D);\n1\n", count := 
                                                                    [ 5, 3, 
                                                                      17, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 17, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 199563, 
                                                          root := ~, 
                                                          start := 199025, 
                                                          stop := 199562 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 17, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 199580, root := ~, 
                                                  start := 198430, 
                                                  stop := 199579 ) ], 
                                          count := [ 5, 3, 17, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 199594, root := ~, 
                                          start := 198337, stop := 199593 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 17, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, func, n\
opath, edge", Name := "DigraphFloydWarshall" ), content := 0, 
                                                  count := [ 5, 3, 18, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 199684, root := ~, 
                                                  start := 199615, 
                                                  stop := 199683 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A matrix.\
", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 5, 3, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 199715, root := ~, 
                                                  start := 199687, 
                                                  stop := 199714 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 199753, 
                                                          root := ~, 
                                                          start := 199739, 
                                                          stop := 199752 ), 
                                                      rec( 
                                                          content := " is a di\
graph with ", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 199780, 
                                                          root := ~, 
                                                          start := 199772, 
                                                          stop := 199779 ), 
                                                      rec( 
                                                          content := " vertice\
s, then\n    this operation returns an ", count := [ 5, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
 \\times n", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 199843, 
                                                          root := ~, 
                                                          start := 199826, 
                                                          stop := 199842 ), 
                                                      rec( 
                                                          content := " matrix \
", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 199861, 
                                                          root := ~, 
                                                          start := 199851, 
                                                          stop := 199860 ), 
                                                      rec( 
                                                          content := " contain\
ing\n    the output of a generalised version of the Floyd-Warshall algorithm,\
\n    applied to ", count := [ 5, 3, 18, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 199975, 
                                                          root := ~, 
                                                          start := 199961, 
                                                          stop := 199974 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 199981, 
                                                          root := ~, 
                                                          start := 199977, 
                                                          stop := 199980 ), 
                                                      rec( 
                                                          content := "\n\n    \
The operation ", count := [ 5, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphFloydWarshall", count := [ 5, 3, 18, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 200028, 
                                                          root := ~, 
                                                          start := 200001, 
                                                          stop := 200027 ), 
                                                      rec( 
                                                          content := " is cust\
omised by the arguments\n    ", count := [ 5, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
unc", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200075, 
                                                          root := ~, 
                                                          start := 200064, 
                                                          stop := 200074 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
opath", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200090, 
                                                          root := ~, 
                                                          start := 200077, 
                                                          stop := 200089 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200107, 
                                                          root := ~, 
                                                          start := 200096, 
                                                          stop := 200106 ), 
                                                      rec( 
                                                          content := ".\n    T\
he arguments ", count := [ 5, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
opath", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200140, 
                                                          root := ~, 
                                                          start := 200127, 
                                                          stop := 200139 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200156, 
                                                          root := ~, 
                                                          start := 200145, 
                                                          stop := 200155 ), 
                                                      rec( 
                                                          content := " can be \
arbitrary ", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " objects\
.\n    The argument ", count := [ 5, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
unc", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200217, 
                                                          root := ~, 
                                                          start := 200206, 
                                                          stop := 200216 ), 
                                                      rec( 
                                                          content := " must be\
 a function which accepts 4 arguments:\n    the matrix ", count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 200289, 
                                                          root := ~, 
                                                          start := 200279, 
                                                          stop := 200288 ), 
                                                      rec( 
                                                          content := ", follow\
ed by 3 postive integers. The function\n    ", count := [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
unc", count := [ 5, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200351, 
                                                          root := ~, 
                                                          start := 200340, 
                                                          stop := 200350 ), 
                                                      rec( 
                                                          content := " is wher\
e the work to calculate the desired outcome must be\n    performed. ", 
                                                          count := 
                                                            [ 5, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 200430, 
                                                          root := ~, 
                                                          start := 200426, 
                                                          stop := 200429 ), 
                                                      rec( 
                                                          content := "\n\n    \
This method initialises the matrix ", count := [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 200481, 
                                                          root := ~, 
                                                          start := 200471, 
                                                          stop := 200480 ), 
                                                      rec( 
                                                          content := " by sett\
ing entry\n    ", count := [ 5, 3, 18, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at[i][j]", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 200519, 
                                                          root := ~, 
                                                          start := 200503, 
                                                          stop := 200518 ), 
                                                      rec( 
                                                          content := " to equa\
l ", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200540, 
                                                          root := ~, 
                                                          start := 200529, 
                                                          stop := 200539 ), 
                                                      rec( 
                                                          content := " if ther\
e is an edge with source\n    ", count := [ 5, 3, 18, 5 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 200585, 
                                                          root := ~, 
                                                          start := 200577, 
                                                          stop := 200584 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 200604, 
                                                          root := ~, 
                                                          start := 200596, 
                                                          stop := 200603 ), 
                                                      rec( 
                                                          content := ", and by\
 setting entry ", count := [ 5, 3, 18, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at[i][j]", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 200643, 
                                                          root := ~, 
                                                          start := 200627, 
                                                          stop := 200642 ), 
                                                      rec( 
                                                          content := " to equa\
l\n    ", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
opath", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200670, 
                                                          root := ~, 
                                                          start := 200657, 
                                                          stop := 200669 ), 
                                                      rec( 
                                                          content := " otherwi\
se.\n    The final part of ", count := [ 5, 3, 18, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphFloydWarshall", count := [ 5, 3, 18, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 18, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 200731, 
                                                          root := ~, 
                                                          start := 200704, 
                                                          stop := 200730 ), 
                                                      rec( 
                                                          content := " then ca\
lls the function\n    ", count := [ 5, 3, 18, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
unc", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200771, 
                                                          root := ~, 
                                                          start := 200760, 
                                                          stop := 200770 ), 
                                                      rec( 
                                                          content := " inside \
three nested for loops, over the vertices of\n    ", count := [ 5, 3, 18, 5 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 200842, 
                                                          root := ~, 
                                                          start := 200828, 
                                                          stop := 200841 ), 
                                                      rec( content := ": ", 
                                                          count := 
                                                            [ 5, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 18, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 200848, 
                                                          root := ~, 
                                                          start := 200844, 
                                                          stop := 200847 ), 
                                                      rec( content := "\n\n", 
                                                          count := 
                                                            [ 5, 3, 18, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
nfor i in DigraphsVertices(digraph) do\n  for j in DigraphsVertices(digraph) d\
o\n    for k in DigraphsVertices(digraph) do\n      func(mat, i, j, k);\n    o\
d;\n  od;\nod;\n", count := [ 5, 3, 18, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 18, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Listing", 
                                                          next := 201046, 
                                                          root := ~, 
                                                          start := 200850, 
                                                          stop := 201045 ), 
                                                      rec( 
                                                          content := "\n\n    \
The matrix ", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
at", count := [ 5, 3, 18, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 18, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 201073, 
                                                          root := ~, 
                                                          start := 201063, 
                                                          stop := 201072 ), 
                                                      rec( 
                                                          content := " is then\
 returned as the result. An example of using\n    ", count := [ 5, 3, 18, 8 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphFloydWarshall", count := [ 5, 3, 18, 8 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 18, 8 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 201157, 
                                                          root := ~, 
                                                          start := 201130, 
                                                          stop := 201156 ), 
                                                      rec( 
                                                          content := " to calc\
ulate the shortest (non-zero) distances\n    between the vertices of a digraph\
 is shown below: ", count := [ 5, 3, 18, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 201263, 
                                                          root := ~, 
                                                          start := 201259, 
                                                          stop := 201262 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 3, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDigraph6String(\"&EAHQeDB\");\n<immutable digraph with 6\
 vertices, 12 edges>\ngap> func := function(mat, i, j, k)\n>   if mat[i][k] <>\
 -1 and mat[k][j] <> -1 then\n>     if (mat[i][j] = -1) or (mat[i][j] > mat[i]\
[k] + mat[k][j]) then\n>       mat[i][j] := mat[i][k] + mat[k][j];\n>     fi;\
\n>   fi;\n> end;\nfunction( mat, i, j, k ) ... end\ngap> shortest_distances :\
= DigraphFloydWarshall(D, func, -1, 1);;\ngap> Display(shortest_distances);\n[\
 [   3,  -1,  -1,   2,   1,   2 ],\n  [   4,   2,   1,   3,   2,   1 ],\n  [  \
 3,   1,   2,   2,   1,   2 ],\n  [   1,  -1,  -1,   1,   1,   2 ],\n  [   2, \
 -1,  -1,   1,   2,   1 ],\n  [   3,  -1,  -1,   2,   1,   1 ] ]\n", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      18, 10 ]
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 18, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 201969, 
                                                          root := ~, 
                                                          start := 201269, 
                                                          stop := 201968 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 18, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 201986, root := ~, 
                                                  start := 199718, 
                                                  stop := 201985 ) ], 
                                          count := [ 5, 3, 18, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 202000, root := ~, 
                                          start := 199600, stop := 201999 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 18, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, u, v", 
                                                      Name := "IsReachable" ),
                                                  content := 0, 
                                                  count := [ 5, 3, 19, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 202067, root := ~, 
                                                  start := 202021, 
                                                  stop := 202066 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 202090, 
                                                          root := ~, 
                                                          start := 202079, 
                                                          stop := 202089 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 202106, 
                                                          root := ~, 
                                                          start := 202094, 
                                                          stop := 202105 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 19, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 202117, root := ~, 
                                                  start := 202070, 
                                                  stop := 202116 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns ", count := [ 5, 3, 19, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 202172, 
                                                          root := ~, 
                                                          start := 202161, 
                                                          stop := 202171 ), 
                                                      rec( 
                                                          content := " if ther\
e exists a non-trivial directed\n    walk from vertex ", count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 202241, 
                                                          root := ~, 
                                                          start := 202233, 
                                                          stop := 202240 ), 
                                                      rec( 
                                                          content := " to vert\
ex ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 202260, 
                                                          root := ~, 
                                                          start := 202252, 
                                                          stop := 202259 ), 
                                                      rec( 
                                                          content := " in the \
digraph ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 202290, 
                                                          root := ~, 
                                                          start := 202276, 
                                                          stop := 202289 ), 
                                                      rec( 
                                                          content := ",\n    a\
nd ", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 5, 3, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 202312, 
                                                          root := ~, 
                                                          start := 202300, 
                                                          stop := 202311 ), 
                                                      rec( 
                                                          content := " if ther\
e does not exist such a directed walk.  See Section\n    ", 
                                                          count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 202420, 
                                                          root := ~, 
                                                          start := 202376, 
                                                          stop := 202419 ), 
                                                      rec( 
                                                          content := " for the\
 definition of a\n    non-trivial directed walk.\n    ", count := 
                                                            [ 5, 3, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 202484, 
                                                          root := ~, 
                                                          start := 202480, 
                                                          stop := 202483 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method for ", count := [ 5, 3, 19, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sReachable", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 202523, 
                                                          root := ~, 
                                                          start := 202505, 
                                                          stop := 202522 ), 
                                                      rec( 
                                                          content := " has wor\
st case complexity of ", count := [ 5, 3, 19, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m +\n      n)", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "M", 
                                                          next := 202574, 
                                                          root := ~, 
                                                          start := 202553, 
                                                          stop := 202573 ), 
                                                      rec( 
                                                          content := " where "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 202589, 
                                                          root := ~, 
                                                          start := 202581, 
                                                          stop := 202588 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and ", count := [ 5, 3, 19, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 202625, 
                                                          root := ~, 
                                                          start := 202617, 
                                                          stop := 202624 ), 
                                                      rec( 
                                                          content := " the num\
ber of\n    vertices in ", count := [ 5, 3, 19, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 202670, 
                                                          root := ~, 
                                                          start := 202656, 
                                                          stop := 202669 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 3, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2], [3], [2, 3]]);\n<immutable digraph with 3 vertices, 4\
 edges>\ngap> IsReachable(D, 1, 3);\ntrue\ngap> IsReachable(D, 2, 1);\nfalse\n\
gap> IsReachable(D, 3, 3);\ntrue\ngap> IsReachable(D, 1, 1);\nfalse\n", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      19, 5 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 19, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 202919, 
                                                          root := ~, 
                                                          start := 202673, 
                                                          stop := 202918 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 19, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 19, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 202936, root := ~, 
                                                  start := 202120, 
                                                  stop := 202935 ) ], 
                                          count := [ 5, 3, 19, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 202950, root := ~, 
                                          start := 202006, stop := 202949 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 19, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, root", 
                                                      Name := "VerticesReachab\
leFrom" ), content := 0, count := [ 5, 3, 20, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 203027, root := ~, 
                                                  start := 202971, 
                                                  stop := 203026 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list.",
                                                          count := 
                                                            [ 5, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 20, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 203056, root := ~, 
                                                  start := 203030, 
                                                  stop := 203055 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns a list of the vertices  ", count := [ 5, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 203132, 
                                                          root := ~, 
                                                          start := 203124, 
                                                          stop := 203131 ), 
                                                      rec( 
                                                          content := ", for wh\
ich there exists\n    a non-trivial directed walk from vertex ", 
                                                          count := 
                                                            [ 5, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
oot", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 203212, 
                                                          root := ~, 
                                                          start := 203201, 
                                                          stop := 203211 ), 
                                                      rec( 
                                                          content := " to vert\
ex ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 203231, 
                                                          root := ~, 
                                                          start := 203223, 
                                                          stop := 203230 ), 
                                                      rec( 
                                                          content := " in the \
digraph\n    ", count := [ 5, 3, 20, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 203265, 
                                                          root := ~, 
                                                          start := 203251, 
                                                          stop := 203264 ), 
                                                      rec( 
                                                          content := ". See Se\
ction ", count := [ 5, 3, 20, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 203323, 
                                                          root := ~, 
                                                          start := 203279, 
                                                          stop := 203322 ), 
                                                      rec( 
                                                          content := "\n    fo\
r the definition of a non-trivial directed walk.\n    ", count := 
                                                            [ 5, 3, 20, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 203387, 
                                                          root := ~, 
                                                          start := 203383, 
                                                          stop := 203386 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method for ", count := [ 5, 3, 20, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
erticesReachableFrom", count := [ 5, 3, 20, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 20, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 203436, 
                                                          root := ~, 
                                                          start := 203408, 
                                                          stop := 203435 ), 
                                                      rec( 
                                                          content := " has wor\
st case complexity of ", count := [ 5, 3, 20, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m +\n      n)", count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "M", 
                                                          next := 203487, 
                                                          root := ~, 
                                                          start := 203466, 
                                                          stop := 203486 ), 
                                                      rec( 
                                                          content := " where "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 203502, 
                                                          root := ~, 
                                                          start := 203494, 
                                                          stop := 203501 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and ", count := [ 5, 3, 20, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 203538, 
                                                          root := ~, 
                                                          start := 203530, 
                                                          stop := 203537 ), 
                                                      rec( 
                                                          content := " the num\
ber of\n    vertices in ", count := [ 5, 3, 20, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 20, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 203583, 
                                                          root := ~, 
                                                          start := 203569, 
                                                          stop := 203582 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 3, 20, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(5);\n<immutable complete digraph with 5 vertices>\n\
gap> VerticesReachableFrom(D, 1);\n[ 2, 1, 3, 4, 5 ]\ngap> VerticesReachableFr\
om(D, 3);\n[ 1, 2, 3, 4, 5 ]\ngap> D := EmptyDigraph(5);\n<immutable empty dig\
raph with 5 vertices>\ngap> VerticesReachableFrom(D, 1);\n[  ]\ngap> VerticesR\
eachableFrom(D, 3);\n[  ]\ngap> D := CycleDigraph(4);\n<immutable cycle digrap\
h with 4 vertices>\ngap> VerticesReachableFrom(D, 1);\n[ 2, 3, 4, 1 ]\ngap> Ve\
rticesReachableFrom(D, 3);\n[ 4, 1, 2, 3 ]\ngap> D := ChainDigraph(5);\n<immut\
able chain digraph with 5 vertices>\ngap> VerticesReachableFrom(D, 1);\n[ 2, 3\
, 4, 5 ]\ngap> VerticesReachableFrom(D, 3);\n[ 4, 5 ]\ngap> VerticesReachableF\
rom(D, 5);\n[  ]\n", count := [ 5, 3, 20, 5 ], name := "PCDATA", root := ~ ) ]
                                                            , 
                                                          count := 
                                                            [ 5, 3, 20, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 204311, 
                                                          root := ~, 
                                                          start := 203586, 
                                                          stop := 204310 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 20, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 20, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 204328, root := ~, 
                                                  start := 203059, 
                                                  stop := 204327 ) ], 
                                          count := [ 5, 3, 20, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 204342, root := ~, 
                                          start := 202956, stop := 204341 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 20, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, u, v", 
                                                      Name := "DigraphPath" ),
                                                  content := 0, 
                                                  count := [ 5, 3, 21, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 204409, root := ~, 
                                                  start := 204363, 
                                                  stop := 204408 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A pair of\
 lists, or ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 204452, 
                                                          root := ~, 
                                                          start := 204441, 
                                                          stop := 204451 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 21, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 204463, root := ~, 
                                                  start := 204412, 
                                                  stop := 204462 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
there exists a non-trivial directed path (or a non-trivial cycle, in the\n    \
case that ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 204582, 
                                                          root := ~, 
                                                          start := 204574, 
                                                          stop := 204581 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "=\
", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 204591, 
                                                          root := ~, 
                                                          start := 204583, 
                                                          stop := 204590 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 204600, 
                                                          root := ~, 
                                                          start := 204592, 
                                                          stop := 204599 ), 
                                                      rec( 
                                                          content := ") from v\
ertex ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 204622, 
                                                          root := ~, 
                                                          start := 204614, 
                                                          stop := 204621 ), 
                                                      rec( 
                                                          content := " to vert\
ex\n    ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 204645, 
                                                          root := ~, 
                                                          start := 204637, 
                                                          stop := 204644 ), 
                                                      rec( 
                                                          content := " in the \
digraph ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 204675, 
                                                          root := ~, 
                                                          start := 204661, 
                                                          stop := 204674 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns such a\n    directed path (or directed cycle). Otherwise\
, this operation returns\n    ", count := [ 5, 3, 21, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 204800, 
                                                          root := ~, 
                                                          start := 204789, 
                                                          stop := 204799 ), 
                                                      rec( 
                                                          content := ".  See S\
ection ", count := [ 5, 3, 21, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Text",
                                                              Subsect := "Defi\
nitions" ), content := 0, count := [ 5, 3, 21, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 204856, 
                                                          root := ~, 
                                                          start := 204815, 
                                                          stop := 204855 ), 
                                                      rec( 
                                                          content := " for the\
\n    definition of a directed path and a directed cycle.\n    ", 
                                                          count := 
                                                            [ 5, 3, 21, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 21, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 204929, 
                                                          root := ~, 
                                                          start := 204925, 
                                                          stop := 204928 ), 
                                                      rec( 
                                                          content := "\n\n    \
A directed path (or directed cycle) of non-zero length ", count := 
                                                            [ 5, 3, 21, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
-1", count := [ 5, 3, 21, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 21, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 205000, 
                                                          root := ~, 
                                                          start := 204990, 
                                                          stop := 204999 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 21, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "(\
v_1, e_1, v_2, e_2, ..., e_{n-1}, v_n)", count := [ 5, 3, 21, 4 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 205052, 
                                                          root := ~, 
                                                          start := 205006, 
                                                          stop := 205051 ), 
                                                      rec( 
                                                          content := ",\n    i\
s represented by a pair of lists ", count := [ 5, 3, 21, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
v,a]", count := [ 5, 3, 21, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 21, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 205104, 
                                                          root := ~, 
                                                          start := 205092, 
                                                          stop := 205103 ), 
                                                      rec( 
                                                          content := " as foll\
ows:\n\n    ", count := [ 5, 3, 21, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 5, 3, 21, 6 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "v", count := [ 5, 3, 21, 6 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 6 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 205158, root := ~, start := 205150, stop := 205157 ), 
                                                                      rec( 
                                                                          cont\
ent := " is the list ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := \
"PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :\
= "[v_1, v_2, ..., v_n]", count := [ 5, 3, 21, 6 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 6 ], mathmode := "Text", name \
:= "M", next := 205198, root := ~, start := 205171, stop := 205197 ), rec( 
                                                                          cont\
ent := ".\n      ", count := [ 5, 3, 21, 6 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 21, 6 ], name := "Item", next := 205213,
                                                                  root := ~, 
                                                                  start := 205\
135, stop := 205212 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        ", count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "a", count :\
= [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \
:= [ 5, 3, 21, 8 ], mathmode := "Text", name := "C", next := 205243, root := ~
                                                                            , 
                                                                          star\
t := 205235, stop := 205242 ), rec( content := " is the list of positive integ\
ers ", count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA", root :=\
 ~ ), rec( attributes := rec(  ), content := [ rec( content := "[a_1, a_2, ...\
, a_{n-1}]", count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "M", next \
:= 205308, root := ~, start := 205277, stop := 205307 ), rec( content := "\n  \
      where for each each ", count := [ 5, 3, 21, 8 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "i < n", count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA",\
 root := ~ ) ], count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "M", 
                                                                          next\
 := 205352, root := ~, start := 205337, stop := 205351 ), rec( content := ", "
                                                                            , 
                                                                          coun\
t := [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "a_i", count := [ 5, 3, 21, 8 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 8\
 ], mathmode := "Text", name := "M", next := 205364, root := ~, start := 20535\
4, stop := 205363 ), rec( content := " is the position of\n        ", count :=\
 [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\
ibutes := rec(  ), content := [ rec( content := "v_{i+1}", count := [ 5, 3, 21\
, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 2\
1, 8 ], mathmode := "Text", name := "M", next := 205406, root := ~, start := 2\
05392, stop := 205405 ), rec( content := " in\n        ", count := [ 5, 3, 21,\
 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\
c(  ), content := [ rec( content := "OutNeighboursOfVertex(", count := [ 5, 3,\
 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3\
, 21, 8 ], mathmode := "Text", name := "C", next := 205447, root := ~, start :\
= 205418, stop := 205446 ), rec( attributes := rec(  ), content := [ rec( cont\
ent := "digraph", count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 205461, root := ~, start := 205447, stop := 205460 ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := ",", count := [ 5, 3, 21, 8 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 21, 8 ], mathmode :\
= "Text", name := "C", next := 205469, root := ~, start := 205461, stop := 205\
468 ), rec( attributes := rec(  ), content := [ rec( content := "v_i", count :\
= [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \
:= [ 5, 3, 21, 8 ], mathmode := "Text", name := "M", next := 205479, root := ~
                                                                            , 
                                                                          star\
t := 205469, stop := 205478 ), rec( attributes := rec(  ), content := [ rec( c\
ontent := ")", count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA",\
 root := ~ ) ], count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 205487, root := ~, start := 205479, stop := 205486 ), rec( content := "\n \
       corresponding to the edge ", count := [ 5, 3, 21, 8 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ re\
c( content := "e_i", count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "M\
", next := 205532, root := ~, start := 205522, stop := 205531 ), rec( content \
:= ".  This is can be useful if the\n        position of a vertex in a list of\
 out-neighours is significant, for\n        example in orbit digraphs.\n      \
", count := [ 5, 3, 21, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      21, 8 ],
                                                                  name := "Ite\
m", next := 205688, root := ~, start := 205220, stop := 205687 ) ], 
                                                          count := 
                                                            [ 5, 3, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 205700, 
                                                          root := ~, 
                                                          start := 205122, 
                                                          stop := 205699 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method for ", count := [ 5, 3, 21, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphPath", count := [ 5, 3, 21, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 21, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 205739, 
                                                          root := ~, 
                                                          start := 205721, 
                                                          stop := 205738 ), 
                                                      rec( 
                                                          content := " has wor\
st case complexity of ", count := [ 5, 3, 21, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m +\n      n)", count := [ 5, 3, 21, 10 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 5, 3, 21, 10 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 205790, 
                                                          root := ~, 
                                                          start := 205769, 
                                                          stop := 205789 ), 
                                                      rec( 
                                                          content := " where "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 21, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 3, 21, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 21, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 205805, 
                                                          root := ~, 
                                                          start := 205797, 
                                                          stop := 205804 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and ", count := [ 5, 3, 21, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 21, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 21, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 205841, 
                                                          root := ~, 
                                                          start := 205833, 
                                                          stop := 205840 ), 
                                                      rec( 
                                                          content := " the num\
ber of\n    vertices in ", count := [ 5, 3, 21, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 21, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 21, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 205886, 
                                                          root := ~, 
                                                          start := 205872, 
                                                          stop := 205885 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 3, 21, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2], [3], [2, 3]]);\n<immutable digraph with 3 vertices, 4\
 edges>\ngap> DigraphPath(D, 1, 3);\n[ [ 1, 2, 3 ], [ 1, 1 ] ]\ngap> DigraphPa\
th(D, 2, 1);\nfail\ngap> DigraphPath(D, 3, 3);\n[ [ 3, 3 ], [ 2 ] ]\ngap> Digr\
aphPath(D, 1, 1);\nfail\n", count := [ 5, 3, 21, 11 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 21, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 206169, 
                                                          root := ~, 
                                                          start := 205889, 
                                                          stop := 206168 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 21, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 21, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 206186, root := ~, 
                                                  start := 204466, 
                                                  stop := 206185 ) ], 
                                          count := [ 5, 3, 21, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 206200, root := ~, 
                                          start := 204348, stop := 206199 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 21, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, u, v", 
                                                      Name := "DigraphShortest\
Path" ), content := 0, count := [ 5, 3, 22, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 206275, root := ~, 
                                                  start := 206221, 
                                                  stop := 206274 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A pair of\
 lists, or ", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 206318, 
                                                          root := ~, 
                                                          start := 206307, 
                                                          stop := 206317 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 22, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 206329, root := ~, 
                                                  start := 206278, 
                                                  stop := 206328 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns the shortest directed path in the digraph digraph from the vertex\n    ",
                                                          count := 
                                                            [ 5, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 206436, 
                                                          root := ~, 
                                                          start := 206428, 
                                                          stop := 206435 ), 
                                                      rec( 
                                                          content := " to the \
vertex ", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 206459, 
                                                          root := ~, 
                                                          start := 206451, 
                                                          stop := 206458 ), 
                                                      rec( 
                                                          content := ", if suc\
h a path exists. If ", count := [ 5, 3, 22, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "u", count := [ 5, 3, 22, 3 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 22, 3 ], 
                                                                  mathmode := \
"Text", name := "A", next := 206498, root := ~, start := 206490, stop := 20649\
7 ), rec( content := " =\n    ", count := [ 5, 3, 22, 3 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "v\
", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      22, 3 ],
                                                                  mathmode := \
"Text", name := "A", next := 206513, root := ~, start := 206505, stop := 20651\
2 ) ], count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "C", 
                                                          next := 206517, 
                                                          root := ~, 
                                                          start := 206487, 
                                                          stop := 206516 ), 
                                                      rec( 
                                                          content := ", then t\
he shortest non-trivial cycle is returned, again, if it\n    exists. Otherwise\
, this operation returns ", count := [ 5, 3, 22, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 206638, 
                                                          root := ~, 
                                                          start := 206627, 
                                                          stop := 206637 ), 
                                                      rec( 
                                                          content := ".  See S\
ection\n    ", count := [ 5, 3, 22, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Text",
                                                              Subsect := "Defi\
nitions" ), content := 0, count := [ 5, 3, 22, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 206698, 
                                                          root := ~, 
                                                          start := 206657, 
                                                          stop := 206697 ), 
                                                      rec( 
                                                          content := " for the\
 definition of a directed\n    path and a directed cycle.\n    ", 
                                                          count := 
                                                            [ 5, 3, 22, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 206771, 
                                                          root := ~, 
                                                          start := 206767, 
                                                          stop := 206770 ), 
                                                      rec( 
                                                          content := "\n\n    \
See ", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Path" ), content := 0, count := [ 5, 3, 22, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 206806, 
                                                          root := ~, 
                                                          start := 206781, 
                                                          stop := 206805 ), 
                                                      rec( 
                                                          content := " for det\
ails on the output.\n\n    The method for ", count := [ 5, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphShortestPath", count := [ 5, 3, 22, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 22, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 206880, 
                                                          root := ~, 
                                                          start := 206854, 
                                                          stop := 206879 ), 
                                                      rec( 
                                                          content := " has wor\
st case complexity of\n    ", count := [ 5, 3, 22, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m + n)", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 206929, 
                                                          root := ~, 
                                                          start := 206914, 
                                                          stop := 206928 ), 
                                                      rec( 
                                                          content := " where "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 206944, 
                                                          root := ~, 
                                                          start := 206936, 
                                                          stop := 206943 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and ", count := [ 5, 3, 22, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 206980, 
                                                          root := ~, 
                                                          start := 206972, 
                                                          stop := 206979 ), 
                                                      rec( 
                                                          content := " the\n  \
  number of vertices in ", count := [ 5, 3, 22, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 22, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 207025, 
                                                          root := ~, 
                                                          start := 207011, 
                                                          stop := 207024 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 3, 22, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2], [3], [2, 4], [1], [2, 4]]);\n<immutable digraph wi\
th 5 vertices, 8 edges>\ngap> DigraphShortestPath(D, 5, 1);\n[ [ 5, 4, 1 ], [ \
2, 1 ] ]\ngap> DigraphShortestPath(D, 3, 3);\n[ [ 3, 2, 3 ], [ 1, 1 ] ]\ngap> \
DigraphShortestPath(D, 5, 5);\nfail\ngap> DigraphShortestPath(D, 1, 1);\n[ [ 1\
, 1 ], [ 1 ] ]\n", count := [ 5, 3, 22, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 22, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 207377, 
                                                          root := ~, 
                                                          start := 207028, 
                                                          stop := 207376 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 22, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 22, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 207394, root := ~, 
                                                  start := 206332, 
                                                  stop := 207393 ) ], 
                                          count := [ 5, 3, 22, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 207408, root := ~, 
                                          start := 206206, stop := 207407 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 22, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, u, v", 
                                                      Name := "IteratorOfPaths\
" ), content := 0, count := [ 5, 3, 23, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 207479, root := ~, 
                                                  start := 207429, 
                                                  stop := 207478 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An iterat\
or.", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 23, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 207513, root := ~, 
                                                  start := 207482, 
                                                  stop := 207512 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 207551, 
                                                          root := ~, 
                                                          start := 207537, 
                                                          stop := 207550 ), 
                                                      rec( 
                                                          content := " is a di\
graph or a list of adjacencies which defines a\n    digraph - see ", 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "OutNeig\
hbours" ), content := 0, count := [ 5, 3, 23, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 207651, 
                                                          root := ~, 
                                                          start := 207624, 
                                                          stop := 207650 ), 
                                                      rec( 
                                                          content := " - then \
this operation returns an\n    iterator of the non-trivial directed paths (or \
directed cycles, in the case\n    that ", count := [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 207782, 
                                                          root := ~, 
                                                          start := 207774, 
                                                          stop := 207781 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "=\
", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 207791, 
                                                          root := ~, 
                                                          start := 207783, 
                                                          stop := 207790 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 207800, 
                                                          root := ~, 
                                                          start := 207792, 
                                                          stop := 207799 ), 
                                                      rec( content := ") in ",
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 207819, 
                                                          root := ~, 
                                                          start := 207805, 
                                                          stop := 207818 ), 
                                                      rec( 
                                                          content := " from th\
e vertex ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 207844, 
                                                          root := ~, 
                                                          start := 207836, 
                                                          stop := 207843 ), 
                                                      rec( 
                                                          content := "\n    to\
 the vertex ", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 5, 3, 23, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 207871, 
                                                          root := ~, 
                                                          start := 207863, 
                                                          stop := 207870 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 23, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 23, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 207881, 
                                                          root := ~, 
                                                          start := 207877, 
                                                          stop := 207880 ), 
                                                      rec( 
                                                          content := "\n\n    \
See ", count := [ 5, 3, 23, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Path" ), content := 0, count := [ 5, 3, 23, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 207916, 
                                                          root := ~, 
                                                          start := 207891, 
                                                          stop := 207915 ), 
                                                      rec( 
                                                          content := " for mor\
e information about the repesentation\n    of a directed path or directed cycl\
e which is used, and see ", count := [ 5, 3, 23, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Sect := "Iterators" ), content := 0, count := [ 5, 3, 23, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 208070, 
                                                          root := ~, 
                                                          start := 208026, 
                                                          stop := 208069 ), 
                                                      rec( 
                                                          content := " for mor\
e information about iterators.\n    See Section ", count := [ 5, 3, 23, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Text",
                                                              Subsect := "Defi\
nitions" ), content := 0, count := [ 5, 3, 23, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 208166, 
                                                          root := ~, 
                                                          start := 208125, 
                                                          stop := 208165 ), 
                                                      rec( 
                                                          content := " for the\
 definition of\n    a directed path and a directed cycle.\n    ", 
                                                          count := 
                                                            [ 5, 3, 23, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 23, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 208239, 
                                                          root := ~, 
                                                          start := 208235, 
                                                          stop := 208238 ), 
                                                      rec( content := "\n\n", 
                                                          count := 
                                                            [ 5, 3, 23, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 4, 4, 2], [3, 5], [2, 3], [1, 2], [4]]);\n<immutable m\
ultidigraph with 5 vertices, 11 edges>\ngap> iter := IteratorOfPaths(D, 1, 4);\
\n<iterator>\ngap> NextIterator(iter);\n[ [ 1, 4 ], [ 2 ] ]\ngap> NextIterator\
(iter);\n[ [ 1, 4 ], [ 3 ] ]\ngap> NextIterator(iter);\n[ [ 1, 2, 5, 4 ], [ 4,\
 2, 1 ] ]\ngap> IsDoneIterator(iter);\ntrue\ngap> iter := IteratorOfPaths(D, 4\
, 3);\n<iterator>\ngap> NextIterator(iter);\n[ [ 4, 1, 2, 3 ], [ 1, 4, 1 ] ]\n\
", count := [ 5, 3, 23, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 23, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 208724, 
                                                          root := ~, 
                                                          start := 208241, 
                                                          stop := 208723 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 23, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 23, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 208741, root := ~, 
                                                  start := 207516, 
                                                  stop := 208740 ) ], 
                                          count := [ 5, 3, 23, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 208755, root := ~, 
                                          start := 207414, stop := 208754 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 23, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphAllSimpl\
eCircuits" ), content := 0, count := [ 5, 3, 24, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 208829, root := ~, 
                                                  start := 208776, 
                                                  stop := 208828 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 lists of vertices.", count := [ 5, 3, 24, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 24, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 208879, root := ~, 
                                                  start := 208832, 
                                                  stop := 208878 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 24, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 208917, 
                                                          root := ~, 
                                                          start := 208903, 
                                                          stop := 208916 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphAllSimpleCircuits", count := [ 5, 3, 24, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 24, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 208968, 
                                                          root := ~, 
                                                          start := 208937, 
                                                          stop := 208967 ), 
                                                      rec( 
                                                          content := "\n    re\
turns a list of the ", count := [ 5, 3, 24, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
imple circuits", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "E", 
                                                          next := 209017, 
                                                          root := ~, 
                                                          start := 208995, 
                                                          stop := 209016 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 5, 3, 24, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 24, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 24, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 209035, 
                                                          root := ~, 
                                                          start := 209021, 
                                                          stop := 209034 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 24, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 24, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 209041, 
                                                          root := ~, 
                                                          start := 209037, 
                                                          stop := 209040 ), 
                                                      rec( 
                                                          content := "\n\n    \
See Section ", count := [ 5, 3, 24, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 24, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 209103, 
                                                          root := ~, 
                                                          start := 209059, 
                                                          stop := 209102 ), 
                                                      rec( 
                                                          content := " for the\
 definition\n    of a simple circuit, and related notions. Note that a loop is\
 a simple\n    circuit. ", count := [ 5, 3, 24, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 209215, 
                                                          root := ~, 
                                                          start := 209211, 
                                                          stop := 209214 ), 
                                                      rec( 
                                                          content := "\n\n    \
For a digraph without multiple edges, a simple circuit is uniquely\n    determ\
ined by its subsequence of vertices. However this is not the case for\n    a m\
ultidigraph.  The attribute ", count := [ 5, 3, 24, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphAllSimpleCircuits", count := [ 5, 3, 24, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 24, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 209434, 
                                                          root := ~, 
                                                          start := 209403, 
                                                          stop := 209433 ), 
                                                      rec( 
                                                          content := " ignores\
\n    multiple edges, and identifies a simple circuit using only its subsequen\
ce\n    of vertices. For example, although the simple circuits ", 
                                                          count := 
                                                            [ 5, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "(\
v, e, v)", count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 209597, 
                                                          root := ~, 
                                                          start := 209581, 
                                                          stop := 209596 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "(\
v, e', v)", count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 209623, 
                                                          root := ~, 
                                                          start := 209606, 
                                                          stop := 209622 ), 
                                                      rec( 
                                                          content := " (for di\
stinct edges ", count := [ 5, 3, 24, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
", count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 209652, 
                                                          root := ~, 
                                                          start := 209644, 
                                                          stop := 209651 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
'", count := [ 5, 3, 24, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 24, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 209666, 
                                                          root := ~, 
                                                          start := 209657, 
                                                          stop := 209665 ), 
                                                      rec( 
                                                          content := ") are\n \
   mathematically distinct, ", count := [ 5, 3, 24, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphAllSimpleCircuits", count := [ 5, 3, 24, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 24, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 209732, 
                                                          root := ~, 
                                                          start := 209701, 
                                                          stop := 209731 ), 
                                                      rec( 
                                                          content := " conside\
rs them to\n    be the same. ", count := [ 5, 3, 24, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 209772, 
                                                          root := ~, 
                                                          start := 209768, 
                                                          stop := 209771 ), 
                                                      rec( 
                                                          content := "\n\n    \
With this approach, a directed circuit of length ", count := [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 209835, 
                                                          root := ~, 
                                                          start := 209827, 
                                                          stop := 209834 ), 
                                                      rec( 
                                                          content := " can be \
determined\n    by a list of its first ", count := [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 209889, 
                                                          root := ~, 
                                                          start := 209881, 
                                                          stop := 209888 ), 
                                                      rec( 
                                                          content := " vertice\
s. Thus a simple circuit ", count := [ 5, 3, 24, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "(\
v_1,\n      e_1, v_2, e_2, ..., e_{n-1}, v_n, e_{n+1}, v_1)", count := 
                                                                    [ 5, 3, 
                                                                      24, 6 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 209988, 
                                                          root := ~, 
                                                          start := 209922, 
                                                          stop := 209987 ), 
                                                      rec( 
                                                          content := " can be \
represented as\n    the list ", count := [ 5, 3, 24, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
v_1, \\ldots, v_n]", count := [ 5, 3, 24, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 24, 6 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 210049, 
                                                          root := ~, 
                                                          start := 210024, 
                                                          stop := 210048 ), 
                                                      rec( 
                                                          content := ", or any\
 cyclic permutation thereof.  For\n    each simple circuit of ", 
                                                          count := 
                                                            [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 210132, 
                                                          root := ~, 
                                                          start := 210118, 
                                                          stop := 210131 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphAllSimpleCircuits(", count := [ 5, 3, 24, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "d\
igraph", count := [ 5, 3, 24, 6 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 5, 3, 24, 6 ], mathmode := "Text", name := "A", 
                                                                  next := 2101\
80, root := ~, start := 210166, stop := 210179 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      24, 6 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 210185, 
                                                          root := ~, 
                                                          start := 210138, 
                                                          stop := 210184 ), 
                                                      rec( 
                                                          content := " include\
s precisely one such\n    list to represent the circuit.  ", 
                                                          count := 
                                                            [ 5, 3, 24, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 24, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 210254, 
                                                          root := ~, 
                                                          start := 210250, 
                                                          stop := 210253 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 3, 24, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[], [3], [2, 4], [5, 4], [4]]);\n<immutable digraph with 5\
 vertices, 6 edges>\ngap> DigraphAllSimpleCircuits(D);\n[ [ 4 ], [ 4, 5 ], [ 2\
, 3 ] ]\ngap> D := ChainDigraph(10);;\ngap> DigraphAllSimpleCircuits(D);\n[  ]\
\ngap> D := Digraph([[3], [1], [1]]);\n<immutable digraph with 3 vertices, 3 e\
dges>\ngap> DigraphAllSimpleCircuits(D);\n[ [ 1, 3 ] ]\ngap> D := Digraph([[1,\
 1]]);\n<immutable multidigraph with 1 vertex, 2 edges>\ngap> DigraphAllSimple\
Circuits(D);\n[ [ 1 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutabl\
e digraph with 3 vertices, 3 edges>\ngap> DigraphAllSimpleCircuits(D);\n[ [ 1,\
 2, 3 ] ]\n", count := [ 5, 3, 24, 8 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 24, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 210907, 
                                                          root := ~, 
                                                          start := 210260, 
                                                          stop := 210906 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 24, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 24, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 210924, root := ~, 
                                                  start := 208882, 
                                                  stop := 210923 ) ], 
                                          count := [ 5, 3, 24, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 210938, root := ~, 
                                          start := 208761, stop := 210937 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 24, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphLongestS\
impleCircuit" ), content := 0, count := [ 5, 3, 25, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 211015, root := ~, 
                                                  start := 210959, 
                                                  stop := 211014 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 vertices, or ", count := [ 5, 3, 25, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 25, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 211061, 
                                                          root := ~, 
                                                          start := 211050, 
                                                          stop := 211060 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 25, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 25, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 211072, root := ~, 
                                                  start := 211018, 
                                                  stop := 211071 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 25, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 211110, 
                                                          root := ~, 
                                                          start := 211096, 
                                                          stop := 211109 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphLongestSimpleCircuit", count := [ 5, 3, 25, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 25, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 211164, 
                                                          root := ~, 
                                                          start := 211130, 
                                                          stop := 211163 ), 
                                                      rec( 
                                                          content := "\n    re\
turns the longest ", count := [ 5, 3, 25, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
imple circuit", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 25, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 211210, 
                                                          root := ~, 
                                                          start := 211189, 
                                                          stop := 211209 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 5, 3, 25, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 25, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 211228, 
                                                          root := ~, 
                                                          start := 211214, 
                                                          stop := 211227 ), 
                                                      rec( 
                                                          content := ". See Se\
ction\n    ", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 5, 3, 25, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 211290, 
                                                          root := ~, 
                                                          start := 211246, 
                                                          stop := 211289 ), 
                                                      rec( 
                                                          content := " for the\
 definition of simple\n    circuit, and the definition of length for a simple \
circuit.", count := [ 5, 3, 25, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 25, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 211387, 
                                                          root := ~, 
                                                          start := 211383, 
                                                          stop := 211386 ), 
                                                      rec( 
                                                          content := "\n\n    \
This attribute computes\n    ", count := [ 5, 3, 25, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphAllSimpleCircuits(", count := [ 5, 3, 25, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 25, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 211453, 
                                                          root := ~, 
                                                          start := 211421, 
                                                          stop := 211452 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 25, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 211467, 
                                                          root := ~, 
                                                          start := 211453, 
                                                          stop := 211466 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 25, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 211475, 
                                                          root := ~, 
                                                          start := 211467, 
                                                          stop := 211474 ), 
                                                      rec( 
                                                          content := " to find\
 all the\n    simple circuits of ", count := [ 5, 3, 25, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 25, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 25, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 211529, 
                                                          root := ~, 
                                                          start := 211515, 
                                                          stop := 211528 ), 
                                                      rec( 
                                                          content := ", and re\
turns one of maximal length.  A\n    simple circuit is represented as a list o\
f vertices, in the same way as\n    described in ", count := [ 5, 3, 25, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
AllSimpleCircuits" ), content := 0, count := [ 5, 3, 25, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 211700, 
                                                          root := ~, 
                                                          start := 211662, 
                                                          stop := 211699 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 25, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 211705, 
                                                          root := ~, 
                                                          start := 211701, 
                                                          stop := 211704 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 211728, 
                                                          root := ~, 
                                                          start := 211714, 
                                                          stop := 211727 ), 
                                                      rec( 
                                                          content := " has no \
simple circuits, then this attribute returns\n    ", count := [ 5, 3, 25, 5 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 211796, 
                                                          root := ~, 
                                                          start := 211785, 
                                                          stop := 211795 ), 
                                                      rec( 
                                                          content := ".  If ",
                                                          count := 
                                                            [ 5, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 25, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 211816, 
                                                          root := ~, 
                                                          start := 211802, 
                                                          stop := 211815 ), 
                                                      rec( 
                                                          content := " has mul\
tiple simple circuits of maximal\n    length, then this attribute returns one \
of them.", count := [ 5, 3, 25, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 25, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 211913, 
                                                          root := ~, 
                                                          start := 211909, 
                                                          stop := 211912 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 5, 3, 25, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[], [3], [2, 4], [5, 4], [4]]);;\ngap> DigraphLongestSimpl\
eCircuit(D);\n[ 4, 5 ]\ngap> D := ChainDigraph(10);;\ngap> DigraphLongestSimpl\
eCircuit(D);\nfail\ngap> D := Digraph([[3], [1], [1, 4], [1, 1]]);;\ngap> Digr\
aphLongestSimpleCircuit(D);\n[ 1, 3, 4 ]\ngap> D := GeneralisedPetersenGraph(I\
sMutableDigraph, 4, 1);\n<mutable digraph with 8 vertices, 24 edges>\ngap> Dig\
raphLongestSimpleCircuit(D);\n[ 1, 2, 3, 4, 8, 7, 6, 5 ]\n", count := 
                                                                    [ 5, 3, 
                                                                      25, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 25, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 212385, 
                                                          root := ~, 
                                                          start := 211919, 
                                                          stop := 212384 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 25, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 25, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 212402, root := ~, 
                                                  start := 211075, 
                                                  stop := 212401 ) ], 
                                          count := [ 5, 3, 25, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 212416, root := ~, 
                                          start := 210944, stop := 212415 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 25, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex"
                                                        , 
                                                      Name := "DigraphLayers" 
                                                     ), content := 0, 
                                                  count := [ 5, 3, 26, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 212487, root := ~, 
                                                  start := 212437, 
                                                  stop := 212486 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list.",
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 26, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 212516, root := ~, 
                                                  start := 212490, 
                                                  stop := 212515 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns a list ", count := [ 5, 3, 26, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 212578, 
                                                          root := ~, 
                                                          start := 212567, 
                                                          stop := 212577 ), 
                                                      rec( 
                                                          content := " such th\
at ", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist[i]", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 212603, 
                                                          root := ~, 
                                                          start := 212589, 
                                                          stop := 212602 ), 
                                                      rec( 
                                                          content := " is the\\
n    list of vertices whose minimum distance from the vertex ", 
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 212684, 
                                                          root := ~, 
                                                          start := 212671, 
                                                          stop := 212683 ), 
                                                      rec( 
                                                          content := " in\n   \
 ", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 212706, 
                                                          root := ~, 
                                                          start := 212692, 
                                                          stop := 212705 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 - 1", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 212722, 
                                                          root := ~, 
                                                          start := 212710, 
                                                          stop := 212721 ), 
                                                      rec( 
                                                          content := ". Vertex\
 ", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 212744, 
                                                          root := ~, 
                                                          start := 212731, 
                                                          stop := 212743 ), 
                                                      rec( 
                                                          content := " is\n   \
 assumed to be at distance ", count := [ 5, 3, 26, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 26, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 212786, 
                                                          root := ~, 
                                                          start := 212778, 
                                                          stop := 212785 ), 
                                                      rec( 
                                                          content := " from it\
self.\n    ", count := [ 5, 3, 26, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(4);;\ngap> DigraphLayers(D, 1);\n[ [ 1 ], [ 2, 3, 4\
 ] ]\n", count := [ 5, 3, 26, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 3, 26, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 212916, 
                                                          root := ~, 
                                                          start := 212804, 
                                                          stop := 212915 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 26, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 26, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 212933, root := ~, 
                                                  start := 212519, 
                                                  stop := 212932 ) ], 
                                          count := [ 5, 3, 26, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 212947, root := ~, 
                                          start := 212422, stop := 212946 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 26, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphDegenera\
cy" ), content := 0, count := [ 5, 3, 27, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 213014, root := ~, 
                                                  start := 212968, 
                                                  stop := 213013 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A non-neg\
ative integer, or ", count := [ 5, 3, 27, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 27, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 213064, 
                                                          root := ~, 
                                                          start := 213053, 
                                                          stop := 213063 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 27, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 27, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 213075, root := ~, 
                                                  start := 213017, 
                                                  stop := 213074 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 27, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 213113, 
                                                          root := ~, 
                                                          start := 213099, 
                                                          stop := 213112 ), 
                                                      rec( 
                                                          content := " is a sy\
mmetric digraph without multiple edges - see\n    ", count := [ 5, 3, 27, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsSymme\
tricDigraph" ), content := 0, count := [ 5, 3, 27, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 213202, 
                                                          root := ~, 
                                                          start := 213170, 
                                                          stop := 213201 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 27, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsMulti\
Digraph" ), content := 0, count := [ 5, 3, 27, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 213235, 
                                                          root := ~, 
                                                          start := 213207, 
                                                          stop := 213234 ), 
                                                      rec( 
                                                          content := " - then\\
n    this attribute returns the degeneracy of ", count := [ 5, 3, 27, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 27, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 27, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 213302, 
                                                          root := ~, 
                                                          start := 213288, 
                                                          stop := 213301 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 3, 27, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 27, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 213308, 
                                                          root := ~, 
                                                          start := 213304, 
                                                          stop := 213307 ), 
                                                      rec( 
                                                          content := "\n\n    \
The degeneracy of a digraph is the least integer ", count := [ 5, 3, 27, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 5, 3, 27, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 27, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 213371, 
                                                          root := ~, 
                                                          start := 213363, 
                                                          stop := 213370 ), 
                                                      rec( 
                                                          content := " such\n \
   that every induced of ", count := [ 5, 3, 27, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 27, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 27, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 213417, 
                                                          root := ~, 
                                                          start := 213403, 
                                                          stop := 213416 ), 
                                                      rec( 
                                                          content := " contain\
s a vertex whose number of\n    neighbours (excluding itself) is at most ", 
                                                          count := 
                                                            [ 5, 3, 27, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 5, 3, 27, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 27, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 213505, 
                                                          root := ~, 
                                                          start := 213497, 
                                                          stop := 213504 ), 
                                                      rec( 
                                                          content := ". Note t\
hat this means\n    that loops are ignored.", count := [ 5, 3, 27, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 213559, 
                                                          root := ~, 
                                                          start := 213555, 
                                                          stop := 213558 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 213582, 
                                                          root := ~, 
                                                          start := 213568, 
                                                          stop := 213581 ), 
                                                      rec( 
                                                          content := " is not \
symmetric or has multiple edges then this\n    attribute returns ", 
                                                          count := 
                                                            [ 5, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 27, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 213665, 
                                                          root := ~, 
                                                          start := 213654, 
                                                          stop := 213664 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 27, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphSymmetricClosure(ChainDigraph(5));;\ngap> DigraphDegeneracy(\
D);\n1\ngap> D := CompleteDigraph(5);;\ngap> DigraphDegeneracy(D);\n4\ngap> D \
:= Digraph([[1], [2, 4, 5], [3, 4], [2, 3, 4], [2], []]);\n<immutable digraph \
with 6 vertices, 10 edges>\ngap> DigraphDegeneracy(D);\n1\ngap> D := Generalis\
edPetersenGraph(IsMutableDigraph, 10, 3);\n<mutable digraph with 20 vertices, \
60 edges>\ngap> DigraphDegeneracy(D);\n3\n", count := [ 5, 3, 27, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 27, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 214120, 
                                                          root := ~, 
                                                          start := 213671, 
                                                          stop := 214119 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 27, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 27, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 214137, root := ~, 
                                                  start := 213078, 
                                                  stop := 214136 ) ], 
                                          count := [ 5, 3, 27, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 214151, root := ~, 
                                          start := 212953, stop := 214150 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 27, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphDegenera\
cyOrdering" ), content := 0, count := [ 5, 3, 28, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 214226, root := ~, 
                                                  start := 214172, 
                                                  stop := 214225 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 integers, or ", count := [ 5, 3, 28, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 28, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 214272, 
                                                          root := ~, 
                                                          start := 214261, 
                                                          stop := 214271 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 28, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 28, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 214283, root := ~, 
                                                  start := 214229, 
                                                  stop := 214282 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 3, 28, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 28, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 214321, 
                                                          root := ~, 
                                                          start := 214307, 
                                                          stop := 214320 ), 
                                                      rec( 
                                                          content := " is a di\
graph for which\n    ", count := [ 5, 3, 28, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDegeneracy(", count := [ 5, 3, 28, 3 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 28, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 214374, 
                                                          root := ~, 
                                                          start := 214349, 
                                                          stop := 214373 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 28, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 214388, 
                                                          root := ~, 
                                                          start := 214374, 
                                                          stop := 214387 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 5, 3, 28, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 28, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 214396, 
                                                          root := ~, 
                                                          start := 214388, 
                                                          stop := 214395 ), 
                                                      rec( 
                                                          content := " is a no\
n-negative integer\n    ", count := [ 5, 3, 28, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 5, 3, 28, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 28, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 214435, 
                                                          root := ~, 
                                                          start := 214427, 
                                                          stop := 214434 ), 
                                                      rec( 
                                                          content := " - see "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 28, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Degeneracy" ), content := 0, count := [ 5, 3, 28, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 214473, 
                                                          root := ~, 
                                                          start := 214442, 
                                                          stop := 214472 ), 
                                                      rec( 
                                                          content := " - then \
this attribute\n    returns a degeneracy ordering of the vertices of the verti\
ces of\n    ", count := [ 5, 3, 28, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 28, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 214583, 
                                                          root := ~, 
                                                          start := 214569, 
                                                          stop := 214582 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 28, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 28, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 214588, 
                                                          root := ~, 
                                                          start := 214584, 
                                                          stop := 214587 ), 
                                                      rec( 
                                                          content := "\n\n    \
A degeneracy ordering of ", count := [ 5, 3, 28, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 28, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 214633, 
                                                          root := ~, 
                                                          start := 214619, 
                                                          stop := 214632 ), 
                                                      rec( 
                                                          content := " is a li\
st ", count := [ 5, 3, 28, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
rdering", count := [ 5, 3, 28, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 214659, 
                                                          root := ~, 
                                                          start := 214644, 
                                                          stop := 214658 ), 
                                                      rec( 
                                                          content := " of the\\
n    vertices of ", count := [ 5, 3, 28, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 28, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 214697, 
                                                          root := ~, 
                                                          start := 214683, 
                                                          stop := 214696 ), 
                                                      rec( 
                                                          content := " ordered\
 such that for any\n    position ", count := [ 5, 3, 28, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 5, 3, 28, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 28, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 214745, 
                                                          root := ~, 
                                                          start := 214737, 
                                                          stop := 214744 ), 
                                                      rec( 
                                                          content := " of the \
list, the vertex ", count := [ 5, 3, 28, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
rdering[i]", count := [ 5, 3, 28, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 214788, 
                                                          root := ~, 
                                                          start := 214770, 
                                                          stop := 214787 ), 
                                                      rec( 
                                                          content := " has at \
most\n    ", count := [ 5, 3, 28, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "k\
", count := [ 5, 3, 28, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 28, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 214813, 
                                                          root := ~, 
                                                          start := 214805, 
                                                          stop := 214812 ), 
                                                      rec( 
                                                          content := " neighbo\
urs in later position of the list.", count := [ 5, 3, 28, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 214859, 
                                                          root := ~, 
                                                          start := 214855, 
                                                          stop := 214858 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDegeneracy(", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 28, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 214893, 
                                                          root := ~, 
                                                          start := 214868, 
                                                          stop := 214892 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 214907, 
                                                          root := ~, 
                                                          start := 214893, 
                                                          stop := 214906 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 214915, 
                                                          root := ~, 
                                                          start := 214907, 
                                                          stop := 214914 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 214935, 
                                                          root := ~, 
                                                          start := 214924, 
                                                          stop := 214934 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen this attribute returns ", count := [ 5, 3, 28, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 28, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 214980, 
                                                          root := ~, 
                                                          start := 214969, 
                                                          stop := 214979 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 28, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphSymmetricClosure(ChainDigraph(5));;\ngap> DigraphDegeneracyO\
rdering(D);\n[ 5, 4, 3, 2, 1 ]\ngap> D := CompleteDigraph(5);;\ngap> DigraphDe\
generacyOrdering(D);\n[ 5, 4, 3, 2, 1 ]\ngap> D := Digraph([[1], [2, 4, 5], [3\
, 4], [2, 3, 4], [2], []]);\n<immutable digraph with 6 vertices, 10 edges>\nga\
p> DigraphDegeneracyOrdering(D);\n[ 1, 6, 5, 2, 4, 3 ]\ngap> D := GeneralisedP\
etersenGraph(IsMutableDigraph, 3, 1);\n<mutable digraph with 6 vertices, 18 ed\
ges>\ngap> DigraphDegeneracyOrdering(D);\n[ 6, 5, 4, 1, 3, 2 ]\n", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      28, 6 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 28, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 215535, 
                                                          root := ~, 
                                                          start := 214986, 
                                                          stop := 215534 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 28, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 28, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 215552, root := ~, 
                                                  start := 214286, 
                                                  stop := 215551 ) ], 
                                          count := [ 5, 3, 28, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 215566, root := ~, 
                                          start := 214157, stop := 215565 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 28, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "HamiltonianPath\
" ), content := 0, count := [ 5, 3, 29, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 215631, root := ~, 
                                                  start := 215587, 
                                                  stop := 215630 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list or\
 ", count := [ 5, 3, 29, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 29, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 29, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 215664, 
                                                          root := ~, 
                                                          start := 215653, 
                                                          stop := 215663 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 29, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 29, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 215675, root := ~, 
                                                  start := 215634, 
                                                  stop := 215674 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns a Hamiltonian path if one exists, ", count := [ 5, 3, 29, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 3, 29, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 29, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 215749, 
                                                          root := ~, 
                                                          start := 215738, 
                                                          stop := 215748 ), 
                                                      rec( 
                                                          content := " if not.\
", count := [ 5, 3, 29, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 215761, 
                                                          root := ~, 
                                                          start := 215757, 
                                                          stop := 215760 ), 
                                                      rec( 
                                                          content := "\n\n    \
A ", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
amiltonian path", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "E", 
                                                          next := 215792, 
                                                          root := ~, 
                                                          start := 215769, 
                                                          stop := 215791 ), 
                                                      rec( 
                                                          content := " of a di\
graph with ", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 215819, 
                                                          root := ~, 
                                                          start := 215811, 
                                                          stop := 215818 ), 
                                                      rec( 
                                                          content := " vertice\
s is directed\n    cycle of length ", count := [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 215869, 
                                                          root := ~, 
                                                          start := 215861, 
                                                          stop := 215868 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 215888, 
                                                          root := ~, 
                                                          start := 215874, 
                                                          stop := 215887 ), 
                                                      rec( 
                                                          content := " is a di\
graph that contains a\n    Hamiltonian path, then this function returns one, d\
escribed in the form\n    used by ", count := [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
AllSimpleCircuits" ), content := 0, count := [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 216044, 
                                                          root := ~, 
                                                          start := 216006, 
                                                          stop := 216043 ), 
                                                      rec( 
                                                          content := ". Note i\
f ", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 216068, 
                                                          root := ~, 
                                                          start := 216054, 
                                                          stop := 216067 ), 
                                                      rec( 
                                                          content := " has\n  \
  0 or 1 vertices, then ", count := [ 5, 3, 29, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
amiltonianPath", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "C", 
                                                          next := 216121, 
                                                          root := ~, 
                                                          start := 216099, 
                                                          stop := 216120 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
]", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 216139, 
                                                          root := ~, 
                                                          start := 216130, 
                                                          stop := 216138 ), 
                                                      rec( 
                                                          content := " or\n   \
 ", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1]", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 29, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 216157, 
                                                          root := ~, 
                                                          start := 216147, 
                                                          stop := 216156 ), 
                                                      rec( 
                                                          content := ", respec\
tively.", count := [ 5, 3, 29, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 216176, 
                                                          root := ~, 
                                                          start := 216172, 
                                                          stop := 216175 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this attribute has the same worst case complexity as\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 29, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Monomorphism" ), content := 0, count := [ 5, 3, 29, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 216291, 
                                                          root := ~, 
                                                          start := 216258, 
                                                          stop := 216290 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 5, 3, 29, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[]]);\n<immutable empty digraph with 1 vertex>\ngap> Hamil\
tonianPath(D);\n[ 1 ]\ngap> D := Digraph([[2], [1]]);\n<immutable digraph with\
 2 vertices, 2 edges>\ngap> HamiltonianPath(D);\n[ 1, 2 ]\ngap> D := Digraph([\
[3], [], [2]]);\n<immutable digraph with 3 vertices, 2 edges>\ngap> Hamiltonia\
nPath(D);\nfail\ngap> D := Digraph([[2], [3], [1]]);\n<immutable digraph with \
3 vertices, 3 edges>\ngap> HamiltonianPath(D);\n[ 1, 2, 3 ]\ngap> D := General\
isedPetersenGraph(IsMutableDigraph, 5, 2);\n<mutable digraph with 10 vertices,\
 30 edges>\ngap> HamiltonianPath(D);\nfail\n", count := [ 5, 3, 29, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 29, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 216899, 
                                                          root := ~, 
                                                          start := 216298, 
                                                          stop := 216898 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 29, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 29, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 216916, root := ~, 
                                                  start := 215678, 
                                                  stop := 216915 ) ], 
                                          count := [ 5, 3, 29, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 216930, root := ~, 
                                          start := 215572, stop := 216929 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 29, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "NrSpanningTrees\
" ), content := 0, count := [ 5, 3, 30, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 216995, root := ~, 
                                                  start := 216951, 
                                                  stop := 216994 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An intege\
r.", count := [ 5, 3, 30, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 30, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 217028, root := ~, 
                                                  start := 216998, 
                                                  stop := 217027 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns the number of spanning trees of the symmetric digraph\n    ", 
                                                          count := 
                                                            [ 5, 3, 30, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 30, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 30, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 217129, 
                                                          root := ~, 
                                                          start := 217115, 
                                                          stop := 217128 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 30, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "N\
rSpanningTrees", count := [ 5, 3, 30, 3 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 5, 3, 30, 3 ], mathmode := "Text", name := "C", 
                                                          next := 217157, 
                                                          root := ~, 
                                                          start := 217135, 
                                                          stop := 217156 ), 
                                                      rec( 
                                                          content := " will re\
turn an error if ", count := [ 5, 3, 30, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 30, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 30, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 217196, 
                                                          root := ~, 
                                                          start := 217182, 
                                                          stop := 217195 ), 
                                                      rec( 
                                                          content := " is not \
a\n    symmetric digraph. ", count := [ 5, 3, 30, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 30, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 217233, 
                                                          root := ~, 
                                                          start := 217229, 
                                                          stop := 217232 ), 
                                                      rec( 
                                                          content := " \n\n   \
 See ", count := [ 5, 3, 30, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsSymme\
tricDigraph" ), content := 0, count := [ 5, 3, 30, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 217276, 
                                                          root := ~, 
                                                          start := 217244, 
                                                          stop := 217275 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 5, 3, 30, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsUndir\
ectedSpanningTree" ), content := 0, count := [ 5, 3, 30, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 217324, 
                                                          root := ~, 
                                                          start := 217285, 
                                                          stop := 217323 ), 
                                                      rec( 
                                                          content := " for mor\
e information. \n\n    ", count := [ 5, 3, 30, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(5);\n<immutable complete digraph with 5 vertices>\n\
gap> NrSpanningTrees(D);\n125\ngap> D := DigraphSymmetricClosure(CycleDigraph(\
24));;\ngap> NrSpanningTrees(D);\n24\ngap> NrSpanningTrees(EmptyDigraph(0));\n\
0\ngap> D := GeneralisedPetersenGraph(IsMutableDigraph, 9, 2);\n<mutable digra\
ph with 18 vertices, 54 edges>\ngap> NrSpanningTrees(D);\n1134225\n", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      30, 5 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 30, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 217750, 
                                                          root := ~, 
                                                          start := 217353, 
                                                          stop := 217749 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 3, 30, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 30, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 217767, root := ~, 
                                                  start := 217031, 
                                                  stop := 217766 ) ], 
                                          count := [ 5, 3, 30, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 217781, root := ~, 
                                          start := 216936, stop := 217780 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 3, 30, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, source,\
 target", Label := "for a source and target", Name := "DigraphDijkstra" ), 
                                                  content := 0, 
                                                  count := [ 5, 3, 31, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 217894, root := ~, 
                                                  start := 217802, 
                                                  stop := 217893 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, source"
                                                        , 
                                                      Label := "for a source",
                                                      Name := "DigraphDijkstra\
" ), content := 0, count := [ 5, 3, 31, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 217970, root := ~, 
                                                  start := 217897, 
                                                  stop := 217969 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Two lists\
.", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 5, 3, 31, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 218002, root := ~, 
                                                  start := 217973, 
                                                  stop := 218001 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n  If ",
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218038, 
                                                          root := ~, 
                                                          start := 218024, 
                                                          stop := 218037 ), 
                                                      rec( 
                                                          content := " is a di\
graph and ", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ource", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218069, 
                                                          root := ~, 
                                                          start := 218056, 
                                                          stop := 218068 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
arget", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218087, 
                                                          root := ~, 
                                                          start := 218074, 
                                                          stop := 218086 ), 
                                                      rec( 
                                                          content := "  are\n \
 vertices of ", count := [ 5, 3, 31, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218121, 
                                                          root := ~, 
                                                          start := 218107, 
                                                          stop := 218120 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDijkstra", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "C", 
                                                          next := 218150, 
                                                          root := ~, 
                                                          start := 218128, 
                                                          stop := 218149 ), 
                                                      rec( 
                                                          content := " calcula\
tes the\n  length of the shortest path from ", count := [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ource", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218214, 
                                                          root := ~, 
                                                          start := 218201, 
                                                          stop := 218213 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
arget", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218231, 
                                                          root := ~, 
                                                          start := 218218, 
                                                          stop := 218230 ), 
                                                      rec( 
                                                          content := " and ret\
urns\n  two lists. Each element of the first list is the distance of the\n  co\
rresponding element from ", count := [ 5, 3, 31, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ource", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218353, 
                                                          root := ~, 
                                                          start := 218340, 
                                                          stop := 218352 ), 
                                                      rec( 
                                                          content := ".  If a \
vertex was not visited in\n  the process of calculating the shortest distance \
to ", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
arget", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218454, 
                                                          root := ~, 
                                                          start := 218441, 
                                                          stop := 218453 ), 
                                                      rec( 
                                                          content := " or if\n\
  there is no path connecting that vertex with ", count := [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ource", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218521, 
                                                          root := ~, 
                                                          start := 218508, 
                                                          stop := 218520 ), 
                                                      rec( 
                                                          content := ", then\n\
  the corresponding distance is ", count := [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 218575, 
                                                          root := ~, 
                                                          start := 218560, 
                                                          stop := 218574 ), 
                                                      rec( 
                                                          content := ".  Each \
element of the\n  second list gives the previous vertex in the shortest path\n\
  from ", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ource", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218679, 
                                                          root := ~, 
                                                          start := 218666, 
                                                          stop := 218678 ), 
                                                      rec( 
                                                          content := " to the \
corresponding vertex.  For\n  ", count := [ 5, 3, 31, 5 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ource", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218729, 
                                                          root := ~, 
                                                          start := 218716, 
                                                          stop := 218728 ), 
                                                      rec( 
                                                          content := " and for\
 any vertices that remained unvisited this\n    will be ", 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "-\
1", count := [ 5, 3, 31, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 218801, 
                                                          root := ~, 
                                                          start := 218792, 
                                                          stop := 218800 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 3, 31, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 218806, 
                                                          root := ~, 
                                                          start := 218802, 
                                                          stop := 218805 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional second argument ", count := [ 5, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
arget", count := [ 5, 3, 31, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218857, 
                                                          root := ~, 
                                                          start := 218844, 
                                                          stop := 218856 ), 
                                                      rec( 
                                                          content := " is not \
present, then\n    ", count := [ 5, 3, 31, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphDijkstra", count := [ 5, 3, 31, 6 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 5, 3, 31, 6 ], mathmode := "Text", name := "C", 
                                                          next := 218905, 
                                                          root := ~, 
                                                          start := 218883, 
                                                          stop := 218904 ), 
                                                      rec( 
                                                          content := " returns\
 the shortest path from ", count := [ 5, 3, 31, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ource", count := [ 5, 3, 31, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 218950, 
                                                          root := ~, 
                                                          start := 218937, 
                                                          stop := 218949 ), 
                                                      rec( 
                                                          content := " to\n   \
 every vertex that is reachable from ", count := [ 5, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ource", count := [ 5, 3, 31, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 219007, 
                                                          root := ~, 
                                                          start := 218994, 
                                                          stop := 219006 ), 
                                                      rec( 
                                                          content := ".\n\n  "
                                                            , 
                                                          count := 
                                                            [ 5, 3, 31, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> mat := [[0, 1, 1], [0, 0, 1], [0, 0, 0]];\n[ [ 0, 1, 1 ], [ 0, 0, 1 ], [\
 0, 0, 0 ] ]\ngap> D := DigraphByAdjacencyMatrix(mat);\n<immutable digraph wit\
h 3 vertices, 3 edges>\ngap> DigraphDijkstra(D, 2, 3);\n[ [ infinity, 0, 1 ], \
[ -1, -1, 2 ] ]\ngap> DigraphDijkstra(D, 1, 3);\n[ [ 0, 1, 1 ], [ -1, 1, 1 ] ]\
\ngap> DigraphDijkstra(D, 1, 2);\n[ [ 0, 1, 1 ], [ -1, 1, 1 ] ]\n", 
                                                                  count := 
                                                                    [ 5, 3, 
                                                                      31, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 3, 31, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 219410, 
                                                          root := ~, 
                                                          start := 219012, 
                                                          stop := 219409 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 5, 3, 31, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 3, 31, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 219425, root := ~, 
                                                  start := 218005, 
                                                  stop := 219424 ) ], 
                                          count := [ 5, 3, 31, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 219439, root := ~, 
                                          start := 217787, stop := 219438 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 5, 3, 31, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 5, 3, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 219453, 
                                  root := ~, start := 173430, stop := 219452 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 5, 3, 31, 8 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Cayley graphs of \
groups", count := [ 5, 4, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 5, 4, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 219508, 
                                          root := ~, start := 219466, 
                                          stop := 219507 ), 
                                      rec( content := "\n    ", 
                                          count := [ 5, 4, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "GroupOfCayleyDi\
graph" ), content := 0, count := [ 5, 4, 1, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 219577, root := ~, 
                                                  start := 219528, 
                                                  stop := 219576 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "SemigroupOfCayl\
eyDigraph" ), content := 0, count := [ 5, 4, 1, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 219633, root := ~, 
                                                  start := 219580, 
                                                  stop := 219632 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A group o\
r semigroup.", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 4, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 219676, root := ~, 
                                                  start := 219636, 
                                                  stop := 219675 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 219714, 
                                                          root := ~, 
                                                          start := 219700, 
                                                          stop := 219713 ), 
                                                      rec( 
                                                          content := " is an i\
mmutable Cayley graph of a group ", count := [ 5, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 219763, 
                                                          root := ~, 
                                                          start := 219755, 
                                                          stop := 219762 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 219786, 
                                                          root := ~, 
                                                          start := 219772, 
                                                          stop := 219785 ), 
                                                      rec( 
                                                          content := " belongs\
 to the category ", count := [ 5, 4, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsCayle\
yDigraph" ), content := 0, count := [ 5, 4, 1, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 219840, 
                                                          root := ~, 
                                                          start := 219811, 
                                                          stop := 219839 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
roupOfCayleyDigraph", count := [ 5, 4, 1, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 4, 1, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 219878, 
                                                          root := ~, 
                                                          start := 219851, 
                                                          stop := 219877 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 5, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 219895, 
                                                          root := ~, 
                                                          start := 219887, 
                                                          stop := 219894 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 219905, 
                                                          root := ~, 
                                                          start := 219901, 
                                                          stop := 219904 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 219928, 
                                                          root := ~, 
                                                          start := 219914, 
                                                          stop := 219927 ), 
                                                      rec( 
                                                          content := " is a Ca\
yley graph of a semigroup ", count := [ 5, 4, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 219970, 
                                                          root := ~, 
                                                          start := 219962, 
                                                          stop := 219969 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 219993, 
                                                          root := ~, 
                                                          start := 219979, 
                                                          stop := 219992 ), 
                                                      rec( 
                                                          content := " belongs\
 to the category ", count := [ 5, 4, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsCayle\
yDigraph" ), content := 0, count := [ 5, 4, 1, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 220047, 
                                                          root := ~, 
                                                          start := 220018, 
                                                          stop := 220046 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
emigroupOfCayleyDigraph", count := [ 5, 4, 1, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 4, 1, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 220089, 
                                                          root := ~, 
                                                          start := 220058, 
                                                          stop := 220088 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
", count := [ 5, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 220106, 
                                                          root := ~, 
                                                          start := 220098, 
                                                          stop := 220105 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 4, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 220116, 
                                                          root := ~, 
                                                          start := 220112, 
                                                          stop := 220115 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 5, 4, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Generat\
orsOfCayleyDigraph" ), content := 0, count := [ 5, 4, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 220170, 
                                                          root := ~, 
                                                          start := 220131, 
                                                          stop := 220169 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 4, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> G := DihedralGroup(IsPermGroup, 8);\nGroup([ (1,2,3,4), (2,4) ])\ngap> d\
igraph := CayleyDigraph(G);\n<immutable digraph with 8 vertices, 16 edges>\nga\
p> GroupOfCayleyDigraph(digraph) = G;\ntrue\n", count := [ 5, 4, 1, 8 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 4, 1, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 220402, 
                                                          root := ~, 
                                                          start := 220176, 
                                                          stop := 220401 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 4, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 4, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 220419, root := ~, 
                                                  start := 219679, 
                                                  stop := 220418 ) ], 
                                          count := [ 5, 4, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 220433, root := ~, 
                                          start := 219513, stop := 220432 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 4, 1, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "GeneratorsOfCay\
leyDigraph" ), content := 0, count := [ 5, 4, 2, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 220508, root := ~, 
                                                  start := 220454, 
                                                  stop := 220507 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 generators.", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 4, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 220551, root := ~, 
                                                  start := 220511, 
                                                  stop := 220550 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 220589, 
                                                          root := ~, 
                                                          start := 220575, 
                                                          stop := 220588 ), 
                                                      rec( 
                                                          content := " is an i\
mmutable Cayley graph of a group or semigroup with\n    respect to a set of ge\
nerators ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ens", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 220694, 
                                                          root := ~, 
                                                          start := 220683, 
                                                          stop := 220693 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 220713, 
                                                          root := ~, 
                                                          start := 220699, 
                                                          stop := 220712 ), 
                                                      rec( 
                                                          content := " belongs\
 to\n    the category ", count := [ 5, 4, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsCayle\
yDigraph" ), content := 0, count := [ 5, 4, 2, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 220771, 
                                                          root := ~, 
                                                          start := 220742, 
                                                          stop := 220770 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
eneratorsOfCayleyDigraph", count := [ 5, 4, 2, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 4, 2, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 220814, 
                                                          root := ~, 
                                                          start := 220782, 
                                                          stop := 220813 ), 
                                                      rec( 
                                                          content := " return \
the list of generators ", count := [ 5, 4, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ens", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 220856, 
                                                          root := ~, 
                                                          start := 220845, 
                                                          stop := 220855 ), 
                                                      rec( 
                                                          content := "\n    ov\
er which ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 220886, 
                                                          root := ~, 
                                                          start := 220872, 
                                                          stop := 220885 ), 
                                                      rec( 
                                                          content := " is defi\
ned.\n    ", count := [ 5, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 220907, 
                                                          root := ~, 
                                                          start := 220903, 
                                                          stop := 220906 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 5, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "GroupOf\
CayleyDigraph" ), content := 0, count := [ 5, 4, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 220956, 
                                                          root := ~, 
                                                          start := 220922, 
                                                          stop := 220955 ), 
                                                      rec( 
                                                          content := " \n    o\
r ", count := [ 5, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Semigro\
upOfCayleyDigraph" ), content := 0, count := [ 5, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 221003, 
                                                          root := ~, 
                                                          start := 220965, 
                                                          stop := 221002 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> G := DihedralGroup(IsPermGroup, 8);\nGroup([ (1,2,3,4), (2,4) ])\ngap> d\
igraph := CayleyDigraph(G);\n<immutable digraph with 8 vertices, 16 edges>\nga\
p> GeneratorsOfCayleyDigraph(digraph) = GeneratorsOfGroup(G);\ntrue\ngap> digr\
aph := CayleyDigraph(G, [()]);\n<immutable digraph with 8 vertices, 8 edges>\n\
gap> GeneratorsOfCayleyDigraph(digraph) = [()];\ntrue", count := [ 5, 4, 2, 5 
                                                                     ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 4, 2, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 221396, 
                                                          root := ~, 
                                                          start := 221009, 
                                                          stop := 221395 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 4, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 4, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 221413, root := ~, 
                                                  start := 220554, 
                                                  stop := 221412 ) ], 
                                          count := [ 5, 4, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 221427, root := ~, 
                                          start := 220439, stop := 221426 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 5, 4, 2, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 5, 4, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 221441, 
                                  root := ~, start := 219457, stop := 221440 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 5, 4, 2, 6 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Associated semigr\
oups", count := [ 5, 5, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 5, 5, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 221494, 
                                          root := ~, start := 221454, 
                                          stop := 221493 ), 
                                      rec( content := "\n      ", 
                                          count := [ 5, 5, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filt, digraph", 
                                                      Label := "for a filter a\
nd a digraph", Name := "AsSemigroup" ), content := 0, count := [ 5, 5, 1, 2 ],
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 221605, root := ~, 
                                                  start := 221518, 
                                                  stop := 221604 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filt, digraph", 
                                                      Name := "AsMonoid" ), 
                                                  content := 0, 
                                                  count := [ 5, 5, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 221653, root := ~, 
                                                  start := 221610, 
                                                  stop := 221652 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A semilat\
tice of partial perms.", count := [ 5, 5, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 5, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 221708, root := ~, 
                                                  start := 221658, 
                                                  stop := 221707 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      T\
he operation ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sSemigroup", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 221765, 
                                                          root := ~, 
                                                          start := 221747, 
                                                          stop := 221764 ), 
                                                      rec( 
                                                          content := " require\
s that ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 221791, 
                                                          root := ~, 
                                                          start := 221780, 
                                                          stop := 221790 ), 
                                                      rec( 
                                                          content := " be equa\
l to\n      ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Filt := "IsPartialPermSemigroup" ), content := 0, count := [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 221861, 
                                                          root := ~, 
                                                          start := 221810, 
                                                          stop := 221860 ), 
                                                      rec( 
                                                          content := ".\n     \
 If ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 221886, 
                                                          root := ~, 
                                                          start := 221872, 
                                                          stop := 221885 ), 
                                                      rec( 
                                                          content := " is a\n \
     ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsJoinS\
emilatticeDigraph" ), content := 0, count := [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 221936, 
                                                          root := ~, 
                                                          start := 221898, 
                                                          stop := 221935 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsLatti\
ceDigraph" ), content := 0, count := [ 5, 5, 1, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 221970, 
                                                          root := ~, 
                                                          start := 221940, 
                                                          stop := 221969 ), 
                                                      rec( 
                                                          content := "\n      \
then ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sSemigroup", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 222000, 
                                                          root := ~, 
                                                          start := 221982, 
                                                          stop := 221999 ), 
                                                      rec( 
                                                          content := " returns\
 a semigroup of partial perms which is\n      isomorphic to the semigroup whos\
e elements are the vertices of\n      ", count := [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 222136, 
                                                          root := ~, 
                                                          start := 222122, 
                                                          stop := 222135 ), 
                                                      rec( 
                                                          content := " with th\
e binary operation\n      ", count := [ 5, 5, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Partial\
OrderDigraphJoinOfVertices" ), content := 0, count := [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 222216, 
                                                          root := ~, 
                                                          start := 222169, 
                                                          stop := 222215 ), 
                                                      rec( 
                                                          content := ".\n     \
 If ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 222241, 
                                                          root := ~, 
                                                          start := 222227, 
                                                          stop := 222240 ), 
                                                      rec( 
                                                          content := "\n      \
satisfies  ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsMeetS\
emilatticeDigraph" ), content := 0, count := [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 222297, 
                                                          root := ~, 
                                                          start := 222259, 
                                                          stop := 222296 ), 
                                                      rec( 
                                                          content := " but not\
\n      ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsJoinS\
emilatticeDigraph" ), content := 0, count := [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 222350, 
                                                          root := ~, 
                                                          start := 222312, 
                                                          stop := 222349 ), 
                                                      rec( 
                                                          content := " then\n \
     ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sSemigroup", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 222380, 
                                                          root := ~, 
                                                          start := 222362, 
                                                          stop := 222379 ), 
                                                      rec( 
                                                          content := " returns\
 a semigroup of partial perms which is\n      isomorphic to the semigroup whos\
e elements are the vertices of\n      ", count := [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 222516, 
                                                          root := ~, 
                                                          start := 222502, 
                                                          stop := 222515 ), 
                                                      rec( 
                                                          content := " with th\
e binary operation\n      ", count := [ 5, 5, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Partial\
OrderDigraphMeetOfVertices" ), content := 0, count := [ 5, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 222596, 
                                                          root := ~, 
                                                          start := 222549, 
                                                          stop := 222595 ), 
                                                      rec( 
                                                          content := ".\n     \
 ", count := [ 5, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 222608, 
                                                          root := ~, 
                                                          start := 222604, 
                                                          stop := 222607 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The operation ", count := [ 5, 5, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sMonoid", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 222645, 
                                                          root := ~, 
                                                          start := 222630, 
                                                          stop := 222644 ), 
                                                      rec( 
                                                          content := " behaves\
 similarly to ", count := [ 5, 5, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sSemigroup", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 222685, 
                                                          root := ~, 
                                                          start := 222667, 
                                                          stop := 222684 ), 
                                                      rec( 
                                                          content := "\n      \
except that ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 222715, 
                                                          root := ~, 
                                                          start := 222704, 
                                                          stop := 222714 ), 
                                                      rec( 
                                                          content := " may als\
o be equal to\n      ", count := [ 5, 5, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Filt := "IsPartialPermMonoid" ), content := 0, count := [ 5, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 222791, 
                                                          root := ~, 
                                                          start := 222743, 
                                                          stop := 222790 ), 
                                                      rec( 
                                                          content := ",\n     \
 ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 222813, 
                                                          root := ~, 
                                                          start := 222799, 
                                                          stop := 222812 ), 
                                                      rec( 
                                                          content := " must sa\
tisfy ", count := [ 5, 5, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsLatti\
ceDigraph" ), content := 0, count := [ 5, 5, 1, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 222857, 
                                                          root := ~, 
                                                          start := 222827, 
                                                          stop := 222856 ), 
                                                      rec( 
                                                          content := ", and th\
e\n      output satisfies ", count := [ 5, 5, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Filt := "IsMonoid" ), content := 0, count := [ 5, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 222927, 
                                                          root := ~, 
                                                          start := 222890, 
                                                          stop := 222926 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 5, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 222933, 
                                                          root := ~, 
                                                          start := 222929, 
                                                          stop := 222932 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The output of both of these operations is guaranteed to be of minimal\n     \
 degree (see ", count := [ 5, 5, 1, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "DegreeO\
fPartialPermSemigroup", BookName := "ref" ), content := 0, 
                                                          count := 
                                                            [ 5, 5, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 223086, 
                                                          root := ~, 
                                                          start := 223029, 
                                                          stop := 223085 ), 
                                                      rec( 
                                                          content := ").\n    \
  Furthermore the ", count := [ 5, 5, 1, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Generat\
orsOfSemigroup", BookName := "ref" ), content := 0, count := [ 5, 5, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 223161, 
                                                          root := ~, 
                                                          start := 223111, 
                                                          stop := 223160 ), 
                                                      rec( 
                                                          content := " of\n   \
   the output is guaranteed to be the unique generating set of minimal size.\n\
      ", count := [ 5, 5, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> di := Digraph([[1], [1, 2], [1, 3], [1, 4], [1, 2, 3, 5]]);\n<immutable \
digraph with 5 vertices, 11 edges>\ngap> S := AsSemigroup(IsPartialPermSemigro\
up, di);\n<partial perm semigroup of rank 3 with 4 generators>\ngap> ForAll(El\
ements(S), IsIdempotent);\ntrue\ngap> IsInverseSemigroup(S);\ntrue\ngap> Size(\
S);\n5\ngap> di := Digraph([[1], [1, 2], [1, 2, 3]]);\n<immutable digraph with\
 3 vertices, 6 edges>\ngap> M := AsMonoid(IsPartialPermMonoid, di);\n<partial \
perm monoid of rank 2 with 3 generators>\ngap> Size(M);\n3", count := 
                                                                    [ 5, 5, 
                                                                      1, 8 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 5, 1, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 223793, 
                                                          root := ~, 
                                                          start := 223251, 
                                                          stop := 223792 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 5, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 5, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 223812, root := ~, 
                                                  start := 221713, 
                                                  stop := 223811 ) ], 
                                          count := [ 5, 5, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 223828, root := ~, 
                                          start := 221501, stop := 223827 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 5, 5, 1, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filt, Y, gps, ho\
ms", Label := "for a filter, semilattice digraph, and two lists", 
                                                      Name := "AsSemigroup" ),
                                                  content := 0, 
                                                  count := [ 5, 5, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 223967, root := ~, 
                                                  start := 223853, 
                                                  stop := 223966 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A Cliffo\
rd semigroup of partial perms. ", count := [ 5, 5, 2, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 5, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 224031, root := ~, 
                                                  start := 223972, 
                                                  stop := 224030 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      T\
he operation ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sSemigroup", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 224088, 
                                                          root := ~, 
                                                          start := 224070, 
                                                          stop := 224087 ), 
                                                      rec( 
                                                          content := " require\
s that ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 224114, 
                                                          root := ~, 
                                                          start := 224103, 
                                                          stop := 224113 ), 
                                                      rec( 
                                                          content := " be equa\
l to\n      ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Filt := "IsPartialPermSemigroup" ), content := 0, count := [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 224184, 
                                                          root := ~, 
                                                          start := 224133, 
                                                          stop := 224183 ), 
                                                      rec( 
                                                          content := ".\n     \
 If ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "Y\
", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 224203, 
                                                          root := ~, 
                                                          start := 224195, 
                                                          stop := 224202 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsJoinS\
emilatticeDigraph" ), content := 0, count := [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 224247, 
                                                          root := ~, 
                                                          start := 224209, 
                                                          stop := 224246 ), 
                                                      rec( 
                                                          content := " or\n   \
   ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsMeetS\
emilatticeDigraph" ), content := 0, count := [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 224295, 
                                                          root := ~, 
                                                          start := 224257, 
                                                          stop := 224294 ), 
                                                      rec( 
                                                          content := ",\n     \
 ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ps", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 224313, 
                                                          root := ~, 
                                                          start := 224303, 
                                                          stop := 224312 ), 
                                                      rec( 
                                                          content := " is a li\
st of groups corresponding to each vertex, and\n      ", count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
oms", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 224385, 
                                                          root := ~, 
                                                          start := 224374, 
                                                          stop := 224384 ), 
                                                      rec( 
                                                          content := " is a li\
st containing for each edge ", count := [ 5, 5, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "(\
i, j)", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 224434, 
                                                          root := ~, 
                                                          start := 224421, 
                                                          stop := 224433 ), 
                                                      rec( 
                                                          content := " in\n   \
   the transitive reduction of ", count := [ 5, 5, 2, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 224486, 
                                                          root := ~, 
                                                          start := 224472, 
                                                          stop := 224485 ), 
                                                      rec( 
                                                          content := " a tripl\
e ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i, j, hom]", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 224514, 
                                                          root := ~, 
                                                          start := 224496, 
                                                          stop := 224513 ), 
                                                      rec( 
                                                          content := "\n      \
where ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
om", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 224537, 
                                                          root := ~, 
                                                          start := 224527, 
                                                          stop := 224536 ), 
                                                      rec( 
                                                          content := " is a gr\
oup homomorphism from ", count := [ 5, 5, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ps[i]", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 224580, 
                                                          root := ~, 
                                                          start := 224567, 
                                                          stop := 224579 ), 
                                                      rec( 
                                                          content := " to\n   \
   ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ps[j]", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 224603, 
                                                          root := ~, 
                                                          start := 224590, 
                                                          stop := 224602 ), 
                                                      rec( 
                                                          content := ", and th\
e diagram of homomorphisms commutes, then\n      ", count := [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
sSemigroup", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 224677, 
                                                          root := ~, 
                                                          start := 224659, 
                                                          stop := 224676 ), 
                                                      rec( 
                                                          content := " returns\
 a semigroup of partial perms which is\n      isomorphic to the strong semilat\
tice of groups ", count := [ 5, 5, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
[Y; gps; homs]", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 224799, 
                                                          root := ~, 
                                                          start := 224777, 
                                                          stop := 224798 ), 
                                                      rec( 
                                                          content := ".\n     \
 ", count := [ 5, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> G1 := AlternatingGroup(4);;\ngap> G2 := SymmetricGroup(2);;\ngap> G3 := \
SymmetricGroup(3);;\ngap> gr := Digraph([[1, 3], [2, 3], [3]]);;\ngap> sgn := \
function(x)\n> if SignPerm(x) = 1 then\n> return ();\n> fi;\n> return (1, 2);\
\n> end;;\ngap> hom13 := GroupHomomorphismByFunction(G1, G3, sgn);;\ngap> hom2\
3 := GroupHomomorphismByFunction(G2, G3, sgn);;\ngap> T := AsSemigroup(IsParti\
alPermSemigroup,\n> gr,\n> [G1, G2, G3], [[1, 3, hom13], [2, 3, hom23]]);;\nga\
p> Size(T);\n20\ngap> D := GreensDClasses(T);;\ngap> List(D, x -> Size(x));\n[\
 6, 12, 2 ]\n", count := [ 5, 5, 2, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 225376, 
                                                          root := ~, 
                                                          start := 224807, 
                                                          stop := 225375 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 5, 5, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 5, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 225395, root := ~, 
                                                  start := 224036, 
                                                  stop := 225394 ) ], 
                                          count := [ 5, 5, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 225411, root := ~, 
                                          start := 223836, stop := 225410 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 5, 5, 2, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 5, 5, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 225425, 
                                  root := ~, start := 221445, stop := 225424 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 5, 5, 2, 5 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Planarity", 
                                                  count := [ 5, 6, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 5, 6, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 225466, 
                                          root := ~, start := 225438, 
                                          stop := 225465 ), 
                                      rec( content := "\n    ", 
                                          count := [ 5, 6, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "KuratowskiPlana\
rSubdigraph" ), content := 0, count := [ 5, 6, 1, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 225541, root := ~, 
                                                  start := 225486, 
                                                  stop := 225540 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list or\
 ", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 225574, 
                                                          root := ~, 
                                                          start := 225563, 
                                                          stop := 225573 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 225585, root := ~, 
                                                  start := 225544, 
                                                  stop := 225584 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "K\
uratowskiPlanarSubdigraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 225639, 
                                                          root := ~, 
                                                          start := 225606, 
                                                          stop := 225638 ), 
                                                      rec( 
                                                          content := " returns\
 the immutable list of\n    lists of out-neighbours of a (not necessarily indu\
ced) subdigraph of the\n    digraph ", count := [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 225773, 
                                                          root := ~, 
                                                          start := 225759, 
                                                          stop := 225772 ), 
                                                      rec( 
                                                          content := " that wi\
tnesses the fact that ", count := [ 5, 6, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 225817, 
                                                          root := ~, 
                                                          start := 225803, 
                                                          stop := 225816 ), 
                                                      rec( 
                                                          content := " is not\\
n    planar, or ", count := [ 5, 6, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 225851, 
                                                          root := ~, 
                                                          start := 225840, 
                                                          stop := 225850 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 225869, 
                                                          root := ~, 
                                                          start := 225855, 
                                                          stop := 225868 ), 
                                                      rec( 
                                                          content := " is plan\
ar.  In other words,\n    ", count := [ 5, 6, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "K\
uratowskiPlanarSubdigraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 1, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 225935, 
                                                          root := ~, 
                                                          start := 225902, 
                                                          stop := 225934 ), 
                                                      rec( 
                                                          content := " returns\
 the out-neighbours of a\n    subdigraph of ", count := [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 226000, 
                                                          root := ~, 
                                                          start := 225986, 
                                                          stop := 225999 ), 
                                                      rec( 
                                                          content := " that is\
 homeomorphic to the complete graph\n    with ", count := [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "5\
", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 226061, 
                                                          root := ~, 
                                                          start := 226053, 
                                                          stop := 226060 ), 
                                                      rec( 
                                                          content := " vertice\
s, or to the complete bipartite graph with vertex sets\n    of sizes ", 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 226145, 
                                                          root := ~, 
                                                          start := 226137, 
                                                          stop := 226144 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 5, 6, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 226158, 
                                                          root := ~, 
                                                          start := 226150, 
                                                          stop := 226157 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 6, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 226164, 
                                                          root := ~, 
                                                          start := 226160, 
                                                          stop := 226163 ), 
                                                      rec( 
                                                          content := "\n    \n\
    The directions and multiplicities of any edges in ", count := 
                                                            [ 5, 6, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 226238, 
                                                          root := ~, 
                                                          start := 226224, 
                                                          stop := 226237 ), 
                                                      rec( 
                                                          content := " are\n  \
  ignored when considering whether or not ", count := [ 5, 6, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 226301, 
                                                          root := ~, 
                                                          start := 226287, 
                                                          stop := 226300 ), 
                                                      rec( 
                                                          content := " is plan\
ar. ", count := [ 5, 6, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 226317, 
                                                          root := ~, 
                                                          start := 226313, 
                                                          stop := 226316 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 5, 6, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsPlana\
rDigraph" ), content := 0, count := [ 5, 6, 1, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 226361, 
                                                          root := ~, 
                                                          start := 226332, 
                                                          stop := 226360 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 5, 6, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Subdigr\
aphHomeomorphicToK33" ), content := 0, count := [ 5, 6, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 226411, 
                                                          root := ~, 
                                                          start := 226370, 
                                                          stop := 226410 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 6, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 226421, 
                                                          root := ~, 
                                                          start := 226417, 
                                                          stop := 226420 ), 
                                                      rec( 
                                                          content := "\n    \n\
    This method uses the reference implementation in\n    ", 
                                                          count := 
                                                            [ 5, 6, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \
"https://github.com/graph-algorithms/edge-addition-planarity-suite", count := 
                                                                            [ \
5, 6, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 5, 6, 
                                                                      1, 6 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], 
                                                          count := 
                                                            [ 5, 6, 1, 6 ], 
                                                          name := "Alt", 
                                                          next := 146, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 145 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "edge-addition-planarity-suite", count \
:= [ 5, 6, 1, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 1, 6 ], 
                                                                  name := "Pac\
kage", next := 218, root := ~, start := 170, stop := 217 ) ], 
                                                          count := 
                                                            [ 5, 6, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 224, 
                                                          root := ~, 
                                                          start := 146, 
                                                          stop := 223 ), 
                                                      rec( 
                                                          content := " by John\
 Boyer of the algorithms described\n    in ", count := [ 5, 6, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "BM06" ),
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 226583, 
                                                          root := ~, 
                                                          start := 226565, 
                                                          stop := 226582 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 6, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4\
, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 v\
ertices, 25 edges>\ngap> KuratowskiPlanarSubdigraph(D);\nfail\ngap> D := Digra\
ph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1, 2, 3\
, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, \
9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n<immutable digraph with 10 vertices, 50 edg\
es>\ngap> IsPlanarDigraph(D);\nfalse\ngap> KuratowskiPlanarSubdigraph(D);\n[ [\
 2, 9, 7 ], [ 3 ], [ 6 ], [ 5, 9 ], [ 6 ], [  ], [ 4 ], \n  [ 7, 9, 3 ], [  ],\
 [  ] ]\ngap> D := Digraph(IsMutableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\
\n> [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<m\
utable digraph with 11 vertices, 25 edges>\ngap> KuratowskiPlanarSubdigraph(D)\
;\nfail\ngap> D := Digraph(IsMutableDigraph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6\
, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9,\
 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n\
<mutable digraph with 10 vertices, 50 edges>\ngap> IsPlanarDigraph(D);\nfalse\
\ngap> KuratowskiPlanarSubdigraph(D);\n[ [ 2, 9, 7 ], [ 3 ], [ 6 ], [ 5, 9 ], \
[ 6 ], [  ], [ 4 ], \n  [ 7, 9, 3 ], [  ], [  ] ]\n", count := [ 5, 6, 1, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 1, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 227885, 
                                                          root := ~, 
                                                          start := 226586, 
                                                          stop := 227884 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 6, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 227902, root := ~, 
                                                  start := 225588, 
                                                  stop := 227901 ) ], 
                                          count := [ 5, 6, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 227916, root := ~, 
                                          start := 225471, stop := 227915 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 6, 1, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "KuratowskiOuter\
PlanarSubdigraph" ), content := 0, count := [ 5, 6, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 227997, root := ~, 
                                                  start := 227937, 
                                                  stop := 227996 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list or\
 ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 228030, 
                                                          root := ~, 
                                                          start := 228019, 
                                                          stop := 228029 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 228041, root := ~, 
                                                  start := 228000, 
                                                  stop := 228040 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "K\
uratowskiOuterPlanarSubdigraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 228100, 
                                                          root := ~, 
                                                          start := 228062, 
                                                          stop := 228099 ), 
                                                      rec( 
                                                          content := " returns\
 the immutable list of\n    immutable lists of out-neighbours of a (not necess\
arily induced)\n    subdigraph of the digraph ", count := [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 228244, 
                                                          root := ~, 
                                                          start := 228230, 
                                                          stop := 228243 ), 
                                                      rec( 
                                                          content := " that wi\
tnesses the fact\n    that ", count := [ 5, 6, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 228292, 
                                                          root := ~, 
                                                          start := 228278, 
                                                          stop := 228291 ), 
                                                      rec( 
                                                          content := " is not \
outer planar, or ", count := [ 5, 6, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 228328, 
                                                          root := ~, 
                                                          start := 228317, 
                                                          stop := 228327 ), 
                                                      rec( 
                                                          content := " if\n   \
 ", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 228350, 
                                                          root := ~, 
                                                          start := 228336, 
                                                          stop := 228349 ), 
                                                      rec( 
                                                          content := " is oute\
r planar.  In other words,\n    ", count := [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "K\
uratowskiOuterPlanarSubdigraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 2, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 228427, 
                                                          root := ~, 
                                                          start := 228389, 
                                                          stop := 228426 ), 
                                                      rec( 
                                                          content := " returns\
 the out-neighbours of a\n    subdigraph of ", count := [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 228492, 
                                                          root := ~, 
                                                          start := 228478, 
                                                          stop := 228491 ), 
                                                      rec( 
                                                          content := " that is\
 homeomorphic to the complete graph\n    with ", count := [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "4\
", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 228553, 
                                                          root := ~, 
                                                          start := 228545, 
                                                          stop := 228552 ), 
                                                      rec( 
                                                          content := " vertice\
s, or to the complete bipartite graph with vertex sets\n    of sizes ", 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 228637, 
                                                          root := ~, 
                                                          start := 228629, 
                                                          stop := 228636 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 5, 6, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 228650, 
                                                          root := ~, 
                                                          start := 228642, 
                                                          stop := 228649 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 5, 6, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 228656, 
                                                          root := ~, 
                                                          start := 228652, 
                                                          stop := 228655 ), 
                                                      rec( 
                                                          content := "\n    \n\
    The directions and multiplicities of any edges in ", count := 
                                                            [ 5, 6, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 228730, 
                                                          root := ~, 
                                                          start := 228716, 
                                                          stop := 228729 ), 
                                                      rec( 
                                                          content := " are\n  \
  ignored when considering whether or not ", count := [ 5, 6, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 228793, 
                                                          root := ~, 
                                                          start := 228779, 
                                                          stop := 228792 ), 
                                                      rec( 
                                                          content := " is oute\
r planar. \n    ", count := [ 5, 6, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 228820, 
                                                          root := ~, 
                                                          start := 228816, 
                                                          stop := 228819 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also \n    ", count := [ 5, 6, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsOuter\
PlanarDigraph" ), content := 0, count := [ 5, 6, 2, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 228874, 
                                                          root := ~, 
                                                          start := 228840, 
                                                          stop := 228873 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 6, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Subdigr\
aphHomeomorphicToK4" ), content := 0, count := [ 5, 6, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 228920, 
                                                          root := ~, 
                                                          start := 228880, 
                                                          stop := 228919 ), 
                                                      rec( 
                                                          content := ", and \n\
    ", count := [ 5, 6, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Subdigr\
aphHomeomorphicToK23" ), content := 0, count := [ 5, 6, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 228972, 
                                                          root := ~, 
                                                          start := 228931, 
                                                          stop := 228971 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 6, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 228982, 
                                                          root := ~, 
                                                          start := 228978, 
                                                          stop := 228981 ), 
                                                      rec( 
                                                          content := "\n\n    \
This method uses the reference implementation in\n    ", count := 
                                                            [ 5, 6, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \
"https://github.com/graph-algorithms/edge-addition-planarity-suite", count := 
                                                                            [ \
5, 6, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 5, 6, 
                                                                      2, 6 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], 
                                                          count := 
                                                            [ 5, 6, 2, 6 ], 
                                                          name := "Alt", 
                                                          next := 146, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 145 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "edge-addition-planarity-suite", count \
:= [ 5, 6, 2, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 2, 6 ], 
                                                                  name := "Pac\
kage", next := 218, root := ~, start := 170, stop := 217 ) ], 
                                                          count := 
                                                            [ 5, 6, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 224, 
                                                          root := ~, 
                                                          start := 146, 
                                                          stop := 223 ), 
                                                      rec( 
                                                          content := " by John\
 Boyer of the algorithms described\n    in ", count := [ 5, 6, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "BM06" ),
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 229140, 
                                                          root := ~, 
                                                          start := 229122, 
                                                          stop := 229139 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 6, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4\
, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 v\
ertices, 25 edges>\ngap> KuratowskiOuterPlanarSubdigraph(D);\n[ [ 3, 5, 10 ], \
[ 9, 8, 10 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ]\
 ]\ngap> D := Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2,\
 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9,\
 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n<immutable digraph with \
10 vertices, 50 edges>\ngap> IsOuterPlanarDigraph(D);\nfalse\ngap> KuratowskiO\
uterPlanarSubdigraph(D);\n[ [  ], [  ], [  ], [ 8, 9 ], [  ], [  ], [ 9, 4 ], \
[ 7, 9 ], [  ], \n  [  ] ]\ngap> D := Digraph(IsMutableDigraph, [[3, 5, 10], [\
8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1,\
 2], [5, 9]]);\n<mutable digraph with 11 vertices, 25 edges>\ngap> KuratowskiO\
uterPlanarSubdigraph(D);\n[ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [ 6 ], [ 11 ], \
[ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D := Digraph(IsMutableDigra\
ph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1, 2\
, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7\
, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n<mutable digraph with 10 vertices, 50 edg\
es>\ngap> IsOuterPlanarDigraph(D);\nfalse\ngap> KuratowskiOuterPlanarSubdigrap\
h(D);\n[ [  ], [  ], [  ], [ 8, 9 ], [  ], [  ], [ 9, 4 ], [ 7, 9 ], [  ], \n \
 [  ] ]", count := [ 5, 6, 2, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 5, 6, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 230633, 
                                                          root := ~, 
                                                          start := 229143, 
                                                          stop := 230632 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 6, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 230650, root := ~, 
                                                  start := 228044, 
                                                  stop := 230649 ) ], 
                                          count := [ 5, 6, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 230664, root := ~, 
                                          start := 227922, stop := 230663 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 6, 2, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "PlanarEmbedding\
" ), content := 0, count := [ 5, 6, 3, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 230729, root := ~, 
                                                  start := 230685, 
                                                  stop := 230728 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list or\
 ", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 230762, 
                                                          root := ~, 
                                                          start := 230751, 
                                                          stop := 230761 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 230773, root := ~, 
                                                  start := 230732, 
                                                  stop := 230772 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 230811, 
                                                          root := ~, 
                                                          start := 230797, 
                                                          stop := 230810 ), 
                                                      rec( 
                                                          content := " is a pl\
anar digraph, then \n    ", count := [ 5, 6, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "P\
lanarEmbedding", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 230865, 
                                                          root := ~, 
                                                          start := 230843, 
                                                          stop := 230864 ), 
                                                      rec( 
                                                          content := " returns\
 the immutable list of lists of\n    out-neighbours of a subdigraph of ", 
                                                          count := 
                                                            [ 5, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 230957, 
                                                          root := ~, 
                                                          start := 230943, 
                                                          stop := 230956 ), 
                                                      rec( 
                                                          content := " such th\
at each vertex's\n    neighbours are given in clockwise order. If ", 
                                                          count := 
                                                            [ 5, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 231044, 
                                                          root := ~, 
                                                          start := 231030, 
                                                          stop := 231043 ), 
                                                      rec( 
                                                          content := " is not \
planar,\n    then ", count := [ 5, 6, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 231080, 
                                                          root := ~, 
                                                          start := 231069, 
                                                          stop := 231079 ), 
                                                      rec( 
                                                          content := " is retu\
rned. ", count := [ 5, 6, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 231098, 
                                                          root := ~, 
                                                          start := 231094, 
                                                          stop := 231097 ), 
                                                      rec( 
                                                          content := "\n    \n\
    The directions and multiplicities of any edges in ", count := 
                                                            [ 5, 6, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 231172, 
                                                          root := ~, 
                                                          start := 231158, 
                                                          stop := 231171 ), 
                                                      rec( 
                                                          content := " are\n  \
  ignored by ", count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "P\
lanarEmbedding", count := [ 5, 6, 3, 4 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 231214, 
                                                          root := ~, 
                                                          start := 231192, 
                                                          stop := 231213 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 6, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 231224, 
                                                          root := ~, 
                                                          start := 231220, 
                                                          stop := 231223 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also \n    ", count := [ 5, 6, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsPlana\
rDigraph" ), content := 0, count := [ 5, 6, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 231273, 
                                                          root := ~, 
                                                          start := 231244, 
                                                          stop := 231272 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 6, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 231283, 
                                                          root := ~, 
                                                          start := 231279, 
                                                          stop := 231282 ), 
                                                      rec( 
                                                          content := "\n\n    \
This method uses the reference implementation in\n    ", count := 
                                                            [ 5, 6, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \
"https://github.com/graph-algorithms/edge-addition-planarity-suite", count := 
                                                                            [ \
5, 6, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 5, 6, 
                                                                      3, 6 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], 
                                                          count := 
                                                            [ 5, 6, 3, 6 ], 
                                                          name := "Alt", 
                                                          next := 146, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 145 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "edge-addition-planarity-suite", count \
:= [ 5, 6, 3, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 3, 6 ], 
                                                                  name := "Pac\
kage", next := 218, root := ~, start := 170, stop := 217 ) ], 
                                                          count := 
                                                            [ 5, 6, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 224, 
                                                          root := ~, 
                                                          start := 146, 
                                                          stop := 223 ), 
                                                      rec( 
                                                          content := " by John\
 Boyer of the algorithms described\n    in ", count := [ 5, 6, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "BM06" ),
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 231441, 
                                                          root := ~, 
                                                          start := 231423, 
                                                          stop := 231440 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 6, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4\
, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 v\
ertices, 25 edges>\ngap> PlanarEmbedding(D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ \
4 ], [ 6 ], [ 11, 7 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D :=\
 Digraph([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1\
, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, \
5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n<immutable digraph with 10 vertices, \
50 edges>\ngap> PlanarEmbedding(D);\nfail\ngap> D := Digraph(IsMutableDigraph,\
 [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7\
], [2, 11], [1, 2], [5, 9]]);\n<mutable digraph with 11 vertices, 25 edges>\ng\
ap> PlanarEmbedding(D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11, 7 ]\
, [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D := Digraph(IsMutableDig\
raph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1,\
 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5,\
 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n<mutable digraph with 10 vertices, 50 e\
dges>\ngap> PlanarEmbedding(D);\nfail\n", count := [ 5, 6, 3, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 3, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 232659, 
                                                          root := ~, 
                                                          start := 231444, 
                                                          stop := 232658 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 6, 3, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 232676, root := ~, 
                                                  start := 230776, 
                                                  stop := 232675 ) ], 
                                          count := [ 5, 6, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 232690, root := ~, 
                                          start := 230670, stop := 232689 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 6, 3, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "OuterPlanarEmbe\
dding" ), content := 0, count := [ 5, 6, 4, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 232760, root := ~, 
                                                  start := 232711, 
                                                  stop := 232759 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list or\
 ", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 232793, 
                                                          root := ~, 
                                                          start := 232782, 
                                                          stop := 232792 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 6, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 232804, root := ~, 
                                                  start := 232763, 
                                                  stop := 232803 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 232842, 
                                                          root := ~, 
                                                          start := 232828, 
                                                          stop := 232841 ), 
                                                      rec( 
                                                          content := " is an o\
uter planar digraph, then\n    ", count := [ 5, 6, 4, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
uterPlanarEmbedding", count := [ 5, 6, 4, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 4, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 232907, 
                                                          root := ~, 
                                                          start := 232880, 
                                                          stop := 232906 ), 
                                                      rec( 
                                                          content := " returns\
 the immutable list of lists\n    of out-neighbours of a subdigraph of ", 
                                                          count := 
                                                            [ 5, 6, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 232999, 
                                                          root := ~, 
                                                          start := 232985, 
                                                          stop := 232998 ), 
                                                      rec( 
                                                          content := " such th\
at each\n    vertex's neighbours are given in clockwise order. If ", 
                                                          count := 
                                                            [ 5, 6, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 233086, 
                                                          root := ~, 
                                                          start := 233072, 
                                                          stop := 233085 ), 
                                                      rec( 
                                                          content := " is not\\
n    outer planar, then ", count := [ 5, 6, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 233128, 
                                                          root := ~, 
                                                          start := 233117, 
                                                          stop := 233127 ), 
                                                      rec( 
                                                          content := " is retu\
rned. ", count := [ 5, 6, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 233146, 
                                                          root := ~, 
                                                          start := 233142, 
                                                          stop := 233145 ), 
                                                      rec( 
                                                          content := "\n    \n\
    The directions and multiplicities of any edges in ", count := 
                                                            [ 5, 6, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 233220, 
                                                          root := ~, 
                                                          start := 233206, 
                                                          stop := 233219 ), 
                                                      rec( 
                                                          content := " are\n  \
  ignored by ", count := [ 5, 6, 4, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
uterPlanarEmbedding", count := [ 5, 6, 4, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 4, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 233267, 
                                                          root := ~, 
                                                          start := 233240, 
                                                          stop := 233266 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 6, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 233277, 
                                                          root := ~, 
                                                          start := 233273, 
                                                          stop := 233276 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 5, 6, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsOuter\
PlanarDigraph" ), content := 0, count := [ 5, 6, 4, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 233326, 
                                                          root := ~, 
                                                          start := 233292, 
                                                          stop := 233325 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 5, 6, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 233336, 
                                                          root := ~, 
                                                          start := 233332, 
                                                          stop := 233335 ), 
                                                      rec( 
                                                          content := "\n\n    \
This method uses the reference implementation in\n    ", count := 
                                                            [ 5, 6, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \
"https://github.com/graph-algorithms/edge-addition-planarity-suite", count := 
                                                                            [ \
5, 6, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 5, 6, 
                                                                      4, 6 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], 
                                                          count := 
                                                            [ 5, 6, 4, 6 ], 
                                                          name := "Alt", 
                                                          next := 146, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 145 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "edge-addition-planarity-suite", count \
:= [ 5, 6, 4, 6 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 4, 6 ], 
                                                                  name := "Pac\
kage", next := 218, root := ~, start := 170, stop := 217 ) ], 
                                                          count := 
                                                            [ 5, 6, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 224, 
                                                          root := ~, 
                                                          start := 146, 
                                                          stop := 223 ), 
                                                      rec( 
                                                          content := " by John\
 Boyer of the algorithms described\n    in ", count := [ 5, 6, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "BM06" ),
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 233494, 
                                                          root := ~, 
                                                          start := 233476, 
                                                          stop := 233493 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 6, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4\
, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 v\
ertices, 25 edges>\ngap> OuterPlanarEmbedding(D);\nfail\ngap> D := Digraph([[2\
, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1, 2, 3, 4, 6\
, 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2\
, 3, 5, 6, 7, 8], [3, 5]]);\n<immutable digraph with 10 vertices, 50 edges>\ng\
ap> OuterPlanarEmbedding(D);\nfail\ngap> OuterPlanarEmbedding(CompleteBipartit\
eDigraph(2, 2));\n[ [ 3, 4 ], [ 4, 3 ], [  ], [  ] ]\ngap> D := Digraph(IsMuta\
bleDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, 7], [6\
, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<mutable digraph with 11 vertices, 2\
5 edges>\ngap> OuterPlanarEmbedding(D);\nfail\ngap> D := Digraph(IsMutableDigr\
aph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1, \
2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5, \
7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n<mutable digraph with 10 vertices, 50 ed\
ges>\ngap> OuterPlanarEmbedding(D);\nfail\ngap> OuterPlanarEmbedding(CompleteB\
ipartiteDigraph(2, 2));\n[ [ 3, 4 ], [ 4, 3 ], [  ], [  ] ]\n", count := 
                                                                    [ 5, 6, 
                                                                      4, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 4, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 234732, 
                                                          root := ~, 
                                                          start := 233497, 
                                                          stop := 234731 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 6, 4, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 234749, root := ~, 
                                                  start := 232807, 
                                                  stop := 234748 ) ], 
                                          count := [ 5, 6, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 234763, root := ~, 
                                          start := 232696, stop := 234762 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 5, 6, 4, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "SubdigraphHomeo\
morphicToK23" ), content := 0, count := [ 5, 6, 5, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 234840, root := ~, 
                                                  start := 234784, 
                                                  stop := 234839 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "SubdigraphHomeo\
morphicToK33" ), content := 0, count := [ 5, 6, 5, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 234899, root := ~, 
                                                  start := 234843, 
                                                  stop := 234898 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "SubdigraphHomeo\
morphicToK4" ), content := 0, count := [ 5, 6, 5, 6 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 234957, root := ~, 
                                                  start := 234902, 
                                                  stop := 234956 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list or\
 ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 234990, 
                                                          root := ~, 
                                                          start := 234979, 
                                                          stop := 234989 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 5, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 235001, root := ~, 
                                                  start := 234960, 
                                                  stop := 235000 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
se attributes return the immutable list of lists of\n    out-neighbours of a s\
ubdigraph of the digraph ", count := [ 5, 6, 5, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 235141, 
                                                          root := ~, 
                                                          start := 235127, 
                                                          stop := 235140 ), 
                                                      rec( 
                                                          content := " which i\
s\n    homeomorphic to one of the following:\n    the complete bipartite graph\
 with vertex sets of sizes ", count := [ 5, 6, 5, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 235260, 
                                                          root := ~, 
                                                          start := 235252, 
                                                          stop := 235259 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 235277, 
                                                          root := ~, 
                                                          start := 235269, 
                                                          stop := 235276 ), 
                                                      rec( 
                                                          content := "; the co\
mplete bipartite graph with vertex sets of sizes ", count := [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 235342, 
                                                          root := ~, 
                                                          start := 235334, 
                                                          stop := 235341 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 235359, 
                                                          root := ~, 
                                                          start := 235351, 
                                                          stop := 235358 ), 
                                                      rec( 
                                                          content := "; or the\
 complete graph with ", count := [ 5, 6, 5, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "4\
", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 235396, 
                                                          root := ~, 
                                                          start := 235388, 
                                                          stop := 235395 ), 
                                                      rec( 
                                                          content := " vertice\
s. If\n    ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 235428, 
                                                          root := ~, 
                                                          start := 235414, 
                                                          stop := 235427 ), 
                                                      rec( 
                                                          content := " has no \
such subdigraphs, then ", count := [ 5, 6, 5, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 5, 6, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 235470, 
                                                          root := ~, 
                                                          start := 235459, 
                                                          stop := 235469 ), 
                                                      rec( 
                                                          content := " is retu\
rned. \n    ", count := [ 5, 6, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 235493, 
                                                          root := ~, 
                                                          start := 235489, 
                                                          stop := 235492 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 5, 6, 5, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsPlana\
rDigraph" ), content := 0, count := [ 5, 6, 5, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 235537, 
                                                          root := ~, 
                                                          start := 235508, 
                                                          stop := 235536 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 5, 6, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsOuter\
PlanarDigraph" ), content := 0, count := [ 5, 6, 5, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 235582, 
                                                          root := ~, 
                                                          start := 235542, 
                                                          stop := 235581 ), 
                                                      rec( 
                                                          content := " for mor\
e details.", count := [ 5, 6, 5, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 235604, 
                                                          root := ~, 
                                                          start := 235600, 
                                                          stop := 235603 ), 
                                                      rec( 
                                                          content := "\n\n    \
This method uses the reference implementation in\n    ", count := 
                                                            [ 5, 6, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \
"https://github.com/graph-algorithms/edge-addition-planarity-suite", count := 
                                                                            [ \
5, 6, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 5, 6, 
                                                                      5, 9 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], 
                                                          count := 
                                                            [ 5, 6, 5, 9 ], 
                                                          name := "Alt", 
                                                          next := 146, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 145 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "edge-addition-planarity-suite", count \
:= [ 5, 6, 5, 9 ], name := "PCDATA", root := ~ ) ], count := [ 5, 6, 5, 9 ], 
                                                                  name := "Pac\
kage", next := 218, root := ~, start := 170, stop := 217 ) ], 
                                                          count := 
                                                            [ 5, 6, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 224, 
                                                          root := ~, 
                                                          start := 146, 
                                                          stop := 223 ), 
                                                      rec( 
                                                          content := " by John\
 Boyer of the algorithms described\n    in ", count := [ 5, 6, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "BM06" ),
                                                          content := 0, 
                                                          count := 
                                                            [ 5, 6, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 235762, 
                                                          root := ~, 
                                                          start := 235744, 
                                                          stop := 235761 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 5, 6, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 7, 11], \n> [4\
, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 v\
ertices, 25 edges>\ngap> SubdigraphHomeomorphicToK4(D);\n[ [ 3, 5, 10 ], [ 9, \
8, 10 ], [ 4 ], [ 6 ], [ 7, 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\
\ngap> SubdigraphHomeomorphicToK23(D);\n[ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [\
 6 ], [ 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D := Digraph(\
[[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 11], \n>  [4, 7], [6, 8], [2, 7],\
 [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 vertices, 24 edges>\ng\
ap> SubdigraphHomeomorphicToK4(D);\nfail\ngap> SubdigraphHomeomorphicToK23(D);\
\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], \n  [  ], \
[ 11 ], [  ], [  ] ]\ngap> SubdigraphHomeomorphicToK33(D);\nfail\ngap> Subdigr\
aphHomeomorphicToK23(NullDigraph(0));\nfail\ngap> SubdigraphHomeomorphicToK33(\
CompleteDigraph(5));\nfail\ngap> SubdigraphHomeomorphicToK33(CompleteBipartite\
Digraph(3, 3));\n[ [ 4, 6, 5 ], [ 4, 5, 6 ], [ 6, 5, 4 ], [  ], [  ], [  ] ]\n\
gap> SubdigraphHomeomorphicToK4(CompleteDigraph(3));\nfail\ngap> D := Digraph(\
IsMutableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, \
7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<mutable digraph with 11 verti\
ces, 25 edges>\ngap> SubdigraphHomeomorphicToK4(D);\n[ [ 3, 5, 10 ], [ 9, 8, 1\
0 ], [ 4 ], [ 6 ], [ 7, 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\nga\
p> SubdigraphHomeomorphicToK23(D);\n[ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [ 6 ]\
, [ 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D := Digraph(IsMu\
tableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 11], [4, 7], [6,\
 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<mutable digraph with 11 vertices, 24\
 edges>\ngap> SubdigraphHomeomorphicToK4(D);\nfail\ngap> SubdigraphHomeomorphi\
cToK23(D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], \
\n  [  ], [ 11 ], [  ], [  ] ]\ngap> SubdigraphHomeomorphicToK33(D);\nfail\nga\
p> SubdigraphHomeomorphicToK23(NullDigraph(0));\nfail\ngap> SubdigraphHomeomor\
phicToK33(CompleteDigraph(5));\nfail\ngap> SubdigraphHomeomorphicToK33(Complet\
eBipartiteDigraph(3, 3));\n[ [ 4, 6, 5 ], [ 4, 5, 6 ], [ 6, 5, 4 ], [  ], [  ]\
, [  ] ]\ngap> SubdigraphHomeomorphicToK4(CompleteDigraph(3));\nfail\n", 
                                                                  count := 
                                                                    [ 5, 6, 
                                                                      5, 10 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 5, 6, 5, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 238074, 
                                                          root := ~, 
                                                          start := 235765, 
                                                          stop := 238073 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 5, 6, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 5, 6, 5, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 238091, root := ~, 
                                                  start := 235004, 
                                                  stop := 238090 ) ], 
                                          count := [ 5, 6, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 238105, root := ~, 
                                          start := 234769, stop := 238104 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 5, 6, 5, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 5, 6, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 238119, 
                                  root := ~, start := 225429, stop := 238118 )
                                , 
                              rec( content := "\n\n", 
                                  count := [ 5, 6, 5, 11 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 5, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 238131, root := ~, start := 132079, 
                          stop := 238130 ), 
                      rec( content := "\n ", count := [ 5, 6, 5, 11 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " attributes, operations ", 
                          count := [ 5, 6, 5, 11 ], mathmode := "Text", 
                          name := "XMLCOMMENT", root := ~ ), 
                      rec( content := "\n  ", count := [ 5, 6, 5, 11 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( 
                          attributes := 
                            rec( Label := "Properties of digraphs" ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Properties of digraphs",
                                          count := [ 6, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 6, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 238248, 
                                  root := ~, start := 238207, stop := 238247 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 6, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Edge properties",
                                                  count := [ 6, 1, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 6, 1, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 238295, 
                                          root := ~, start := 238261, 
                                          stop := 238294 ), 
                                      rec( content := "\n    ", 
                                          count := [ 6, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphHasLoops\
" ), content := 0, count := [ 6, 1, 1, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 238359, root := ~, 
                                                  start := 238315, 
                                                  stop := 238358 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 238382, 
                                                          root := ~, 
                                                          start := 238371, 
                                                          stop := 238381 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 238398, 
                                                          root := ~, 
                                                          start := 238386, 
                                                          stop := 238397 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 238409, root := ~, 
                                                  start := 238362, 
                                                  stop := 238408 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns ", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 238449, 
                                                          root := ~, 
                                                          start := 238438, 
                                                          stop := 238448 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 238479, 
                                                          root := ~, 
                                                          start := 238465, 
                                                          stop := 238478 ), 
                                                      rec( 
                                                          content := " has loo\
ps, and\n    ", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 238511, 
                                                          root := ~, 
                                                          start := 238499, 
                                                          stop := 238510 ), 
                                                      rec( 
                                                          content := " if it d\
oes not. A loop is an edge with equal source and range.\n    ", 
                                                          count := 
                                                            [ 6, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 238583, 
                                                          root := ~, 
                                                          start := 238579, 
                                                          stop := 238582 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 238625, 
                                                          root := ~, 
                                                          start := 238611, 
                                                          stop := 238624 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n", count := [ 6, 1, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2], [2]]);\n<immutable digraph with 2 vertices, 3 edge\
s>\ngap> DigraphEdges(D);\n[ [ 1, 1 ], [ 1, 2 ], [ 2, 2 ] ]\ngap> DigraphHasLo\
ops(D);\ntrue\ngap> D := Digraph([[2, 3], [1], [2]]);\n<immutable digraph with\
 3 vertices, 4 edges>\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 3 ], [ 2, 1 ], \
[ 3, 2 ] ]\ngap> DigraphHasLoops(D);\nfalse\ngap> D := CompleteDigraph(IsMutab\
leDigraph, 4);\n<mutable digraph with 4 vertices, 12 edges>\ngap> DigraphHasLo\
ops(D);\nfalse", count := [ 6, 1, 1, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 239220, 
                                                          root := ~, 
                                                          start := 238722, 
                                                          stop := 239219 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 239237, root := ~, 
                                                  start := 238412, 
                                                  stop := 239236 ) ], 
                                          count := [ 6, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 239251, root := ~, 
                                          start := 238300, stop := 239250 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 1, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsAntiSymmetric\
Digraph" ), content := 0, count := [ 6, 1, 2, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 239323, root := ~, 
                                                  start := 239272, 
                                                  stop := 239322 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsAntisymmetric\
Digraph" ), content := 0, count := [ 6, 1, 2, 4 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 239377, root := ~, 
                                                  start := 239326, 
                                                  stop := 239376 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 239400, 
                                                          root := ~, 
                                                          start := 239389, 
                                                          stop := 239399 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 239416, 
                                                          root := ~, 
                                                          start := 239404, 
                                                          stop := 239415 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 239427, root := ~, 
                                                  start := 239380, 
                                                  stop := 239426 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 1, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 239476, 
                                                          root := ~, 
                                                          start := 239465, 
                                                          stop := 239475 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 239506, 
                                                          root := ~, 
                                                          start := 239492, 
                                                          stop := 239505 ), 
                                                      rec( 
                                                          content := "\n    is\
 antisymmetric, and ", count := [ 6, 1, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 239545, 
                                                          root := ~, 
                                                          start := 239533, 
                                                          stop := 239544 ), 
                                                      rec( 
                                                          content := " if it i\
s not.\n    ", count := [ 6, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 239568, 
                                                          root := ~, 
                                                          start := 239564, 
                                                          stop := 239567 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph is ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ntisymmetric", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 239607, 
                                                          root := ~, 
                                                          start := 239587, 
                                                          stop := 239606 ), 
                                                      rec( 
                                                          content := " if when\
ever there is an edge with source\n    ", count := [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 239661, 
                                                          root := ~, 
                                                          start := 239653, 
                                                          stop := 239660 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 239680, 
                                                          root := ~, 
                                                          start := 239672, 
                                                          stop := 239679 ), 
                                                      rec( 
                                                          content := ", and an\
 edge with source ", count := [ 6, 1, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 239714, 
                                                          root := ~, 
                                                          start := 239706, 
                                                          stop := 239713 ), 
                                                      rec( 
                                                          content := " and ran\
ge\n    ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 239737, 
                                                          root := ~, 
                                                          start := 239729, 
                                                          stop := 239736 ), 
                                                      rec( 
                                                          content := ", then t\
he vertices ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 239765, 
                                                          root := ~, 
                                                          start := 239757, 
                                                          stop := 239764 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 239778, 
                                                          root := ~, 
                                                          start := 239770, 
                                                          stop := 239777 ), 
                                                      rec( 
                                                          content := " are equ\
al.\n    ", count := [ 6, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 239798, 
                                                          root := ~, 
                                                          start := 239794, 
                                                          stop := 239797 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 239840, 
                                                          root := ~, 
                                                          start := 239826, 
                                                          stop := 239839 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := Digraph([[2], [1, 3], [2, 3]]);\n<immutable digraph with 3 vertic\
es, 5 edges>\ngap> IsAntisymmetricDigraph(gr1);\nfalse\ngap> DigraphEdges(gr1)\
{[1, 2]};\n[ [ 1, 2 ], [ 2, 1 ] ]\ngap> gr2 := Digraph([[1, 2], [3, 3], [1]]);\
\n<immutable multidigraph with 3 vertices, 5 edges>\ngap> IsAntisymmetricDigra\
ph(gr2);\ntrue\ngap> DigraphEdges(gr2);\n[ [ 1, 1 ], [ 1, 2 ], [ 2, 3 ], [ 2, \
3 ], [ 3, 1 ] ]\n", count := [ 6, 1, 2, 8 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 1, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 240367, 
                                                          root := ~, 
                                                          start := 239941, 
                                                          stop := 240366 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 240384, root := ~, 
                                                  start := 239430, 
                                                  stop := 240383 ) ], 
                                          count := [ 6, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 240398, root := ~, 
                                          start := 239257, stop := 240397 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 2, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsBipartiteDigr\
aph" ), content := 0, count := [ 6, 1, 3, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 240466, root := ~, 
                                                  start := 240419, 
                                                  stop := 240465 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 240489, 
                                                          root := ~, 
                                                          start := 240478, 
                                                          stop := 240488 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 240505, 
                                                          root := ~, 
                                                          start := 240493, 
                                                          stop := 240504 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 240516, root := ~, 
                                                  start := 240469, 
                                                  stop := 240515 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n  This \
property is ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 240563, 
                                                          root := ~, 
                                                          start := 240552, 
                                                          stop := 240562 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 240593, 
                                                          root := ~, 
                                                          start := 240579, 
                                                          stop := 240592 ), 
                                                      rec( 
                                                          content := " is bipa\
rtite, and\n  ", count := [ 6, 1, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 240626, 
                                                          root := ~, 
                                                          start := 240614, 
                                                          stop := 240625 ), 
                                                      rec( 
                                                          content := " if it i\
s not.  A digraph is bipartite if and only if the\n  vertices of ", 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 240712, 
                                                          root := ~, 
                                                          start := 240698, 
                                                          stop := 240711 ), 
                                                      rec( 
                                                          content := " can be \
partitioned into two non-empty sets such\n  that the source and range of any e\
dge of ", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 240818, 
                                                          root := ~, 
                                                          start := 240804, 
                                                          stop := 240817 ), 
                                                      rec( 
                                                          content := " lie in \
distinct sets.\n  Equivalently, a digraph is bipartite if and only if it is 2-\
colorable; see\n  ", count := [ 6, 1, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
GreedyColouring", Label := "for a digraph" ), content := 0, 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 240978, 
                                                          root := ~, 
                                                          start := 240920, 
                                                          stop := 240977 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 6, 1, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 240984, 
                                                          root := ~, 
                                                          start := 240980, 
                                                          stop := 240983 ), 
                                                      rec( 
                                                          content := "\n\n  Se\
e also ", count := [ 6, 1, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Bicomponents" ), content := 0, count := [ 6, 1, 3, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 241030, 
                                                          root := ~, 
                                                          start := 240997, 
                                                          stop := 241029 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 241040, 
                                                          root := ~, 
                                                          start := 241036, 
                                                          stop := 241039 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 241082, 
                                                          root := ~, 
                                                          start := 241068, 
                                                          stop := 241081 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 1, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := ChainDigraph(4);\n<immutable chain digraph with 4 vertices>\ngap> I\
sBipartiteDigraph(D);\ntrue\ngap> D := CycleDigraph(3);\n<immutable cycle digr\
aph with 3 vertices>\ngap> IsBipartiteDigraph(D);\nfalse\ngap> D := CompleteBi\
partiteDigraph(IsMutableDigraph, 5, 4);\n<mutable digraph with 9 vertices, 40 \
edges>\ngap> IsBipartiteDigraph(D);\ntrue", count := [ 6, 1, 3, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 3, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 241555, 
                                                          root := ~, 
                                                          start := 241182, 
                                                          stop := 241554 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 241572, root := ~, 
                                                  start := 240519, 
                                                  stop := 241571 ) ], 
                                          count := [ 6, 1, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 241586, root := ~, 
                                          start := 240404, stop := 241585 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 3, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsCompleteBipar\
titeDigraph" ), content := 0, count := [ 6, 1, 4, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 241662, root := ~, 
                                                  start := 241607, 
                                                  stop := 241661 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 241685, 
                                                          root := ~, 
                                                          start := 241674, 
                                                          stop := 241684 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 241701, 
                                                          root := ~, 
                                                          start := 241689, 
                                                          stop := 241700 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 241712, root := ~, 
                                                  start := 241665, 
                                                  stop := 241711 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns ", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 241752, 
                                                          root := ~, 
                                                          start := 241741, 
                                                          stop := 241751 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 241782, 
                                                          root := ~, 
                                                          start := 241768, 
                                                          stop := 241781 ), 
                                                      rec( 
                                                          content := " is a co\
mplete bipartite\n    digraph, and ", count := [ 6, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 241836, 
                                                          root := ~, 
                                                          start := 241824, 
                                                          stop := 241835 ), 
                                                      rec( 
                                                          content := " if it i\
s not. ", count := [ 6, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 241855, 
                                                          root := ~, 
                                                          start := 241851, 
                                                          stop := 241854 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph is a ", count := [ 6, 1, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omplete bipartite digraph", count := [ 6, 1, 4, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 4, 4 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 241909, 
                                                          root := ~, 
                                                          start := 241876, 
                                                          stop := 241908 ), 
                                                      rec( 
                                                          content := " if it i\
s bipartite, see\n    ", count := [ 6, 1, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBipar\
titeDigraph" ), content := 0, count := [ 6, 1, 4, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 241970, 
                                                          root := ~, 
                                                          start := 241938, 
                                                          stop := 241969 ), 
                                                      rec( 
                                                          content := ", and th\
ere exists a unique edge with\n    source ", count := [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 242027, 
                                                          root := ~, 
                                                          start := 242019, 
                                                          stop := 242026 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 242046, 
                                                          root := ~, 
                                                          start := 242038, 
                                                          stop := 242045 ), 
                                                      rec( 
                                                          content := " if and \
only if ", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 242070, 
                                                          root := ~, 
                                                          start := 242062, 
                                                          stop := 242069 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 242083, 
                                                          root := ~, 
                                                          start := 242075, 
                                                          stop := 242082 ), 
                                                      rec( 
                                                          content := " lie\n  \
  in different bicomponents of ", count := [ 6, 1, 4, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 242135, 
                                                          root := ~, 
                                                          start := 242121, 
                                                          stop := 242134 ), 
                                                      rec( 
                                                          content := ", see ",
                                                          count := 
                                                            [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Bicomponents" ), content := 0, count := [ 6, 1, 4, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 242180, 
                                                          root := ~, 
                                                          start := 242141, 
                                                          stop := 242179 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 6, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 242186, 
                                                          root := ~, 
                                                          start := 242182, 
                                                          stop := 242185 ), 
                                                      rec( 
                                                          content := "\n\n    \
Equivalently, a bipartite digraph with bicomponents of size ", 
                                                          count := 
                                                            [ 6, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 242260, 
                                                          root := ~, 
                                                          start := 242252, 
                                                          stop := 242259 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 242277, 
                                                          root := ~, 
                                                          start := 242269, 
                                                          stop := 242276 ), 
                                                      rec( 
                                                          content := " is comp\
lete precisely when it has ", count := [ 6, 1, 4, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
mn", count := [ 6, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 242322, 
                                                          root := ~, 
                                                          start := 242312, 
                                                          stop := 242321 ), 
                                                      rec( 
                                                          content := " edges, \
none of which\n    are multiple edges. ", count := [ 6, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 242372, 
                                                          root := ~, 
                                                          start := 242368, 
                                                          stop := 242371 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 6, 1, 4, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Complet\
eBipartiteDigraph" ), content := 0, count := [ 6, 1, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 242425, 
                                                          root := ~, 
                                                          start := 242387, 
                                                          stop := 242424 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 242435, 
                                                          root := ~, 
                                                          start := 242431, 
                                                          stop := 242434 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 4, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 4, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 242477, 
                                                          root := ~, 
                                                          start := 242463, 
                                                          stop := 242476 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 1, 4, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(2);\n<immutable cycle digraph with 2 vertices>\ngap> I\
sCompleteBipartiteDigraph(D);\ntrue\ngap> D := CycleDigraph(4);\n<immutable cy\
cle digraph with 4 vertices>\ngap> IsBipartiteDigraph(D);\ntrue\ngap> IsComple\
teBipartiteDigraph(D);\nfalse\ngap> D := CompleteBipartiteDigraph(IsMutableDig\
raph, 5, 4);\n<mutable digraph with 9 vertices, 40 edges>\ngap> IsCompleteBipa\
rtiteDigraph(D);\ntrue", count := [ 6, 1, 4, 8 ], name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 4, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 243008, 
                                                          root := ~, 
                                                          start := 242578, 
                                                          stop := 243007 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 4, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 243025, root := ~, 
                                                  start := 241715, 
                                                  stop := 243024 ) ], 
                                          count := [ 6, 1, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 243039, root := ~, 
                                          start := 241592, stop := 243038 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 4, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsCompleteDigra\
ph" ), content := 0, count := [ 6, 1, 5, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 243106, root := ~, 
                                                  start := 243060, 
                                                  stop := 243105 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 243129, 
                                                          root := ~, 
                                                          start := 243118, 
                                                          stop := 243128 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 243145, 
                                                          root := ~, 
                                                          start := 243133, 
                                                          stop := 243144 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 243156, root := ~, 
                                                  start := 243109, 
                                                  stop := 243155 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns ", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 243196, 
                                                          root := ~, 
                                                          start := 243185, 
                                                          stop := 243195 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 243226, 
                                                          root := ~, 
                                                          start := 243212, 
                                                          stop := 243225 ), 
                                                      rec( 
                                                          content := " is comp\
lete, and\n    ", count := [ 6, 1, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 243260, 
                                                          root := ~, 
                                                          start := 243248, 
                                                          stop := 243259 ), 
                                                      rec( 
                                                          content := " if it i\
s not. ", count := [ 6, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 243279, 
                                                          root := ~, 
                                                          start := 243275, 
                                                          stop := 243278 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph is ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omplete", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 243313, 
                                                          root := ~, 
                                                          start := 243298, 
                                                          stop := 243312 ), 
                                                      rec( 
                                                          content := " if it h\
as no loops, and for all\n    ", count := [ 6, 1, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
istinct", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 243365, 
                                                          root := ~, 
                                                          start := 243350, 
                                                          stop := 243364 ), 
                                                      rec( 
                                                          content := " vertice\
s ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 243383, 
                                                          root := ~, 
                                                          start := 243375, 
                                                          stop := 243382 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 243396, 
                                                          root := ~, 
                                                          start := 243388, 
                                                          stop := 243395 ), 
                                                      rec( 
                                                          content := ",\n    t\
here is exactly one edge with source ", count := [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 243448, 
                                                          root := ~, 
                                                          start := 243440, 
                                                          stop := 243447 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 243467, 
                                                          root := ~, 
                                                          start := 243459, 
                                                          stop := 243466 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 Equivalently, a digraph with ", count := [ 6, 1, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 243511, 
                                                          root := ~, 
                                                          start := 243503, 
                                                          stop := 243510 ), 
                                                      rec( 
                                                          content := " vertice\
s is complete precisely when\n    it has ", count := [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
(n - 1)", count := [ 6, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 243574, 
                                                          root := ~, 
                                                          start := 243559, 
                                                          stop := 243573 ), 
                                                      rec( 
                                                          content := " edges, \
no loops, and no multiple edges.\n    ", count := [ 6, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 243623, 
                                                          root := ~, 
                                                          start := 243619, 
                                                          stop := 243622 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 243665, 
                                                          root := ~, 
                                                          start := 243651, 
                                                          stop := 243664 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 1, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 3], [1, 3], [1, 2]]);\n<immutable digraph with 3 verti\
ces, 6 edges>\ngap> IsCompleteDigraph(D);\ntrue\ngap> D := Digraph([[2, 2], [1\
]]);\n<immutable multidigraph with 2 vertices, 3 edges>\ngap> IsCompleteDigrap\
h(D);\nfalse\ngap> D := CompleteBipartiteDigraph(IsMutableDigraph, 5, 4);\n<mu\
table digraph with 9 vertices, 40 edges>\ngap> IsCompleteDigraph(D);\nfalse", 
                                                                  count := 
                                                                    [ 6, 1, 
                                                                      5, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 5, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 244173, 
                                                          root := ~, 
                                                          start := 243766, 
                                                          stop := 244172 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 244190, root := ~, 
                                                  start := 243159, 
                                                  stop := 244189 ) ], 
                                          count := [ 6, 1, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 244204, root := ~, 
                                          start := 243045, stop := 244203 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 5, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsCompleteMulti\
partiteDigraph" ), content := 0, count := [ 6, 1, 6, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 244283, root := ~, 
                                                  start := 244225, 
                                                  stop := 244282 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 244306, 
                                                          root := ~, 
                                                          start := 244295, 
                                                          stop := 244305 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 244322, 
                                                          root := ~, 
                                                          start := 244310, 
                                                          stop := 244321 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 244333, root := ~, 
                                                  start := 244286, 
                                                  stop := 244332 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property returns ", count := [ 6, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 244387, 
                                                          root := ~, 
                                                          start := 244376, 
                                                          stop := 244386 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 6, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 244405, 
                                                          root := ~, 
                                                          start := 244391, 
                                                          stop := 244404 ), 
                                                      rec( 
                                                          content := " is a co\
mplete\n    multipartite digraph, and ", count := [ 6, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 244462, 
                                                          root := ~, 
                                                          start := 244450, 
                                                          stop := 244461 ), 
                                                      rec( 
                                                          content := " if not.\
 ", count := [ 6, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 244475, 
                                                          root := ~, 
                                                          start := 244471, 
                                                          stop := 244474 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph is a ", count := [ 6, 1, 6, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
omplete multipartite digraph", count := [ 6, 1, 6, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 6, 4 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 244532, 
                                                          root := ~, 
                                                          start := 244496, 
                                                          stop := 244531 ), 
                                                      rec( 
                                                          content := " if and \
only if\n    its vertices can be partitioned into at least two maximal indepen\
dent sets,\n    where every possible edge between these independent sets occur\
s in the\n    digraph exactly once.\n    ", count := [ 6, 1, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 244737, 
                                                          root := ~, 
                                                          start := 244733, 
                                                          stop := 244736 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 6, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 244779, 
                                                          root := ~, 
                                                          start := 244765, 
                                                          stop := 244778 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 1, 6, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteMultipartiteDigraph([2, 4, 6]);\n<immutable complete multip\
artite digraph with 12 vertices, 88 edges>\ngap> IsCompleteMultipartiteDigraph\
(D);\ntrue\ngap> D := CompleteBipartiteDigraph(IsMutableDigraph, 5, 4);\n<muta\
ble digraph with 9 vertices, 40 edges>\ngap> IsCompleteMultipartiteDigraph(D);\
\ntrue", count := [ 6, 1, 6, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 1, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 245222, 
                                                          root := ~, 
                                                          start := 244880, 
                                                          stop := 245221 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 245239, root := ~, 
                                                  start := 244336, 
                                                  stop := 245238 ) ], 
                                          count := [ 6, 1, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 245253, root := ~, 
                                          start := 244210, stop := 245252 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 6, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsEmptyDigraph"\
 ), content := 0, count := [ 6, 1, 7, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 245317, root := ~, 
                                                  start := 245274, 
                                                  stop := 245316 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsNullDigraph" 
                                                     ), content := 0, 
                                                  count := [ 6, 1, 7, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 245362, root := ~, 
                                                  start := 245320, 
                                                  stop := 245361 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 245385, 
                                                          root := ~, 
                                                          start := 245374, 
                                                          stop := 245384 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 245401, 
                                                          root := ~, 
                                                          start := 245389, 
                                                          stop := 245400 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 7, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 245412, root := ~, 
                                                  start := 245365, 
                                                  stop := 245411 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns ", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 245452, 
                                                          root := ~, 
                                                          start := 245441, 
                                                          stop := 245451 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 245482, 
                                                          root := ~, 
                                                          start := 245468, 
                                                          stop := 245481 ), 
                                                      rec( 
                                                          content := " is empt\
y, and\n    ", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 245513, 
                                                          root := ~, 
                                                          start := 245501, 
                                                          stop := 245512 ), 
                                                      rec( 
                                                          content := " if it i\
s not. A digraph is ", count := [ 6, 1, 7, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
mpty", count := [ 6, 1, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 245553, 
                                                          root := ~, 
                                                          start := 245541, 
                                                          stop := 245552 ), 
                                                      rec( 
                                                          content := " if it h\
as no\n    edges.", count := [ 6, 1, 7, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 245581, 
                                                          root := ~, 
                                                          start := 245577, 
                                                          stop := 245580 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sNullDigraph", count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 245607, 
                                                          root := ~, 
                                                          start := 245587, 
                                                          stop := 245606 ), 
                                                      rec( 
                                                          content := " is a sy\
nonym for ", count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sEmptyDigraph", count := [ 6, 1, 7, 6 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 245646, 
                                                          root := ~, 
                                                          start := 245625, 
                                                          stop := 245645 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 245656, 
                                                          root := ~, 
                                                          start := 245652, 
                                                          stop := 245655 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 7, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 7, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 245698, 
                                                          root := ~, 
                                                          start := 245684, 
                                                          stop := 245697 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 1, 7, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[], []]);\n<immutable empty digraph with 2 vertices>\ngap>\
 IsEmptyDigraph(D);\ntrue\ngap> IsNullDigraph(D);\ntrue\ngap> D := Digraph([[]\
, [1]]);\n<immutable digraph with 2 vertices, 1 edge>\ngap> IsEmptyDigraph(D);\
\nfalse\ngap> IsNullDigraph(D);\nfalse", count := [ 6, 1, 7, 8 ], name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 7, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 246091, 
                                                          root := ~, 
                                                          start := 245799, 
                                                          stop := 246090 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 7, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 7, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 246108, root := ~, 
                                                  start := 245415, 
                                                  stop := 246107 ) ], 
                                          count := [ 6, 1, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 246122, root := ~, 
                                          start := 245259, stop := 246121 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 7, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsEquivalenceDi\
graph" ), content := 0, count := [ 6, 1, 8, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 246192, root := ~, 
                                                  start := 246143, 
                                                  stop := 246191 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 246215, 
                                                          root := ~, 
                                                          start := 246204, 
                                                          stop := 246214 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 246231, 
                                                          root := ~, 
                                                          start := 246219, 
                                                          stop := 246230 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 246242, root := ~, 
                                                  start := 246195, 
                                                  stop := 246241 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A d\
igraph is an equivalence digraph if and only if the digraph satisifies\n    al\
l of ", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsRefle\
xiveDigraph" ), content := 0, count := [ 6, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 246380, 
                                                          root := ~, 
                                                          start := 246348, 
                                                          stop := 246379 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsSymme\
tricDigraph" ), content := 0, count := [ 6, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 246418, 
                                                          root := ~, 
                                                          start := 246386, 
                                                          stop := 246417 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsTrans\
itiveDigraph" ), content := 0, count := [ 6, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 246456, 
                                                          root := ~, 
                                                          start := 246423, 
                                                          stop := 246455 ), 
                                                      rec( 
                                                          content := ".\n    A\
 partial order ", count := [ 6, 1, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 246492, 
                                                          root := ~, 
                                                          start := 246478, 
                                                          stop := 246491 ), 
                                                      rec( 
                                                          content := " corresp\
onds to an equivalence relation.\n    ", count := [ 6, 1, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 246541, 
                                                          root := ~, 
                                                          start := 246537, 
                                                          stop := 246540 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 8, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 246583, 
                                                          root := ~, 
                                                          start := 246569, 
                                                          stop := 246582 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n", count := [ 6, 1, 8, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 3], [2], [1, 3]]);\n<immutable digraph with 3 vertices\
, 5 edges>\ngap> IsEquivalenceDigraph(D);\ntrue\n", count := [ 6, 1, 8, 5 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 8, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 246834, 
                                                          root := ~, 
                                                          start := 246680, 
                                                          stop := 246833 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 246851, root := ~, 
                                                  start := 246245, 
                                                  stop := 246850 ) ], 
                                          count := [ 6, 1, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 246865, root := ~, 
                                          start := 246128, stop := 246864 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 8, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsFunctionalDig\
raph" ), content := 0, count := [ 6, 1, 9, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 246934, root := ~, 
                                                  start := 246886, 
                                                  stop := 246933 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 246957, 
                                                          root := ~, 
                                                          start := 246946, 
                                                          stop := 246956 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 246973, 
                                                          root := ~, 
                                                          start := 246961, 
                                                          stop := 246972 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 246984, root := ~, 
                                                  start := 246937, 
                                                  stop := 246983 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 1, 9, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 247033, 
                                                          root := ~, 
                                                          start := 247022, 
                                                          stop := 247032 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 247063, 
                                                          root := ~, 
                                                          start := 247049, 
                                                          stop := 247062 ), 
                                                      rec( 
                                                          content := " is\n   \
 functional. ", count := [ 6, 1, 9, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 247087, 
                                                          root := ~, 
                                                          start := 247083, 
                                                          stop := 247086 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph is ", count := [ 6, 1, 9, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
unctional", count := [ 6, 1, 9, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 247123, 
                                                          root := ~, 
                                                          start := 247106, 
                                                          stop := 247122 ), 
                                                      rec( 
                                                          content := " if ever\
y vertex is the source of a\n    unique edge.\n    ", count := [ 6, 1, 9, 4 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 247184, 
                                                          root := ~, 
                                                          start := 247180, 
                                                          stop := 247183 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 9, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 247226, 
                                                          root := ~, 
                                                          start := 247212, 
                                                          stop := 247225 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 1, 9, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := Digraph([[3], [2], [2], [1], [6], [5]]);\n<immutable digraph with\
 6 vertices, 6 edges>\ngap> IsFunctionalDigraph(gr1);\ntrue\ngap> gr2 := Digra\
ph([[1, 2], [1]]);\n<immutable digraph with 2 vertices, 3 edges>\ngap> IsFunct\
ionalDigraph(gr2);\nfalse\ngap> gr3 := Digraph(3, [1, 2, 3], [2, 3, 1]);\n<imm\
utable digraph with 3 vertices, 3 edges>\ngap> IsFunctionalDigraph(gr3);\ntrue\
\n", count := [ 6, 1, 9, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 1, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 247737, 
                                                          root := ~, 
                                                          start := 247326, 
                                                          stop := 247736 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 247754, root := ~, 
                                                  start := 246987, 
                                                  stop := 247753 ) ], 
                                          count := [ 6, 1, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 247768, root := ~, 
                                          start := 246871, stop := 247767 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 9, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsMultiDigraph"\
 ), content := 0, count := [ 6, 1, 10, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 247832, root := ~, 
                                                  start := 247789, 
                                                  stop := 247831 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 247855, 
                                                          root := ~, 
                                                          start := 247844, 
                                                          stop := 247854 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 247871, 
                                                          root := ~, 
                                                          start := 247859, 
                                                          stop := 247870 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 247882, root := ~, 
                                                  start := 247835, 
                                                  stop := 247881 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
ultidigraph", count := [ 6, 1, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 247924, 
                                                          root := ~, 
                                                          start := 247905, 
                                                          stop := 247923 ), 
                                                      rec( 
                                                          content := " is one \
that has at least two\n    edges with equal source and range.", 
                                                          count := 
                                                            [ 6, 1, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 247996, 
                                                          root := ~, 
                                                          start := 247992, 
                                                          stop := 247995 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the argument ", count := [ 6, 1, 10, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 10, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 248032, 
                                                          root := ~, 
                                                          start := 248018, 
                                                          stop := 248031 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 1, 10, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\"a\", \"b\", \"c\"], [\"a\", \"b\", \"b\"], [\"b\", \"c\"\
, \"a\"]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> IsMultiDigraph(\
D);\nfalse\ngap> D := DigraphFromDigraph6String(\"&Bug\");\n<immutable digraph\
 with 3 vertices, 6 edges>\ngap> IsDuplicateFree(DigraphEdges(D));\ntrue\ngap>\
 IsMultiDigraph(D);\nfalse\ngap> D := Digraph([[1, 2, 3, 2], [2, 1], [3]]);\n<\
immutable multidigraph with 3 vertices, 7 edges>\ngap> IsDuplicateFree(Digraph\
Edges(D));\nfalse\ngap> IsMultiDigraph(D);\ntrue\ngap> D := DigraphMutableCopy\
(D); \n<mutable multidigraph with 3 vertices, 7 edges>\ngap> IsMultiDigraph(D)\
;\ntrue", count := [ 6, 1, 10, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 1, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 248756, 
                                                          root := ~, 
                                                          start := 248133, 
                                                          stop := 248755 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 248773, root := ~, 
                                                  start := 247885, 
                                                  stop := 248772 ) ], 
                                          count := [ 6, 1, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 248787, root := ~, 
                                          start := 247774, stop := 248786 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 10, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsReflexiveDigr\
aph" ), content := 0, count := [ 6, 1, 11, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 248855, root := ~, 
                                                  start := 248808, 
                                                  stop := 248854 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 248878, 
                                                          root := ~, 
                                                          start := 248867, 
                                                          stop := 248877 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 248894, 
                                                          root := ~, 
                                                          start := 248882, 
                                                          stop := 248893 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 248905, root := ~, 
                                                  start := 248858, 
                                                  stop := 248904 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 1, 11, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 248954, 
                                                          root := ~, 
                                                          start := 248943, 
                                                          stop := 248953 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 248984, 
                                                          root := ~, 
                                                          start := 248970, 
                                                          stop := 248983 ), 
                                                      rec( 
                                                          content := " is\n   \
 reflexive, and ", count := [ 6, 1, 11, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 249019, 
                                                          root := ~, 
                                                          start := 249007, 
                                                          stop := 249018 ), 
                                                      rec( 
                                                          content := " if it i\
s not.\n    A digraph is ", count := [ 6, 1, 11, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
eflexive", count := [ 6, 1, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 249067, 
                                                          root := ~, 
                                                          start := 249051, 
                                                          stop := 249066 ), 
                                                      rec( 
                                                          content := " if it h\
as a loop at every vertex. ", count := [ 6, 1, 11, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 249106, 
                                                          root := ~, 
                                                          start := 249102, 
                                                          stop := 249105 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 6, 1, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 249115, 
                                                          root := ~, 
                                                          start := 249111, 
                                                          stop := 249114 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 249157, 
                                                          root := ~, 
                                                          start := 249143, 
                                                          stop := 249156 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 1, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2], [2]]);\n<immutable digraph with 2 vertices, 3 edge\
s>\ngap> IsReflexiveDigraph(D);\ntrue\ngap> D := Digraph([[3, 1], [4, 2], [3],\
 [2, 1]]);\n<immutable digraph with 4 vertices, 7 edges>\ngap> IsReflexiveDigr\
aph(D);\nfalse\n", count := [ 6, 1, 11, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 1, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 249530, 
                                                          root := ~, 
                                                          start := 249257, 
                                                          stop := 249529 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 249547, root := ~, 
                                                  start := 248908, 
                                                  stop := 249546 ) ], 
                                          count := [ 6, 1, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 249561, root := ~, 
                                          start := 248793, stop := 249560 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 11, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsSymmetricDigr\
aph" ), content := 0, count := [ 6, 1, 12, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 249629, root := ~, 
                                                  start := 249582, 
                                                  stop := 249628 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 249652, 
                                                          root := ~, 
                                                          start := 249641, 
                                                          stop := 249651 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 249668, 
                                                          root := ~, 
                                                          start := 249656, 
                                                          stop := 249667 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 249679, root := ~, 
                                                  start := 249632, 
                                                  stop := 249678 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 1, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 249728, 
                                                          root := ~, 
                                                          start := 249717, 
                                                          stop := 249727 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 249758, 
                                                          root := ~, 
                                                          start := 249744, 
                                                          stop := 249757 ), 
                                                      rec( 
                                                          content := "\n    is\
 symmetric, and ", count := [ 6, 1, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 249793, 
                                                          root := ~, 
                                                          start := 249781, 
                                                          stop := 249792 ), 
                                                      rec( 
                                                          content := " if it i\
s not.", count := [ 6, 1, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 249811, 
                                                          root := ~, 
                                                          start := 249807, 
                                                          stop := 249810 ), 
                                                      rec( 
                                                          content := "\n\n    \
A ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ymmetric digraph", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 6, 1, 12, 4 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 249843, 
                                                          root := ~, 
                                                          start := 249819, 
                                                          stop := 249842 ), 
                                                      rec( 
                                                          content := " is one \
where for each non-loop edge, having\n    source ", count := [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 249907, 
                                                          root := ~, 
                                                          start := 249899, 
                                                          stop := 249906 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 249926, 
                                                          root := ~, 
                                                          start := 249918, 
                                                          stop := 249925 ), 
                                                      rec( 
                                                          content := ", there \
is a corresponding edge with\n    source ", count := [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 249982, 
                                                          root := ~, 
                                                          start := 249974, 
                                                          stop := 249981 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 250001, 
                                                          root := ~, 
                                                          start := 249993, 
                                                          stop := 250000 ), 
                                                      rec( 
                                                          content := ".  If th\
ere are ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 250025, 
                                                          root := ~, 
                                                          start := 250017, 
                                                          stop := 250024 ), 
                                                      rec( 
                                                          content := " edges w\
ith\n    source ", count := [ 6, 1, 12, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 250056, 
                                                          root := ~, 
                                                          start := 250048, 
                                                          stop := 250055 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 250075, 
                                                          root := ~, 
                                                          start := 250067, 
                                                          stop := 250074 ), 
                                                      rec( 
                                                          content := ", then t\
here must be precisely ", count := [ 6, 1, 12, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 250114, 
                                                          root := ~, 
                                                          start := 250106, 
                                                          stop := 250113 ), 
                                                      rec( 
                                                          content := "\n    ed\
ges with source ", count := [ 6, 1, 12, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 250145, 
                                                          root := ~, 
                                                          start := 250137, 
                                                          stop := 250144 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 1, 12, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 250164, 
                                                          root := ~, 
                                                          start := 250156, 
                                                          stop := 250163 ), 
                                                      rec( 
                                                          content := ".  In ot\
her words, a symmetric\n    digraph has a symmetric adjacency matrix ", 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Adjacen\
cyMatrix" ), content := 0, count := [ 6, 1, 12, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 250269, 
                                                          root := ~, 
                                                          start := 250240, 
                                                          stop := 250268 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 250279, 
                                                          root := ~, 
                                                          start := 250275, 
                                                          stop := 250278 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 12, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 12, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 250321, 
                                                          root := ~, 
                                                          start := 250307, 
                                                          stop := 250320 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 1, 12, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := Digraph([[2], [1, 3], [2, 3]]);\n<immutable digraph with 3 vertic\
es, 5 edges>\ngap> IsSymmetricDigraph(gr1);\ntrue\ngap> adj1 := AdjacencyMatri\
x(gr1);;\ngap> Display(adj1);\n[ [  0,  1,  0 ],\n  [  1,  0,  1 ],\n  [  0,  \
1,  1 ] ]\ngap> adj1 = TransposedMat(adj1);\ntrue\ngap> gr1 = DigraphReverse(g\
r1);\ntrue\ngap> gr2 := Digraph([[2, 3], [1, 3], [2, 3]]);\n<immutable digraph\
 with 3 vertices, 6 edges>\ngap> IsSymmetricDigraph(gr2);\nfalse\ngap> adj2 :=\
 AdjacencyMatrix(gr2);;\ngap> Display(adj2);\n[ [  0,  1,  1 ],\n  [  1,  0,  \
1 ],\n  [  0,  1,  1 ] ]\ngap> adj2 = TransposedMat(adj2);\nfalse\n", 
                                                                  count := 
                                                                    [ 6, 1, 
                                                                      12, 6 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 12, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 251041, 
                                                          root := ~, 
                                                          start := 250421, 
                                                          stop := 251040 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 251058, root := ~, 
                                                  start := 249682, 
                                                  stop := 251057 ) ], 
                                          count := [ 6, 1, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 251072, root := ~, 
                                          start := 249567, stop := 251071 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 12, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsTournament" )
                                                    , content := 0, 
                                                  count := [ 6, 1, 13, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 251134, root := ~, 
                                                  start := 251093, 
                                                  stop := 251133 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 251157, 
                                                          root := ~, 
                                                          start := 251146, 
                                                          stop := 251156 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 251173, 
                                                          root := ~, 
                                                          start := 251161, 
                                                          stop := 251172 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 13, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 251184, root := ~, 
                                                  start := 251137, 
                                                  stop := 251183 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 1, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 251233, 
                                                          root := ~, 
                                                          start := 251222, 
                                                          stop := 251232 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 251263, 
                                                          root := ~, 
                                                          start := 251249, 
                                                          stop := 251262 ), 
                                                      rec( 
                                                          content := " is a to\
urnament,\n    and ", count := [ 6, 1, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 251301, 
                                                          root := ~, 
                                                          start := 251289, 
                                                          stop := 251300 ), 
                                                      rec( 
                                                          content := " if it i\
s not. ", count := [ 6, 1, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 251320, 
                                                          root := ~, 
                                                          start := 251316, 
                                                          stop := 251319 ), 
                                                      rec( 
                                                          content := "\n\n    \
A tournament is an orientation of a complete (undirected) graph.\n    Specific\
ally, a tournament is a digraph which has a unique directed edge\n    (of some\
 orientation) between any pair of distinct vertices, and no loops.\n    ", 
                                                          count := 
                                                            [ 6, 1, 13, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 251555, 
                                                          root := ~, 
                                                          start := 251551, 
                                                          stop := 251554 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 251597, 
                                                          root := ~, 
                                                          start := 251583, 
                                                          stop := 251596 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 1, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 3, 4], [3, 4], [4], []]);\n<immutable digraph with 4 v\
ertices, 6 edges>\ngap> IsTournament(D);\ntrue\ngap> D := Digraph([[2], [1], [\
3]]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> IsTournament(D);\nfa\
lse\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 ver\
tices, 3 edges>\ngap> IsTournament(D);\ntrue\ngap> DigraphRemoveEdge(D, 1, 2);\
\n<mutable digraph with 3 vertices, 2 edges>\ngap> IsTournament(D);\nfalse\n",
                                                                  count := 
                                                                    [ 6, 1, 
                                                                      13, 6 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 13, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 252178, 
                                                          root := ~, 
                                                          start := 251697, 
                                                          stop := 252177 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 13, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 13, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 252195, root := ~, 
                                                  start := 251187, 
                                                  stop := 252194 ) ], 
                                          count := [ 6, 1, 13, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 252209, root := ~, 
                                          start := 251078, stop := 252208 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 13, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsTransitiveDig\
raph" ), content := 0, count := [ 6, 1, 14, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 252278, root := ~, 
                                                  start := 252230, 
                                                  stop := 252277 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 252301, 
                                                          root := ~, 
                                                          start := 252290, 
                                                          stop := 252300 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 252317, 
                                                          root := ~, 
                                                          start := 252305, 
                                                          stop := 252316 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 252328, root := ~, 
                                                  start := 252281, 
                                                  stop := 252327 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 1, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 252377, 
                                                          root := ~, 
                                                          start := 252366, 
                                                          stop := 252376 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 252407, 
                                                          root := ~, 
                                                          start := 252393, 
                                                          stop := 252406 ), 
                                                      rec( 
                                                          content := "\n    is\
 transitive, and ", count := [ 6, 1, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 252443, 
                                                          root := ~, 
                                                          start := 252431, 
                                                          stop := 252442 ), 
                                                      rec( 
                                                          content := " if it i\
s not.\n\n    A digraph is ", count := [ 6, 1, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
ransitive", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 252493, 
                                                          root := ~, 
                                                          start := 252476, 
                                                          stop := 252492 ), 
                                                      rec( 
                                                          content := " if when\
ever ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
 i, j ]", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 252521, 
                                                          root := ~, 
                                                          start := 252506, 
                                                          stop := 252520 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
 j, k ]", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 252545, 
                                                          root := ~, 
                                                          start := 252530, 
                                                          stop := 252544 ), 
                                                      rec( 
                                                          content := " are edg\
es of the digraph, then ", count := [ 6, 1, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
 i, k ]", count := [ 6, 1, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 252592, 
                                                          root := ~, 
                                                          start := 252577, 
                                                          stop := 252591 ), 
                                                      rec( 
                                                          content := " is also\
 an\n    edge of the digraph. ", count := [ 6, 1, 14, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 252633, 
                                                          root := ~, 
                                                          start := 252629, 
                                                          stop := 252632 ), 
                                                      rec( 
                                                          content := "\n\n    \
Let ", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 252651, 
                                                          root := ~, 
                                                          start := 252643, 
                                                          stop := 252650 ), 
                                                      rec( 
                                                          content := " be the \
number of vertices of an arbitrary digraph, and let\n        ", 
                                                          count := 
                                                            [ 6, 1, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 1, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 252727, 
                                                          root := ~, 
                                                          start := 252719, 
                                                          stop := 252726 ), 
                                                      rec( 
                                                          content := " be the \
number of edges.\n    For general digraphs, the methods used for this property\
 use a version\n    of the Floyd-Warshall algorithm, and have complexity ", 
                                                          count := 
                                                            [ 6, 1, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(n^3)", count := [ 6, 1, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 252897, 
                                                          root := ~, 
                                                          start := 252884, 
                                                          stop := 252896 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 However for digraphs which are topologically sortable\n    [", 
                                                          count := 
                                                            [ 6, 1, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
TopologicalSort" ), content := 0, count := [ 6, 1, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 252999, 
                                                          root := ~, 
                                                          start := 252963, 
                                                          stop := 252998 ), 
                                                      rec( 
                                                          content := "], then \
methods with\n    complexity ", count := [ 6, 1, 14, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m + n + m \\cdot n)", count := [ 6, 1, 14, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 14, 4 ], mathmode := "Text", 
                                                          name := "M", 
                                                          next := 253062, 
                                                          root := ~, 
                                                          start := 253035, 
                                                          stop := 253061 ), 
                                                      rec( 
                                                          content := " will be\
 used when appropriate.\n    ", count := [ 6, 1, 14, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 253102, 
                                                          root := ~, 
                                                          start := 253098, 
                                                          stop := 253101 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 14, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 253144, 
                                                          root := ~, 
                                                          start := 253130, 
                                                          stop := 253143 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 1, 14, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 253248, 
                                                          root := ~, 
                                                          start := 253244, 
                                                          stop := 253247 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 6, 1, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 2], [3], [3]]);\n<immutable digraph with 3 vertices, 4\
 edges>\ngap> IsTransitiveDigraph(D);\nfalse\ngap> gr2 := Digraph([[1, 2, 3], \
[3], [3]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> IsTransitiveDi\
graph(gr2);\ntrue\ngap> gr2 = DigraphTransitiveClosure(D);\ntrue\ngap> gr3 := \
Digraph([[1, 2, 2, 3], [3, 3], [3]]);\n<immutable multidigraph with 3 vertices\
, 7 edges>\ngap> IsTransitiveDigraph(gr3);\ntrue\n", count := [ 6, 1, 14, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 14, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 253710, 
                                                          root := ~, 
                                                          start := 253253, 
                                                          stop := 253709 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 14, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 253727, root := ~, 
                                                  start := 252331, 
                                                  stop := 253726 ) ], 
                                          count := [ 6, 1, 14, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 253741, root := ~, 
                                          start := 252215, stop := 253740 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 14, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsPreorderDigra\
ph" ), content := 0, count := [ 6, 1, 15, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 253808, root := ~, 
                                                  start := 253762, 
                                                  stop := 253807 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsQuasiorderDig\
raph" ), content := 0, count := [ 6, 1, 15, 4 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 253859, root := ~, 
                                                  start := 253811, 
                                                  stop := 253858 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 253882, 
                                                          root := ~, 
                                                          start := 253871, 
                                                          stop := 253881 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 253898, 
                                                          root := ~, 
                                                          start := 253886, 
                                                          stop := 253897 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 15, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 253909, root := ~, 
                                                  start := 253862, 
                                                  stop := 253908 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A d\
igraph is a preorder digraph if and only if the digraph satisifies both\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsRefle\
xiveDigraph" ), content := 0, count := [ 6, 1, 15, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 254041, 
                                                          root := ~, 
                                                          start := 254009, 
                                                          stop := 254040 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsTrans\
itiveDigraph" ), content := 0, count := [ 6, 1, 15, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 254079, 
                                                          root := ~, 
                                                          start := 254046, 
                                                          stop := 254078 ), 
                                                      rec( 
                                                          content := ".\n    A\
 preorder digraph (or quasiorder digraph) ", count := [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 254142, 
                                                          root := ~, 
                                                          start := 254128, 
                                                          stop := 254141 ), 
                                                      rec( 
                                                          content := " corresp\
onds to\n    the preorder relation ", count := [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\leq", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 254195, 
                                                          root := ~, 
                                                          start := 254184, 
                                                          stop := 254194 ), 
                                                      rec( 
                                                          content := " defined\
 by ", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
 \\leq y", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 254222, 
                                                          root := ~, 
                                                          start := 254207, 
                                                          stop := 254221 ), 
                                                      rec( 
                                                          content := " if and \
only\n    if ", count := [ 6, 1, 15, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
x, y]", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 254255, 
                                                          root := ~, 
                                                          start := 254242, 
                                                          stop := 254254 ), 
                                                      rec( 
                                                          content := " is an e\
dge of ", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 15, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 254284, 
                                                          root := ~, 
                                                          start := 254270, 
                                                          stop := 254283 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 15, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 254294, 
                                                          root := ~, 
                                                          start := 254290, 
                                                          stop := 254293 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 15, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 15, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 254336, 
                                                          root := ~, 
                                                          start := 254322, 
                                                          stop := 254335 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n", count := [ 6, 1, 15, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1], [2, 3], [2, 3]]);\n<immutable digraph with 3 vertices\
, 5 edges>\ngap> IsPreorderDigraph(D);\ntrue\ngap> D := Digraph([[1 .. 4], [1 \
.. 4], [1 .. 4], [1 .. 4]]);\n<immutable digraph with 4 vertices, 16 edges>\ng\
ap> IsPreorderDigraph(D);\ntrue\ngap> D := Digraph([[2], [3], [4], [5], [1]]);\
\n<immutable digraph with 5 vertices, 5 edges>\ngap> IsPreorderDigraph(D);\nfa\
lse\ngap> D := Digraph([[1], [1, 2], [2, 3]]);\n<immutable digraph with 3 vert\
ices, 5 edges>\ngap> IsQuasiorderDigraph(D);\nfalse\n", count := [ 6, 1, 15, 
                                                                      7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 15, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 254969, 
                                                          root := ~, 
                                                          start := 254433, 
                                                          stop := 254968 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 15, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 254986, root := ~, 
                                                  start := 253912, 
                                                  stop := 254985 ) ], 
                                          count := [ 6, 1, 15, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 255000, root := ~, 
                                          start := 253747, stop := 254999 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 15, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsPartialOrderD\
igraph" ), content := 0, count := [ 6, 1, 16, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 255071, root := ~, 
                                                  start := 255021, 
                                                  stop := 255070 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 255094, 
                                                          root := ~, 
                                                          start := 255083, 
                                                          stop := 255093 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 255110, 
                                                          root := ~, 
                                                          start := 255098, 
                                                          stop := 255109 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 16, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 255121, root := ~, 
                                                  start := 255074, 
                                                  stop := 255120 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A d\
igraph is a partial order digraph if and only if the digraph satisifies\n    a\
ll of ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsRefle\
xiveDigraph" ), content := 0, count := [ 6, 1, 16, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 255260, 
                                                          root := ~, 
                                                          start := 255228, 
                                                          stop := 255259 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsAntis\
ymmetricDigraph" ), content := 0, count := [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 255302, 
                                                          root := ~, 
                                                          start := 255266, 
                                                          stop := 255301 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsTrans\
itiveDigraph" ), content := 0, count := [ 6, 1, 16, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 255340, 
                                                          root := ~, 
                                                          start := 255307, 
                                                          stop := 255339 ), 
                                                      rec( 
                                                          content := ".\n    A\
 partial order ", count := [ 6, 1, 16, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 255376, 
                                                          root := ~, 
                                                          start := 255362, 
                                                          stop := 255375 ), 
                                                      rec( 
                                                          content := " corresp\
onds\n    to the partial order relation ", count := [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\leq", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 255434, 
                                                          root := ~, 
                                                          start := 255423, 
                                                          stop := 255433 ), 
                                                      rec( 
                                                          content := " defined\
 by ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
 \\leq y", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 255461, 
                                                          root := ~, 
                                                          start := 255446, 
                                                          stop := 255460 ), 
                                                      rec( 
                                                          content := " if and\\
n    only if ", count := [ 6, 1, 16, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
x, y]", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 255494, 
                                                          root := ~, 
                                                          start := 255481, 
                                                          stop := 255493 ), 
                                                      rec( 
                                                          content := " is an e\
dge of ", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 255523, 
                                                          root := ~, 
                                                          start := 255509, 
                                                          stop := 255522 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 1, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 16, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 255533, 
                                                          root := ~, 
                                                          start := 255529, 
                                                          stop := 255532 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 16, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 16, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 16, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 255575, 
                                                          root := ~, 
                                                          start := 255561, 
                                                          stop := 255574 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n", count := [ 6, 1, 16, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 3], [2, 3], [3]]);\n<immutable digraph with 3 vertices\
, 5 edges>\ngap> IsPartialOrderDigraph(D);\ntrue\ngap> D := CycleDigraph(5);\n\
<immutable cycle digraph with 5 vertices>\ngap> IsPartialOrderDigraph(D);\nfal\
se\ngap> D := Digraph([[1, 1], [1, 1, 2], [3], [3, 3, 4, 4]]);\n<immutable mul\
tidigraph with 4 vertices, 10 edges>\ngap> IsPartialOrderDigraph(D);\ntrue\n",
                                                                  count := 
                                                                    [ 6, 1, 
                                                                      16, 5 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 16, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 256079, 
                                                          root := ~, 
                                                          start := 255672, 
                                                          stop := 256078 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 16, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 256096, root := ~, 
                                                  start := 255124, 
                                                  stop := 256095 ) ], 
                                          count := [ 6, 1, 16, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 256110, root := ~, 
                                          start := 255006, stop := 256109 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 1, 16, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsMeetSemilatti\
ceDigraph" ), content := 0, count := [ 6, 1, 17, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 256184, root := ~, 
                                                  start := 256131, 
                                                  stop := 256183 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsJoinSemilatti\
ceDigraph" ), content := 0, count := [ 6, 1, 17, 4 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 256240, root := ~, 
                                                  start := 256187, 
                                                  stop := 256239 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsLatticeDigrap\
h" ), content := 0, count := [ 6, 1, 17, 6 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 256288, root := ~, 
                                                  start := 256243, 
                                                  stop := 256287 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 256311, 
                                                          root := ~, 
                                                          start := 256300, 
                                                          stop := 256310 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 256327, 
                                                          root := ~, 
                                                          start := 256315, 
                                                          stop := 256326 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 17, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 256338, root := ~, 
                                                  start := 256291, 
                                                  stop := 256337 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sMeetSemilatticeDigraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 256390, 
                                                          root := ~, 
                                                          start := 256359, 
                                                          stop := 256389 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 256410, 
                                                          root := ~, 
                                                          start := 256399, 
                                                          stop := 256409 ), 
                                                      rec( 
                                                          content := " if the \
digraph\n    ", count := [ 6, 1, 17, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 256444, 
                                                          root := ~, 
                                                          start := 256430, 
                                                          stop := 256443 ), 
                                                      rec( 
                                                          content := " is a me\
et semilattice; ", count := [ 6, 1, 17, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sJoinSemilatticeDigraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 256499, 
                                                          root := ~, 
                                                          start := 256468, 
                                                          stop := 256498 ), 
                                                      rec( 
                                                          content := "\n    re\
turns ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 256523, 
                                                          root := ~, 
                                                          start := 256512, 
                                                          stop := 256522 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 256553, 
                                                          root := ~, 
                                                          start := 256539, 
                                                          stop := 256552 ), 
                                                      rec( 
                                                          content := " is a jo\
in semilattice;\n    and  ", count := [ 6, 1, 17, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sLatticeDigraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "C", 
                                                          next := 256609, 
                                                          root := ~, 
                                                          start := 256586, 
                                                          stop := 256608 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 256629, 
                                                          root := ~, 
                                                          start := 256618, 
                                                          stop := 256628 ), 
                                                      rec( 
                                                          content := " if the \
digraph\n    ", count := [ 6, 1, 17, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 17, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 256663, 
                                                          root := ~, 
                                                          start := 256649, 
                                                          stop := 256662 ), 
                                                      rec( 
                                                          content := " is both\
 a meet and a join semilattice.\n    ", count := [ 6, 1, 17, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 17, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 256711, 
                                                          root := ~, 
                                                          start := 256707, 
                                                          stop := 256710 ), 
                                                      rec( 
                                                          content := "\n\n    \
For a partial order digraph ", count := [ 6, 1, 17, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsParti\
alOrderDigraph" ), content := 0, count := [ 6, 1, 17, 8 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 256780, 
                                                          root := ~, 
                                                          start := 256745, 
                                                          stop := 256779 ), 
                                                      rec( 
                                                          content := " the\n  \
  corresponding partial order is the relation ", count := [ 6, 1, 17, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\leq", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 256844, 
                                                          root := ~, 
                                                          start := 256833, 
                                                          stop := 256843 ), 
                                                      rec( 
                                                          content := ", define\
d by\n    ", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
 \\leq y", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 256876, 
                                                          root := ~, 
                                                          start := 256861, 
                                                          stop := 256875 ), 
                                                      rec( 
                                                          content := " if and \
only if ", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
x, y]", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 256905, 
                                                          root := ~, 
                                                          start := 256892, 
                                                          stop := 256904 ), 
                                                      rec( 
                                                          content := " is an e\
dge.\n    A digraph is a ", count := [ 6, 1, 17, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
eet semilattice", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "E", 
                                                          next := 256960, 
                                                          root := ~, 
                                                          start := 256937, 
                                                          stop := 256959 ), 
                                                      rec( 
                                                          content := " if it i\
s a partial order and every\n    pair of vertices has a greatest lower bound (\
meet) with respect to the\n    aforementioned relation. A ", 
                                                          count := 
                                                            [ 6, 1, 17, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
oin semilattice", count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 6, 1, 17, 8 ], mathmode := "Text", name := "E", 
                                                          next := 257125, 
                                                          root := ~, 
                                                          start := 257102, 
                                                          stop := 257124 ), 
                                                      rec( 
                                                          content := " is a pa\
rtial order where\n    every pair of vertices has a least upper bound (join) w\
ith respect to\n    the relation.\n    ", count := [ 6, 1, 17, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 1, 17, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 257251, 
                                                          root := ~, 
                                                          start := 257247, 
                                                          stop := 257250 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 1, 17, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 1, 17, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 257293, 
                                                          root := ~, 
                                                          start := 257279, 
                                                          stop := 257292 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 1, 17, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 3], [2, 3], [3]]);\n<immutable digraph with 3 vertices\
, 5 edges>\ngap> IsMeetSemilatticeDigraph(D);\nfalse\ngap> IsJoinSemilatticeDi\
graph(D);\ntrue\ngap> IsLatticeDigraph(D);\nfalse\ngap> D := Digraph([[1], [2]\
, [1 .. 3]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> IsJoinSemila\
tticeDigraph(D);\nfalse\ngap> IsMeetSemilatticeDigraph(D);\ntrue\ngap> IsLatti\
ceDigraph(D);\nfalse\ngap> D := Digraph([[1 .. 4], [2, 4], [3, 4], [4]]);\n<im\
mutable digraph with 4 vertices, 9 edges>\ngap> IsMeetSemilatticeDigraph(D);\n\
true\ngap> IsJoinSemilatticeDigraph(D);\ntrue\ngap> IsLatticeDigraph(D);\ntrue\
\ngap> D := Digraph([[1, 1, 1], [1, 1, 2, 2],\n>                   [1, 3, 3], \
[1, 2, 3, 3, 4]]);\n<immutable multidigraph with 4 vertices, 15 edges>\ngap> I\
sMeetSemilatticeDigraph(D);\ntrue\ngap> IsJoinSemilatticeDigraph(D);\ntrue\nga\
p> IsLatticeDigraph(D);\ntrue\n", count := [ 6, 1, 17, 10 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 1, 17, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 258281, 
                                                          root := ~, 
                                                          start := 257394, 
                                                          stop := 258280 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 1, 17, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 1, 17, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 258298, root := ~, 
                                                  start := 256341, 
                                                  stop := 258297 ) ], 
                                          count := [ 6, 1, 17, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 258312, root := ~, 
                                          start := 256116, stop := 258311 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 6, 1, 17, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 6, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 258326, 
                                  root := ~, start := 238252, stop := 258325 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 6, 1, 17, 11 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Regularity", 
                                                  count := [ 6, 2, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 6, 2, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 258368, 
                                          root := ~, start := 258339, 
                                          stop := 258367 ), 
                                      rec( content := "\n    ", 
                                          count := [ 6, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsInRegularDigr\
aph" ), content := 0, count := [ 6, 2, 1, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 258435, root := ~, 
                                                  start := 258388, 
                                                  stop := 258434 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 258458, 
                                                          root := ~, 
                                                          start := 258447, 
                                                          stop := 258457 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 258474, 
                                                          root := ~, 
                                                          start := 258462, 
                                                          stop := 258473 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 258485, root := ~, 
                                                  start := 258438, 
                                                  stop := 258484 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 2, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 258534, 
                                                          root := ~, 
                                                          start := 258523, 
                                                          stop := 258533 ), 
                                                      rec( 
                                                          content := " if ther\
e is an integer ", count := [ 6, 2, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 258566, 
                                                          root := ~, 
                                                          start := 258558, 
                                                          stop := 258565 ), 
                                                      rec( 
                                                          content := " such th\
at\n    for every vertex ", count := [ 6, 2, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 258606, 
                                                          root := ~, 
                                                          start := 258598, 
                                                          stop := 258605 ), 
                                                      rec( 
                                                          content := " of digr\
aph ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 258632, 
                                                          root := ~, 
                                                          start := 258618, 
                                                          stop := 258631 ), 
                                                      rec( 
                                                          content := " there a\
re exactly\n    ", count := [ 6, 2, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 258663, 
                                                          root := ~, 
                                                          start := 258655, 
                                                          stop := 258662 ), 
                                                      rec( 
                                                          content := " edges t\
erminating in ", count := [ 6, 2, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 258693, 
                                                          root := ~, 
                                                          start := 258685, 
                                                          stop := 258692 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 See also ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsOutRe\
gularDigraph" ), content := 0, count := [ 6, 2, 1, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 258742, 
                                                          root := ~, 
                                                          start := 258709, 
                                                          stop := 258741 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 6, 2, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsRegul\
arDigraph" ), content := 0, count := [ 6, 2, 1, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 258781, 
                                                          root := ~, 
                                                          start := 258751, 
                                                          stop := 258780 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 2, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 258791, 
                                                          root := ~, 
                                                          start := 258787, 
                                                          stop := 258790 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 2, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 258833, 
                                                          root := ~, 
                                                          start := 258819, 
                                                          stop := 258832 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 2, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> IsInRegularDigraph(CompleteDigraph(4));\ntrue\ngap> IsInRegularDigraph(C\
hainDigraph(4));\nfalse\n", count := [ 6, 2, 1, 5 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 259063, 
                                                          root := ~, 
                                                          start := 258933, 
                                                          stop := 259062 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 2, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 259080, root := ~, 
                                                  start := 258488, 
                                                  stop := 259079 ) ], 
                                          count := [ 6, 2, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 259094, root := ~, 
                                          start := 258373, stop := 259093 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 2, 1, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsOutRegularDig\
raph" ), content := 0, count := [ 6, 2, 2, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 259163, root := ~, 
                                                  start := 259115, 
                                                  stop := 259162 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 259186, 
                                                          root := ~, 
                                                          start := 259175, 
                                                          stop := 259185 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 259202, 
                                                          root := ~, 
                                                          start := 259190, 
                                                          stop := 259201 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 259213, root := ~, 
                                                  start := 259166, 
                                                  stop := 259212 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 259262, 
                                                          root := ~, 
                                                          start := 259251, 
                                                          stop := 259261 ), 
                                                      rec( 
                                                          content := " if ther\
e is an integer ", count := [ 6, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 259294, 
                                                          root := ~, 
                                                          start := 259286, 
                                                          stop := 259293 ), 
                                                      rec( 
                                                          content := " such th\
at\n    for every vertex ", count := [ 6, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 259334, 
                                                          root := ~, 
                                                          start := 259326, 
                                                          stop := 259333 ), 
                                                      rec( 
                                                          content := " of digr\
aph ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 259360, 
                                                          root := ~, 
                                                          start := 259346, 
                                                          stop := 259359 ), 
                                                      rec( 
                                                          content := " there a\
re exactly\n    ", count := [ 6, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 259391, 
                                                          root := ~, 
                                                          start := 259383, 
                                                          stop := 259390 ), 
                                                      rec( 
                                                          content := " edges s\
tarting at ", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 259418, 
                                                          root := ~, 
                                                          start := 259410, 
                                                          stop := 259417 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 259428, 
                                                          root := ~, 
                                                          start := 259424, 
                                                          stop := 259427 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 6, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsInReg\
ularDigraph" ), content := 0, count := [ 6, 2, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 259475, 
                                                          root := ~, 
                                                          start := 259443, 
                                                          stop := 259474 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 6, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsRegul\
arDigraph" ), content := 0, count := [ 6, 2, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 259514, 
                                                          root := ~, 
                                                          start := 259484, 
                                                          stop := 259513 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 259524, 
                                                          root := ~, 
                                                          start := 259520, 
                                                          stop := 259523 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 2, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 259566, 
                                                          root := ~, 
                                                          start := 259552, 
                                                          stop := 259565 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 2, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> IsOutRegularDigraph(CompleteDigraph(4));\ntrue\ngap> IsOutRegularDigraph\
(ChainDigraph(4));\nfalse\n", count := [ 6, 2, 2, 6 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 259798, 
                                                          root := ~, 
                                                          start := 259666, 
                                                          stop := 259797 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 2, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 259815, root := ~, 
                                                  start := 259216, 
                                                  stop := 259814 ) ], 
                                          count := [ 6, 2, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 259829, root := ~, 
                                          start := 259100, stop := 259828 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 2, 2, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsRegularDigrap\
h" ), content := 0, count := [ 6, 2, 3, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 259895, root := ~, 
                                                  start := 259850, 
                                                  stop := 259894 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 259918, 
                                                          root := ~, 
                                                          start := 259907, 
                                                          stop := 259917 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 259934, 
                                                          root := ~, 
                                                          start := 259922, 
                                                          stop := 259933 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 2, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 259945, root := ~, 
                                                  start := 259898, 
                                                  stop := 259944 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 2, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 259994, 
                                                          root := ~, 
                                                          start := 259983, 
                                                          stop := 259993 ), 
                                                      rec( 
                                                          content := " if ther\
e is an integer ", count := [ 6, 2, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 260026, 
                                                          root := ~, 
                                                          start := 260018, 
                                                          stop := 260025 ), 
                                                      rec( 
                                                          content := " such th\
at\n    for every vertex ", count := [ 6, 2, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 260066, 
                                                          root := ~, 
                                                          start := 260058, 
                                                          stop := 260065 ), 
                                                      rec( 
                                                          content := " of digr\
aph ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 260092, 
                                                          root := ~, 
                                                          start := 260078, 
                                                          stop := 260091 ), 
                                                      rec( 
                                                          content := " there a\
re exactly\n    ", count := [ 6, 2, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 260123, 
                                                          root := ~, 
                                                          start := 260115, 
                                                          stop := 260122 ), 
                                                      rec( 
                                                          content := " edges s\
tarting and terminating at ", count := [ 6, 2, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 260166, 
                                                          root := ~, 
                                                          start := 260158, 
                                                          stop := 260165 ), 
                                                      rec( 
                                                          content := ". In oth\
er words,\n    the property is ", count := [ 6, 2, 3, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 260215, 
                                                          root := ~, 
                                                          start := 260204, 
                                                          stop := 260214 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 260233, 
                                                          root := ~, 
                                                          start := 260219, 
                                                          stop := 260232 ), 
                                                      rec( 
                                                          content := " is both\
 in-regular and\n    and out-regular.\n\n    See also ", count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsInReg\
ularDigraph" ), content := 0, count := [ 6, 2, 3, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 260324, 
                                                          root := ~, 
                                                          start := 260292, 
                                                          stop := 260323 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 6, 2, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsOutRe\
gularDigraph" ), content := 0, count := [ 6, 2, 3, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 260366, 
                                                          root := ~, 
                                                          start := 260333, 
                                                          stop := 260365 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 2, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 2, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 260376, 
                                                          root := ~, 
                                                          start := 260372, 
                                                          stop := 260375 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 2, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 260418, 
                                                          root := ~, 
                                                          start := 260404, 
                                                          stop := 260417 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 2, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> IsRegularDigraph(CompleteDigraph(4));\ntrue\ngap> IsRegularDigraph(Chain\
Digraph(4));\nfalse\n", count := [ 6, 2, 3, 5 ], name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 2, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 260644, 
                                                          root := ~, 
                                                          start := 260518, 
                                                          stop := 260643 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 2, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 2, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 260661, root := ~, 
                                                  start := 259948, 
                                                  stop := 260660 ) ], 
                                          count := [ 6, 2, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 260675, root := ~, 
                                          start := 259835, stop := 260674 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 2, 3, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsDistanceRegul\
arDigraph" ), content := 0, count := [ 6, 2, 4, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 260749, root := ~, 
                                                  start := 260696, 
                                                  stop := 260748 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 260772, 
                                                          root := ~, 
                                                          start := 260761, 
                                                          stop := 260771 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 260788, 
                                                          root := ~, 
                                                          start := 260776, 
                                                          stop := 260787 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 260799, root := ~, 
                                                  start := 260752, 
                                                  stop := 260798 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 260837, 
                                                          root := ~, 
                                                          start := 260823, 
                                                          stop := 260836 ), 
                                                      rec( 
                                                          content := " is a co\
nnected symmetric graph, this property returns\n    ", count := [ 6, 2, 4, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 260907, 
                                                          root := ~, 
                                                          start := 260896, 
                                                          stop := 260906 ), 
                                                      rec( 
                                                          content := " if for \
any two vertices ", count := [ 6, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 260940, 
                                                          root := ~, 
                                                          start := 260932, 
                                                          stop := 260939 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 260953, 
                                                          root := ~, 
                                                          start := 260945, 
                                                          stop := 260952 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 260971, 
                                                          root := ~, 
                                                          start := 260957, 
                                                          stop := 260970 ), 
                                                      rec( 
                                                          content := "\n    an\
d any two integers ", count := [ 6, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261005, 
                                                          root := ~, 
                                                          start := 260997, 
                                                          stop := 261004 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261018, 
                                                          root := ~, 
                                                          start := 261010, 
                                                          stop := 261017 ), 
                                                      rec( 
                                                          content := " between\
 ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261035, 
                                                          root := ~, 
                                                          start := 261027, 
                                                          stop := 261034 ), 
                                                      rec( 
                                                          content := " and the\
\n    diameter of ", count := [ 6, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 261074, 
                                                          root := ~, 
                                                          start := 261060, 
                                                          stop := 261073 ), 
                                                      rec( 
                                                          content := ", the nu\
mber of vertices at distance ", count := [ 6, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261119, 
                                                          root := ~, 
                                                          start := 261111, 
                                                          stop := 261118 ), 
                                                      rec( 
                                                          content := "\n    fr\
om ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261137, 
                                                          root := ~, 
                                                          start := 261129, 
                                                          stop := 261136 ), 
                                                      rec( 
                                                          content := " and dis\
tance ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261159, 
                                                          root := ~, 
                                                          start := 261151, 
                                                          stop := 261158 ), 
                                                      rec( 
                                                          content := " from ",
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261173, 
                                                          root := ~, 
                                                          start := 261165, 
                                                          stop := 261172 ), 
                                                      rec( 
                                                          content := " depends\
 only on\n    ", count := [ 6, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261202, 
                                                          root := ~, 
                                                          start := 261194, 
                                                          stop := 261201 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261212, 
                                                          root := ~, 
                                                          start := 261204, 
                                                          stop := 261211 ), 
                                                      rec( 
                                                          content := ", and th\
e distance between vertices ", count := [ 6, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261256, 
                                                          root := ~, 
                                                          start := 261248, 
                                                          stop := 261255 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261273, 
                                                          root := ~, 
                                                          start := 261265, 
                                                          stop := 261272 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 261278, 
                                                          root := ~, 
                                                          start := 261274, 
                                                          stop := 261277 ), 
                                                      rec( 
                                                          content := "\n\n    \
Alternatively, a distance regular graph is a graph for which there exist\n    \
integers ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "b\
_i", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261380, 
                                                          root := ~, 
                                                          start := 261370, 
                                                          stop := 261379 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
_i", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261392, 
                                                          root := ~, 
                                                          start := 261382, 
                                                          stop := 261391 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261406, 
                                                          root := ~, 
                                                          start := 261398, 
                                                          stop := 261405 ), 
                                                      rec( 
                                                          content := " such th\
at for any two\n    vertices ", count := [ 6, 2, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261450, 
                                                          root := ~, 
                                                          start := 261442, 
                                                          stop := 261449 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261460, 
                                                          root := ~, 
                                                          start := 261452, 
                                                          stop := 261459 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 261478, 
                                                          root := ~, 
                                                          start := 261464, 
                                                          stop := 261477 ), 
                                                      rec( 
                                                          content := " which a\
re distance ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261506, 
                                                          root := ~, 
                                                          start := 261498, 
                                                          stop := 261505 ), 
                                                      rec( 
                                                          content := "\n    ap\
art, there are exactly ", count := [ 6, 2, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "b\
_i", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261546, 
                                                          root := ~, 
                                                          start := 261536, 
                                                          stop := 261545 ), 
                                                      rec( 
                                                          content := " neighbo\
rs of ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261568, 
                                                          root := ~, 
                                                          start := 261560, 
                                                          stop := 261567 ), 
                                                      rec( 
                                                          content := " which a\
re at\n    distance ", count := [ 6, 2, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 - 1", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261607, 
                                                          root := ~, 
                                                          start := 261595, 
                                                          stop := 261606 ), 
                                                      rec( 
                                                          content := " away fr\
om ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261626, 
                                                          root := ~, 
                                                          start := 261618, 
                                                          stop := 261625 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
_i", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261642, 
                                                          root := ~, 
                                                          start := 261632, 
                                                          stop := 261641 ), 
                                                      rec( 
                                                          content := " neighbo\
rs of\n    ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261668, 
                                                          root := ~, 
                                                          start := 261660, 
                                                          stop := 261667 ), 
                                                      rec( 
                                                          content := " which a\
re at distance ", count := [ 6, 2, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 + 1", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261703, 
                                                          root := ~, 
                                                          start := 261691, 
                                                          stop := 261702 ), 
                                                      rec( 
                                                          content := " away fr\
om ", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 261722, 
                                                          root := ~, 
                                                          start := 261714, 
                                                          stop := 261721 ), 
                                                      rec( 
                                                          content := ". This\n\
    definition is used to check whether ", count := [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 261783, 
                                                          root := ~, 
                                                          start := 261769, 
                                                          stop := 261782 ), 
                                                      rec( 
                                                          content := " is dist\
ance regular.", count := [ 6, 2, 4, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 261808, 
                                                          root := ~, 
                                                          start := 261804, 
                                                          stop := 261807 ), 
                                                      rec( 
                                                          content := "\n\n    \
In the case where ", count := [ 6, 2, 4, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 261846, 
                                                          root := ~, 
                                                          start := 261832, 
                                                          stop := 261845 ), 
                                                      rec( 
                                                          content := " is not \
symmetric or not connected, the\n    property is ", count := [ 6, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 261914, 
                                                          root := ~, 
                                                          start := 261902, 
                                                          stop := 261913 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 2, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 261924, 
                                                          root := ~, 
                                                          start := 261920, 
                                                          stop := 261923 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 2, 4, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 2, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 261966, 
                                                          root := ~, 
                                                          start := 261952, 
                                                          stop := 261965 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 2, 4, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphSymmetricClosure(ChainDigraph(5));;\ngap> IsDistanceRegularD\
igraph(D);\nfalse\ngap> D := Digraph([[2, 3, 4], [1, 3, 4], [1, 2, 4], [1, 2, \
3]]);\n<immutable digraph with 4 vertices, 12 edges>\ngap> IsDistanceRegularDi\
graph(D);\ntrue\n", count := [ 6, 2, 4, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 2, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 262342, 
                                                          root := ~, 
                                                          start := 262067, 
                                                          stop := 262341 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 2, 4, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 262359, root := ~, 
                                                  start := 260802, 
                                                  stop := 262358 ) ], 
                                          count := [ 6, 2, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 262373, root := ~, 
                                          start := 260681, stop := 262372 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 6, 2, 4, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 6, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 262387, 
                                  root := ~, start := 258330, stop := 262386 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 6, 2, 4, 8 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Connectivity and \
cycles", count := [ 6, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 6, 3, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 262442, 
                                          root := ~, start := 262400, 
                                          stop := 262441 ), 
                                      rec( content := "\n    ", 
                                          count := [ 6, 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsAcyclicDigrap\
h" ), content := 0, count := [ 6, 3, 1, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 262507, root := ~, 
                                                  start := 262462, 
                                                  stop := 262506 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 262530, 
                                                          root := ~, 
                                                          start := 262519, 
                                                          stop := 262529 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 262546, 
                                                          root := ~, 
                                                          start := 262534, 
                                                          stop := 262545 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 262557, root := ~, 
                                                  start := 262510, 
                                                  stop := 262556 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 3, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 262606, 
                                                          root := ~, 
                                                          start := 262595, 
                                                          stop := 262605 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 262636, 
                                                          root := ~, 
                                                          start := 262622, 
                                                          stop := 262635 ), 
                                                      rec( 
                                                          content := " is acyc\
lic, and\n    ", count := [ 6, 3, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 262669, 
                                                          root := ~, 
                                                          start := 262657, 
                                                          stop := 262668 ), 
                                                      rec( 
                                                          content := " if it i\
s not. A digraph is ", count := [ 6, 3, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
cyclic", count := [ 6, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 262711, 
                                                          root := ~, 
                                                          start := 262697, 
                                                          stop := 262710 ), 
                                                      rec( 
                                                          content := " if ever\
y directed\n    cycle on the digraph is trivial. See Section ", 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 262829, 
                                                          root := ~, 
                                                          start := 262779, 
                                                          stop := 262828 ), 
                                                      rec( 
                                                          content := " for the\
 definition of a directed cycle, and of a trivial\n    directed cycle.", 
                                                          count := 
                                                            [ 6, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 262910, 
                                                          root := ~, 
                                                          start := 262906, 
                                                          stop := 262909 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this operation has complexity ", count := [ 6, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 262978, 
                                                          root := ~, 
                                                          start := 262965, 
                                                          stop := 262977 ), 
                                                      rec( 
                                                          content := " where\n\
    ", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 262997, 
                                                          root := ~, 
                                                          start := 262989, 
                                                          stop := 262996 ), 
                                                      rec( 
                                                          content := " is the \
number of edges (counting multiple edges as one) and\n    ", 
                                                          count := 
                                                            [ 6, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 263070, 
                                                          root := ~, 
                                                          start := 263062, 
                                                          stop := 263069 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in the digraph. ", count := [ 6, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 263117, 
                                                          root := ~, 
                                                          start := 263113, 
                                                          stop := 263116 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the argument ", count := [ 6, 3, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 263153, 
                                                          root := ~, 
                                                          start := 263139, 
                                                          stop := 263152 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 3, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> Petersen := Graph(SymmetricGroup(5), [[1, 2]], OnSets,\n> function(x, y)\
\n>   return IsEmpty(Intersection(x, y));\n> end);;\ngap> D := Digraph(Peterse\
n);\n<immutable digraph with 10 vertices, 30 edges>\ngap> IsAcyclicDigraph(D);\
\nfalse\ngap> D := DigraphFromDiSparse6String(\n> \".b_OGCIDBaPGkULEbQHCeRIdrH\
cuZMfRyDAbPhTi|zF\");\n<immutable digraph with 35 vertices, 34 edges>\ngap> Is\
AcyclicDigraph(D);\ntrue\ngap> IsAcyclicDigraph(ChainDigraph(10));\ntrue\ngap>\
 D := CompleteDigraph(IsMutableDigraph, 4);\n<mutable digraph with 4 vertices,\
 12 edges>\ngap> IsAcyclicDigraph(D);\nfalse\ngap> IsAcyclicDigraph(CycleDigra\
ph(10));\nfalse", count := [ 6, 3, 1, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 3, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 263902, 
                                                          root := ~, 
                                                          start := 263254, 
                                                          stop := 263901 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 263919, root := ~, 
                                                  start := 262560, 
                                                  stop := 263918 ) ], 
                                          count := [ 6, 3, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 263933, root := ~, 
                                          start := 262447, stop := 263932 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 1, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsChainDigraph"\
 ), content := 0, count := [ 6, 3, 2, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 263997, root := ~, 
                                                  start := 263954, 
                                                  stop := 263996 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 264020, 
                                                          root := ~, 
                                                          start := 264009, 
                                                          stop := 264019 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 264036, 
                                                          root := ~, 
                                                          start := 264024, 
                                                          stop := 264035 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 264047, root := ~, 
                                                  start := 264000, 
                                                  stop := 264046 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sChainDigraph", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 264089, 
                                                          root := ~, 
                                                          start := 264068, 
                                                          stop := 264088 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 264109, 
                                                          root := ~, 
                                                          start := 264098, 
                                                          stop := 264108 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 264139, 
                                                          root := ~, 
                                                          start := 264125, 
                                                          stop := 264138 ), 
                                                      rec( 
                                                          content := " is\n   \
 isomorphic to the chain digraph with the same number of vertices as\n    ", 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 264233, 
                                                          root := ~, 
                                                          start := 264219, 
                                                          stop := 264232 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 264251, 
                                                          root := ~, 
                                                          start := 264239, 
                                                          stop := 264250 ), 
                                                      rec( 
                                                          content := " if it i\
s not; see ", count := [ 6, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "ChainDi\
graph" ), content := 0, count := [ 6, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 264302, 
                                                          root := ~, 
                                                          start := 264270, 
                                                          stop := 264301 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 264307, 
                                                          root := ~, 
                                                          start := 264303, 
                                                          stop := 264306 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph is a ", count := [ 6, 3, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
hain", count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 264340, 
                                                          root := ~, 
                                                          start := 264328, 
                                                          stop := 264339 ), 
                                                      rec( 
                                                          content := " if and \
only if it is a directed tree, in which\n    every vertex has out degree at mo\
st one; see ", count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsDirec\
tedTree" ), content := 0, count := [ 6, 3, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 264465, 
                                                          root := ~, 
                                                          start := 264437, 
                                                          stop := 264464 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 6, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "OutDegr\
ees" ), content := 0, count := [ 6, 3, 2, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 264498, 
                                                          root := ~, 
                                                          start := 264474, 
                                                          stop := 264497 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 264508, 
                                                          root := ~, 
                                                          start := 264504, 
                                                          stop := 264507 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 264550, 
                                                          root := ~, 
                                                          start := 264536, 
                                                          stop := 264549 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n", count := [ 6, 3, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 3], [2, 3], [3]]);\n<immutable digraph with 3 vertices\
, 5 edges>\ngap> IsChainDigraph(D);\nfalse\ngap> D := ChainDigraph(5);\n<immut\
able chain digraph with 5 vertices>\ngap> IsChainDigraph(D);\ntrue\ngap> D := \
DigraphReverse(D);\n<immutable digraph with 5 vertices, 4 edges>\ngap> IsChain\
Digraph(D);\ntrue\ngap> D := ChainDigraph(IsMutableDigraph, 5);\n<mutable digr\
aph with 5 vertices, 4 edges>\ngap> IsChainDigraph(D);\ntrue\ngap> DigraphReve\
rse(D);\n<mutable digraph with 5 vertices, 4 edges>\ngap> IsChainDigraph(D);\n\
true", count := [ 6, 3, 2, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 3, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 265209, 
                                                          root := ~, 
                                                          start := 264647, 
                                                          stop := 265208 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 265226, root := ~, 
                                                  start := 264050, 
                                                  stop := 265225 ) ], 
                                          count := [ 6, 3, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 265240, root := ~, 
                                          start := 263939, stop := 265239 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 2, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsConnectedDigr\
aph" ), content := 0, count := [ 6, 3, 3, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 265308, root := ~, 
                                                  start := 265261, 
                                                  stop := 265307 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 265331, 
                                                          root := ~, 
                                                          start := 265320, 
                                                          stop := 265330 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 265347, 
                                                          root := ~, 
                                                          start := 265335, 
                                                          stop := 265346 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 265358, root := ~, 
                                                  start := 265311, 
                                                  stop := 265357 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 3, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 265407, 
                                                          root := ~, 
                                                          start := 265396, 
                                                          stop := 265406 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 265437, 
                                                          root := ~, 
                                                          start := 265423, 
                                                          stop := 265436 ), 
                                                      rec( 
                                                          content := "\n    is\
 weakly connected and ", count := [ 6, 3, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 265478, 
                                                          root := ~, 
                                                          start := 265466, 
                                                          stop := 265477 ), 
                                                      rec( 
                                                          content := " if it i\
s not.  A digraph\n    ", count := [ 6, 3, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 265522, 
                                                          root := ~, 
                                                          start := 265508, 
                                                          stop := 265521 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 6, 3, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "w\
eakly connected", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "E", 
                                                          next := 265549, 
                                                          root := ~, 
                                                          start := 265526, 
                                                          stop := 265548 ), 
                                                      rec( 
                                                          content := " if it i\
s possible to travel\n    from any vertex to any other vertex by traversing ed\
ges in either\n    direction (possibly against the orientation of some of them\
). ", count := [ 6, 3, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 265718, 
                                                          root := ~, 
                                                          start := 265714, 
                                                          stop := 265717 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this function has complexity ", count := [ 6, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m)", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 265783, 
                                                          root := ~, 
                                                          start := 265772, 
                                                          stop := 265782 ), 
                                                      rec( 
                                                          content := " if the\\
n    digraph's ", count := [ 6, 3, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Source" ), content := 0, count := [ 6, 3, 3, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 265832, 
                                                          root := ~, 
                                                          start := 265805, 
                                                          stop := 265831 ), 
                                                      rec( 
                                                          content := " attribu\
te is set, otherwise it has\n    complexity ", count := [ 6, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 265896, 
                                                          root := ~, 
                                                          start := 265883, 
                                                          stop := 265895 ), 
                                                      rec( 
                                                          content := " (where\\
n    ", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 265916, 
                                                          root := ~, 
                                                          start := 265908, 
                                                          stop := 265915 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and\n    ", count := [ 6, 3, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 3, 3, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 265956, 
                                                          root := ~, 
                                                          start := 265948, 
                                                          stop := 265955 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices of the digraph).\n    ", count := [ 6, 3, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 266008, 
                                                          root := ~, 
                                                          start := 266004, 
                                                          stop := 266007 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 266050, 
                                                          root := ~, 
                                                          start := 266036, 
                                                          stop := 266049 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2], [3], []]);;\ngap> IsConnectedDigraph(D);\ntrue\ngap> \
D := Digraph([[1, 3], [4], [3], []]);;\ngap> IsConnectedDigraph(D);\nfalse\nga\
p> D := Digraph(IsMutableDigraph, [[2], [3], []]);;\ngap> IsConnectedDigraph(D\
);\ntrue\ngap> D := Digraph(IsMutableDigraph, [[1, 3], [4], [3], []]);;\ngap> \
IsConnectedDigraph(D);\nfalse", count := [ 6, 3, 3, 6 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 266512, 
                                                          root := ~, 
                                                          start := 266151, 
                                                          stop := 266511 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 266529, root := ~, 
                                                  start := 265361, 
                                                  stop := 266528 ) ], 
                                          count := [ 6, 3, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 266543, root := ~, 
                                          start := 265246, stop := 266542 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 3, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsBiconnectedDi\
graph" ), content := 0, count := [ 6, 3, 4, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 266613, root := ~, 
                                                  start := 266564, 
                                                  stop := 266612 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 266636, 
                                                          root := ~, 
                                                          start := 266625, 
                                                          stop := 266635 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 266652, 
                                                          root := ~, 
                                                          start := 266640, 
                                                          stop := 266651 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 266663, root := ~, 
                                                  start := 266616, 
                                                  stop := 266662 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A c\
onnected digraph is ", count := [ 6, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "b\
iconnected", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 266725, 
                                                          root := ~, 
                                                          start := 266707, 
                                                          stop := 266724 ), 
                                                      rec( 
                                                          content := " if it i\
s still connected (in the\n    sense of ", count := [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsConne\
ctedDigraph" ), content := 0, count := [ 6, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 266804, 
                                                          root := ~, 
                                                          start := 266772, 
                                                          stop := 266803 ), 
                                                      rec( 
                                                          content := ") when a\
ny vertex is removed. \n      If ", count := [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 266852, 
                                                          root := ~, 
                                                          start := 266844, 
                                                          stop := 266851 ), 
                                                      rec( 
                                                          content := " has at \
least 3 vertices, then ", count := [ 6, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sBiconnectedDigraph", count := [ 6, 3, 4, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 266910, 
                                                          root := ~, 
                                                          start := 266883, 
                                                          stop := 266909 ), 
                                                      rec( 
                                                          content := "\n      \
implies ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBridg\
elessDigraph" ), content := 0, count := [ 6, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 266958, 
                                                          root := ~, 
                                                          start := 266925, 
                                                          stop := 266957 ), 
                                                      rec( 
                                                          content := ";\n    s\
ee ", count := [ 6, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Articul\
ationPoints" ), content := 0, count := [ 6, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 267000, 
                                                          root := ~, 
                                                          start := 266968, 
                                                          stop := 266999 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Bridges\
" ), content := 0, count := [ 6, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 267025, 
                                                          root := ~, 
                                                          start := 267004, 
                                                          stop := 267024 ), 
                                                      rec( 
                                                          content := " for a m\
ore\n    detailed explanation.\n    ", count := [ 6, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 267071, 
                                                          root := ~, 
                                                          start := 267067, 
                                                          stop := 267070 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sBiconnectedDigraph", count := [ 6, 3, 4, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 4, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 267104, 
                                                          root := ~, 
                                                          start := 267077, 
                                                          stop := 267103 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 267124, 
                                                          root := ~, 
                                                          start := 267113, 
                                                          stop := 267123 ), 
                                                      rec( 
                                                          content := " if the \
digraph\n    ", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 267158, 
                                                          root := ~, 
                                                          start := 267144, 
                                                          stop := 267157 ), 
                                                      rec( 
                                                          content := " is bico\
nnected, and ", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 267191, 
                                                          root := ~, 
                                                          start := 267179, 
                                                          stop := 267190 ), 
                                                      rec( 
                                                          content := " if it i\
s not. In\n    particular, ", count := [ 6, 3, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sBiconnectedDigraph", count := [ 6, 3, 4, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 4, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 267252, 
                                                          root := ~, 
                                                          start := 267225, 
                                                          stop := 267251 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 267273, 
                                                          root := ~, 
                                                          start := 267261, 
                                                          stop := 267272 ), 
                                                      rec( 
                                                          content := " if\n   \
 ", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 267295, 
                                                          root := ~, 
                                                          start := 267281, 
                                                          stop := 267294 ), 
                                                      rec( 
                                                          content := " is not \
connected. ", count := [ 6, 3, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 267318, 
                                                          root := ~, 
                                                          start := 267314, 
                                                          stop := 267317 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 4, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 267360, 
                                                          root := ~, 
                                                          start := 267346, 
                                                          stop := 267359 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. ", count := [ 6, 3, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 267459, 
                                                          root := ~, 
                                                          start := 267455, 
                                                          stop := 267458 ), 
                                                      rec( 
                                                          content := "\n\n    \
Multiple edges are ignored by this method. ", count := [ 6, 3, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 267512, 
                                                          root := ~, 
                                                          start := 267508, 
                                                          stop := 267511 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this operation has complexity ", count := [ 6, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 6, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 267580, 
                                                          root := ~, 
                                                          start := 267567, 
                                                          stop := 267579 ), 
                                                      rec( 
                                                          content := " where\n\
    ", count := [ 6, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 6, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 267599, 
                                                          root := ~, 
                                                          start := 267591, 
                                                          stop := 267598 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and ", count := [ 6, 3, 4, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 3, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 267635, 
                                                          root := ~, 
                                                          start := 267627, 
                                                          stop := 267634 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in\n    the digraph.\n    ", count := [ 6, 3, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 4, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 267690, 
                                                          root := ~, 
                                                          start := 267686, 
                                                          stop := 267689 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 6, 3, 4, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Bridges\
" ), content := 0, count := [ 6, 3, 4, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 267726, 
                                                          root := ~, 
                                                          start := 267705, 
                                                          stop := 267725 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 6, 3, 4, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Articul\
ationPoints" ), content := 0, count := [ 6, 3, 4, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 267760, 
                                                          root := ~, 
                                                          start := 267728, 
                                                          stop := 267759 ), 
                                                      rec( 
                                                          content := ", and \n\
    ", count := [ 6, 3, 4, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBridg\
elessDigraph" ), content := 0, count := [ 6, 3, 4, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 267804, 
                                                          root := ~, 
                                                          start := 267771, 
                                                          stop := 267803 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 3, 4, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 4, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 267814, 
                                                          root := ~, 
                                                          start := 267810, 
                                                          stop := 267813 ), 
                                                      rec( 
                                                          content := "\n      \
\n", count := [ 6, 3, 4, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> IsBiconnectedDigraph(Digraph([[1, 3], [2, 3], [3]]));\nfalse\ngap> IsBic\
onnectedDigraph(CycleDigraph(5));\ntrue\ngap> D := Digraph([[1, 1], [1, 1, 2],\
 [3], [3, 3, 4, 4]]);;\ngap> IsBiconnectedDigraph(D);\nfalse\ngap> D := Comple\
teBipartiteDigraph(IsMutableDigraph, 5, 4);\n<mutable digraph with 9 vertices,\
 40 edges>\ngap> IsBiconnectedDigraph(D);\ntrue", count := [ 6, 3, 4, 10 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 4, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 268202, 
                                                          root := ~, 
                                                          start := 267822, 
                                                          stop := 268201 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 4, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 268219, root := ~, 
                                                  start := 266666, 
                                                  stop := 268218 ) ], 
                                          count := [ 6, 3, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 268233, root := ~, 
                                          start := 266549, stop := 268232 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 4, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D", 
                                                      Name := "IsBridgelessDig\
raph" ), content := 0, count := [ 6, 3, 5, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 268296, root := ~, 
                                                  start := 268254, 
                                                  stop := 268295 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 268319, 
                                                          root := ~, 
                                                          start := 268308, 
                                                          stop := 268318 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 268335, 
                                                          root := ~, 
                                                          start := 268323, 
                                                          stop := 268334 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 268346, root := ~, 
                                                  start := 268299, 
                                                  stop := 268345 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A c\
onnected digraph is ", count := [ 6, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "b\
ridgeless", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 268407, 
                                                          root := ~, 
                                                          start := 268390, 
                                                          stop := 268406 ), 
                                                      rec( 
                                                          content := " if it i\
s still connected (in the\n    sense of ", count := [ 6, 3, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsConne\
ctedDigraph" ), content := 0, count := [ 6, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 268486, 
                                                          root := ~, 
                                                          start := 268454, 
                                                          stop := 268485 ), 
                                                      rec( 
                                                          content := ") when a\
ny edge is removed. \n    If ", count := [ 6, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 268530, 
                                                          root := ~, 
                                                          start := 268522, 
                                                          stop := 268529 ), 
                                                      rec( 
                                                          content := " has at \
least 3 vertices, then ", count := [ 6, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBicon\
nectedDigraph" ), content := 0, count := [ 6, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 268599, 
                                                          root := ~, 
                                                          start := 268561, 
                                                          stop := 268598 ), 
                                                      rec( 
                                                          content := " implies\
 ", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sBridgelessDigraph", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 268634, 
                                                          root := ~, 
                                                          start := 268608, 
                                                          stop := 268633 ), 
                                                      rec( 
                                                          content := ";\n    s\
ee ", count := [ 6, 3, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Articul\
ationPoints" ), content := 0, count := [ 6, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 268676, 
                                                          root := ~, 
                                                          start := 268644, 
                                                          stop := 268675 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Bridges\
" ), content := 0, count := [ 6, 3, 5, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 268701, 
                                                          root := ~, 
                                                          start := 268680, 
                                                          stop := 268700 ), 
                                                      rec( 
                                                          content := " for a m\
ore\n    detailed explanation.\n    ", count := [ 6, 3, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 268747, 
                                                          root := ~, 
                                                          start := 268743, 
                                                          stop := 268746 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sBridgelessDigraph", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 5, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 268779, 
                                                          root := ~, 
                                                          start := 268753, 
                                                          stop := 268778 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 268799, 
                                                          root := ~, 
                                                          start := 268788, 
                                                          stop := 268798 ), 
                                                      rec( 
                                                          content := " if the \
digraph\n    ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 268827, 
                                                          root := ~, 
                                                          start := 268819, 
                                                          stop := 268826 ), 
                                                      rec( 
                                                          content := " is brid\
geless, and ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 268859, 
                                                          root := ~, 
                                                          start := 268847, 
                                                          stop := 268858 ), 
                                                      rec( 
                                                          content := " if it i\
s not. In\n    particular, ", count := [ 6, 3, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sBridgelessDigraph", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 5, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 268919, 
                                                          root := ~, 
                                                          start := 268893, 
                                                          stop := 268918 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 268940, 
                                                          root := ~, 
                                                          start := 268928, 
                                                          stop := 268939 ), 
                                                      rec( 
                                                          content := " if\n   \
 ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 268956, 
                                                          root := ~, 
                                                          start := 268948, 
                                                          stop := 268955 ), 
                                                      rec( 
                                                          content := " is not \
connected. ", count := [ 6, 3, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 268979, 
                                                          root := ~, 
                                                          start := 268975, 
                                                          stop := 268978 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 269015, 
                                                          root := ~, 
                                                          start := 269007, 
                                                          stop := 269014 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. ", count := [ 6, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 269114, 
                                                          root := ~, 
                                                          start := 269110, 
                                                          stop := 269113 ), 
                                                      rec( 
                                                          content := "\n\n    \
Multiple edges are ignored by this method. ", count := [ 6, 3, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 269167, 
                                                          root := ~, 
                                                          start := 269163, 
                                                          stop := 269166 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this operation has complexity ", count := [ 6, 3, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 6, 3, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 269235, 
                                                          root := ~, 
                                                          start := 269222, 
                                                          stop := 269234 ), 
                                                      rec( 
                                                          content := " where\n\
    ", count := [ 6, 3, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 6, 3, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 269254, 
                                                          root := ~, 
                                                          start := 269246, 
                                                          stop := 269253 ), 
                                                      rec( 
                                                          content := " is the \
number of edges and ", count := [ 6, 3, 5, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 3, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 269290, 
                                                          root := ~, 
                                                          start := 269282, 
                                                          stop := 269289 ), 
                                                      rec( 
                                                          content := " is the \
number of vertices in\n    the digraph.\n    ", count := [ 6, 3, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 269345, 
                                                          root := ~, 
                                                          start := 269341, 
                                                          stop := 269344 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 6, 3, 5, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Bridges\
" ), content := 0, count := [ 6, 3, 5, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 269381, 
                                                          root := ~, 
                                                          start := 269360, 
                                                          stop := 269380 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 6, 3, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Articul\
ationPoints" ), content := 0, count := [ 6, 3, 5, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 269415, 
                                                          root := ~, 
                                                          start := 269383, 
                                                          stop := 269414 ), 
                                                      rec( 
                                                          content := ", and \n\
    ", count := [ 6, 3, 5, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBicon\
nectedDigraph" ), content := 0, count := [ 6, 3, 5, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 269460, 
                                                          root := ~, 
                                                          start := 269426, 
                                                          stop := 269459 ), 
                                                      rec( 
                                                          content := ".\n     \
 \n", count := [ 6, 3, 5, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> IsBridgelessDigraph(Digraph([[1, 3], [2, 3], [3]]));\nfalse\ngap> IsBrid\
gelessDigraph(CycleDigraph(5));\ntrue\ngap> D := Digraph([[1, 1], [1, 1, 2], [\
3], [3, 3, 4, 4]]);;\ngap> IsBridgelessDigraph(D);\nfalse\ngap> D := CompleteB\
ipartiteDigraph(IsMutableDigraph, 5, 4);\n<mutable digraph with 9 vertices, 40\
 edges>\ngap> IsBridgelessDigraph(D);\ntrue\ngap> D := Digraph([[2, 5], [1, 3,\
 4, 5], [2, 4], [2, 3], [1, 2]]);\n<immutable digraph with 5 vertices, 12 edge\
s>\ngap> IsBridgelessDigraph(D);\ntrue\ngap> IsBiconnectedDigraph(D);\nfalse\n\
gap> D := Digraph([[2], [3], [4], [2]]);\n<immutable digraph with 4 vertices, \
4 edges>\ngap> IsBridgelessDigraph(D);\nfalse\ngap> IsBiconnectedDigraph(D);\n\
false\ngap> IsBridgelessDigraph(ChainDigraph(2));\nfalse\ngap> IsBiconnectedDi\
graph(ChainDigraph(2));\ntrue\n", count := [ 6, 3, 5, 9 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 270284, 
                                                          root := ~, 
                                                          start := 269469, 
                                                          stop := 270283 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 270301, root := ~, 
                                                  start := 268349, 
                                                  stop := 270300 ) ], 
                                          count := [ 6, 3, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 270315, root := ~, 
                                          start := 268239, stop := 270314 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 5, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsStronglyConne\
ctedDigraph" ), content := 0, count := [ 6, 3, 6, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 270391, root := ~, 
                                                  start := 270336, 
                                                  stop := 270390 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 270414, 
                                                          root := ~, 
                                                          start := 270403, 
                                                          stop := 270413 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 270430, 
                                                          root := ~, 
                                                          start := 270418, 
                                                          stop := 270429 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 270441, root := ~, 
                                                  start := 270394, 
                                                  stop := 270440 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 3, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 270490, 
                                                          root := ~, 
                                                          start := 270479, 
                                                          stop := 270489 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 270520, 
                                                          root := ~, 
                                                          start := 270506, 
                                                          stop := 270519 ), 
                                                      rec( 
                                                          content := " is stro\
ngly\n    connected and ", count := [ 6, 3, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 270563, 
                                                          root := ~, 
                                                          start := 270551, 
                                                          stop := 270562 ), 
                                                      rec( 
                                                          content := " if it i\
s not. ", count := [ 6, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 270582, 
                                                          root := ~, 
                                                          start := 270578, 
                                                          stop := 270581 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph ", count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 270612, 
                                                          root := ~, 
                                                          start := 270598, 
                                                          stop := 270611 ), 
                                                      rec( content := " is ", 
                                                          count := 
                                                            [ 6, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
trongly connected", count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "E", 
                                                          next := 270641, 
                                                          root := ~, 
                                                          start := 270616, 
                                                          stop := 270640 ), 
                                                      rec( 
                                                          content := " if ther\
e is a directed\n    path from every vertex to every other vertex.  See Sectio\
n ", count := [ 6, 3, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 270778, 
                                                          root := ~, 
                                                          start := 270728, 
                                                          stop := 270777 ), 
                                                      rec( 
                                                          content := " for the\
 definition of a directed\n    path.    ", count := [ 6, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 270829, 
                                                          root := ~, 
                                                          start := 270825, 
                                                          stop := 270828 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this operation is based on Gabow's Algorithm ", 
                                                          count := 
                                                            [ 6, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "Gab00" )
                                                            , content := 0, 
                                                          count := 
                                                            [ 6, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 270924, 
                                                          root := ~, 
                                                          start := 270899, 
                                                          stop := 270923 ), 
                                                      rec( 
                                                          content := " and has\
 complexity ", count := [ 6, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
(m+n)", count := [ 6, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 270957, 
                                                          root := ~, 
                                                          start := 270944, 
                                                          stop := 270956 ), 
                                                      rec( 
                                                          content := ", where \
", count := [ 6, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
", count := [ 6, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 270973, 
                                                          root := ~, 
                                                          start := 270965, 
                                                          stop := 270972 ), 
                                                      rec( 
                                                          content := " is\n   \
 the number of edges (counting multiple edges as one) and ", 
                                                          count := 
                                                            [ 6, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 3, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 271046, 
                                                          root := ~, 
                                                          start := 271038, 
                                                          stop := 271045 ), 
                                                      rec( 
                                                          content := " is the\\
n    number of vertices in the digraph.\n    ", count := [ 6, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 271101, 
                                                          root := ~, 
                                                          start := 271097, 
                                                          stop := 271100 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 6, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 6, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 6, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 271143, 
                                                          root := ~, 
                                                          start := 271129, 
                                                          stop := 271142 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 3, 6, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(250000);\n<immutable cycle digraph with 250000 vertice\
s>\ngap> IsStronglyConnectedDigraph(D);\ntrue\ngap> D := DigraphRemoveEdges(D,\
 [[250000, 1]]);\n<immutable digraph with 250000 vertices, 249999 edges>\ngap>\
 IsStronglyConnectedDigraph(D);\nfalse\ngap> D := CycleDigraph(IsMutableDigrap\
h, 250000);\n<mutable digraph with 250000 vertices, 250000 edges>\ngap> IsStro\
nglyConnectedDigraph(D);\ntrue\ngap> DigraphRemoveEdge(D, [250000, 1]);\n<muta\
ble digraph with 250000 vertices, 249999 edges>\ngap> IsStronglyConnectedDigra\
ph(D);\nfalse\n", count := [ 6, 3, 6, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 3, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 271820, 
                                                          root := ~, 
                                                          start := 271244, 
                                                          stop := 271819 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 6, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 271837, root := ~, 
                                                  start := 270444, 
                                                  stop := 271836 ) ], 
                                          count := [ 6, 3, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 271851, root := ~, 
                                          start := 270321, stop := 271850 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 6, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsAperiodicDigr\
aph" ), content := 0, count := [ 6, 3, 7, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 271919, root := ~, 
                                                  start := 271872, 
                                                  stop := 271918 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 271942, 
                                                          root := ~, 
                                                          start := 271931, 
                                                          stop := 271941 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 271958, 
                                                          root := ~, 
                                                          start := 271946, 
                                                          stop := 271957 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 271969, root := ~, 
                                                  start := 271922, 
                                                  stop := 271968 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property is ", count := [ 6, 3, 7, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 272018, 
                                                          root := ~, 
                                                          start := 272007, 
                                                          stop := 272017 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 272048, 
                                                          root := ~, 
                                                          start := 272034, 
                                                          stop := 272047 ), 
                                                      rec( 
                                                          content := "\n    is\
 aperiodic, i.e. if its ", count := [ 6, 3, 7, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Period" ), content := 0, count := [ 6, 3, 7, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 272108, 
                                                          root := ~, 
                                                          start := 272079, 
                                                          stop := 272107 ), 
                                                      rec( 
                                                          content := " is equa\
l to 1.\n    Otherwise, the property is ", count := [ 6, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 272167, 
                                                          root := ~, 
                                                          start := 272155, 
                                                          stop := 272166 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 3, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 272177, 
                                                          root := ~, 
                                                          start := 272173, 
                                                          stop := 272176 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 7, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 272219, 
                                                          root := ~, 
                                                          start := 272205, 
                                                          stop := 272218 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n    ", count := [ 6, 3, 7, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[6], [1], [2], [3], [4, 4], [5]]);\n<immutable multidigrap\
h with 6 vertices, 7 edges>\ngap> IsAperiodicDigraph(D);\nfalse\ngap> D := Dig\
raph([[2], [3, 5], [4], [5], [1, 2]]);\n<immutable digraph with 5 vertices, 7 \
edges>\ngap> IsAperiodicDigraph(D);\ntrue\ngap> D := Digraph(IsMutableDigraph,\
 [[2], [3, 5], [4], [5], [1, 2]]);\n<mutable digraph with 5 vertices, 7 edges>\
\ngap> IsAperiodicDigraph(D);\ntrue", count := [ 6, 3, 7, 5 ], name := "PCDATA\
", root := ~ ) ], count := [ 6, 3, 7, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 272764, 
                                                          root := ~, 
                                                          start := 272319, 
                                                          stop := 272763 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 272781, root := ~, 
                                                  start := 271972, 
                                                  stop := 272780 ) ], 
                                          count := [ 6, 3, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 272795, root := ~, 
                                          start := 271857, stop := 272794 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 7, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsDirectedTree"\
 ), content := 0, count := [ 6, 3, 8, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 272859, root := ~, 
                                                  start := 272816, 
                                                  stop := 272858 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 272882, 
                                                          root := ~, 
                                                          start := 272871, 
                                                          stop := 272881 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 272898, 
                                                          root := ~, 
                                                          start := 272886, 
                                                          stop := 272897 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 272909, root := ~, 
                                                  start := 272862, 
                                                  stop := 272908 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns ", count := [ 6, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 272949, 
                                                          root := ~, 
                                                          start := 272938, 
                                                          stop := 272948 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 272979, 
                                                          root := ~, 
                                                          start := 272965, 
                                                          stop := 272978 ), 
                                                      rec( 
                                                          content := " is a di\
rected tree, and\n    ", count := [ 6, 3, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 273020, 
                                                          root := ~, 
                                                          start := 273008, 
                                                          stop := 273019 ), 
                                                      rec( 
                                                          content := " if it i\
s not. ", count := [ 6, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 273039, 
                                                          root := ~, 
                                                          start := 273035, 
                                                          stop := 273038 ), 
                                                      rec( 
                                                          content := "\n\n    \
A ", count := [ 6, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
irected tree", count := [ 6, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 273067, 
                                                          root := ~, 
                                                          start := 273047, 
                                                          stop := 273066 ), 
                                                      rec( 
                                                          content := " is an a\
cyclic digraph with precisely 1 source,\n    such that no two vertices share a\
n out-neighbour.\n    Note the empty digraph is not considered a directed\n   \
 tree as it has no source. ", count := [ 6, 3, 8, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 273259, 
                                                          root := ~, 
                                                          start := 273255, 
                                                          stop := 273258 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 6, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Sources" ), content := 0, count := [ 6, 3, 8, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 273302, 
                                                          root := ~, 
                                                          start := 273274, 
                                                          stop := 273301 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 273312, 
                                                          root := ~, 
                                                          start := 273308, 
                                                          stop := 273311 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 8, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 273354, 
                                                          root := ~, 
                                                          start := 273340, 
                                                          stop := 273353 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 3, 8, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[], [2]]);\n<immutable digraph with 2 vertices, 1 edge>\ng\
ap> IsDirectedTree(D);\nfalse\ngap> D := Digraph([[3], [3], []]);\n<immutable \
digraph with 3 vertices, 2 edges>\ngap> IsDirectedTree(D);\nfalse\ngap> D := D\
igraph([[2], [3], []]);\n<immutable digraph with 3 vertices, 2 edges>\ngap> Is\
DirectedTree(D);\ntrue\ngap> D := Digraph([[2, 3], [6], [4, 5], [], [], []]);\
\n<immutable digraph with 6 vertices, 5 edges>\ngap> IsDirectedTree(D);\ntrue\
\n", count := [ 6, 3, 8, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 3, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 273938, 
                                                          root := ~, 
                                                          start := 273455, 
                                                          stop := 273937 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 273955, root := ~, 
                                                  start := 272912, 
                                                  stop := 273954 ) ], 
                                          count := [ 6, 3, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 273969, root := ~, 
                                          start := 272801, stop := 273968 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 8, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsUndirectedTre\
e" ), content := 0, count := [ 6, 3, 9, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 274035, root := ~, 
                                                  start := 273990, 
                                                  stop := 274034 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsUndirectedFor\
est" ), content := 0, count := [ 6, 3, 9, 4 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 274085, root := ~, 
                                                  start := 274038, 
                                                  stop := 274084 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 274108, 
                                                          root := ~, 
                                                          start := 274097, 
                                                          stop := 274107 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 274124, 
                                                          root := ~, 
                                                          start := 274112, 
                                                          stop := 274123 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 274135, root := ~, 
                                                  start := 274088, 
                                                  stop := 274134 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
 property ", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sUndirectedTree", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "C", 
                                                          next := 274192, 
                                                          root := ~, 
                                                          start := 274169, 
                                                          stop := 274191 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 274212, 
                                                          root := ~, 
                                                          start := 274201, 
                                                          stop := 274211 ), 
                                                      rec( 
                                                          content := " if the \
digraph\n    ", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 274246, 
                                                          root := ~, 
                                                          start := 274232, 
                                                          stop := 274245 ), 
                                                      rec( 
                                                          content := " is an u\
ndirected tree, and the property\n    ", count := [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sUndirectedForest", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "C", 
                                                          next := 274316, 
                                                          root := ~, 
                                                          start := 274291, 
                                                          stop := 274315 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 274336, 
                                                          root := ~, 
                                                          start := 274325, 
                                                          stop := 274335 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 274354, 
                                                          root := ~, 
                                                          start := 274340, 
                                                          stop := 274353 ), 
                                                      rec( 
                                                          content := " is an\n\
    undirected forest; otherwise, these properties return ", 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 274431, 
                                                          root := ~, 
                                                          start := 274419, 
                                                          stop := 274430 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 6, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 274437, 
                                                          root := ~, 
                                                          start := 274433, 
                                                          stop := 274436 ), 
                                                      rec( 
                                                          content := "\n\n    \
An ", count := [ 6, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
ndirected tree", count := [ 6, 3, 9, 6 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 274468, 
                                                          root := ~, 
                                                          start := 274446, 
                                                          stop := 274467 ), 
                                                      rec( 
                                                          content := " is a sy\
mmetric digraph without loops, in which for\n    any pair of distinct vertices\
 ", count := [ 6, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 274562, 
                                                          root := ~, 
                                                          start := 274554, 
                                                          stop := 274561 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 274575, 
                                                          root := ~, 
                                                          start := 274567, 
                                                          stop := 274574 ), 
                                                      rec( 
                                                          content := ", there \
is exactly one\n    directed path from ", count := [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 6, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 274629, 
                                                          root := ~, 
                                                          start := 274621, 
                                                          stop := 274628 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 6, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 274641, 
                                                          root := ~, 
                                                          start := 274633, 
                                                          stop := 274640 ), 
                                                      rec( 
                                                          content := ". See ",
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsSymme\
tricDigraph" ), content := 0, count := [ 6, 3, 9, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 274685, 
                                                          root := ~, 
                                                          start := 274647, 
                                                          stop := 274684 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ 6, 3, 9, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 274719, 
                                                          root := ~, 
                                                          start := 274690, 
                                                          stop := 274718 ), 
                                                      rec( 
                                                          content := ", and se\
e\n    Section ", count := [ 6, 3, 9, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 274785, 
                                                          root := ~, 
                                                          start := 274741, 
                                                          stop := 274784 ), 
                                                      rec( 
                                                          content := " for the\
 definition of\n    directed path. This definition implies that an undirected \
tree has\n    no multiple edges. ", count := [ 6, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 274906, 
                                                          root := ~, 
                                                          start := 274902, 
                                                          stop := 274905 ), 
                                                      rec( 
                                                          content := "\n\n    \
An ", count := [ 6, 3, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
ndirected forest", count := [ 6, 3, 9, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 6, 3, 9, 7 ], mathmode := "Text", name := "E", 
                                                          next := 274939, 
                                                          root := ~, 
                                                          start := 274915, 
                                                          stop := 274938 ), 
                                                      rec( 
                                                          content := " is a di\
graph, each of whose connected components\n    is an undirected tree. In other\
 words, an undirected forest is isomorphic to\n    a disjoint union of undirec\
ted trees. See ", count := [ 6, 3, 9, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
ConnectedComponents" ), content := 0, count := [ 6, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 275163, 
                                                          root := ~, 
                                                          start := 275116, 
                                                          stop := 275162 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
DisjointUnion", Label := "for a list of digraphs" ), content := 0, 
                                                          count := 
                                                            [ 6, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 275240, 
                                                          root := ~, 
                                                          start := 275168, 
                                                          stop := 275239 ), 
                                                      rec( 
                                                          content := ". In par\
ticular, every\n    undirected tree is an undirected forest. ", 
                                                          count := 
                                                            [ 6, 3, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 275312, 
                                                          root := ~, 
                                                          start := 275308, 
                                                          stop := 275311 ), 
                                                      rec( 
                                                          content := "\n\n    \
Please note that the digraph with zero vertices is considered to be neither\n \
   an undirected tree nor an undirected forest.\n    ", count := 
                                                            [ 6, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 9, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 275451, 
                                                          root := ~, 
                                                          start := 275447, 
                                                          stop := 275450 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 9, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 9, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 9, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 275493, 
                                                          root := ~, 
                                                          start := 275479, 
                                                          stop := 275492 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 3, 9, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3], [3], [1, 2]]);\n<immutable digraph with 3 vertices, 4\
 edges>\ngap> IsUndirectedTree(D);\ntrue\ngap> IsSymmetricDigraph(D) and not D\
igraphHasLoops(D);\ntrue\ngap> D := Digraph([[3], [5], [1, 4], [3], [2]]);\n<i\
mmutable digraph with 5 vertices, 6 edges>\ngap> IsConnectedDigraph(D);\nfalse\
\ngap> IsUndirectedTree(D);\nfalse\ngap> IsUndirectedForest(D);\ntrue\ngap> D \
:= Digraph([[1, 2], [1], [2]]);\n<immutable digraph with 3 vertices, 4 edges>\
\ngap> IsUndirectedTree(D) or IsUndirectedForest(D);\nfalse\ngap> IsSymmetricD\
igraph(D) or not DigraphHasLoops(D);\nfalse", count := [ 6, 3, 9, 10 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 9, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 276194, 
                                                          root := ~, 
                                                          start := 275594, 
                                                          stop := 276193 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 9, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 276211, root := ~, 
                                                  start := 274138, 
                                                  stop := 276210 ) ], 
                                          count := [ 6, 3, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 276225, root := ~, 
                                          start := 273975, stop := 276224 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 9, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsEulerianDigra\
ph" ), content := 0, count := [ 6, 3, 10, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 276292, root := ~, 
                                                  start := 276246, 
                                                  stop := 276291 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 276315, 
                                                          root := ~, 
                                                          start := 276304, 
                                                          stop := 276314 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 276331, 
                                                          root := ~, 
                                                          start := 276319, 
                                                          stop := 276330 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 276342, root := ~, 
                                                  start := 276295, 
                                                  stop := 276341 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property returns true if the digraph ", count := [ 6, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 276419, 
                                                          root := ~, 
                                                          start := 276405, 
                                                          stop := 276418 ), 
                                                      rec( 
                                                          content := " is Eule\
rian.\n    ", count := [ 6, 3, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 276441, 
                                                          root := ~, 
                                                          start := 276437, 
                                                          stop := 276440 ), 
                                                      rec( 
                                                          content := "\n\n    \
A connected digraph is called ", count := [ 6, 3, 10, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "E\
ulerian", count := [ 6, 3, 10, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 276492, 
                                                          root := ~, 
                                                          start := 276477, 
                                                          stop := 276491 ), 
                                                      rec( 
                                                          content := " if ther\
e exists a directed\n    circuit on the digraph which includes every edge exac\
tly once.  See\n    Section ", count := [ 6, 3, 10, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 276648, 
                                                          root := ~, 
                                                          start := 276604, 
                                                          stop := 276647 ), 
                                                      rec( 
                                                          content := " for the\
 definition of\n    a directed circuit. Note that the empty digraph with at mo\
st one vertex is\n    considered to be Eulerian.\n    ", count := 
                                                            [ 6, 3, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 276789, 
                                                          root := ~, 
                                                          start := 276785, 
                                                          stop := 276788 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 10, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 276831, 
                                                          root := ~, 
                                                          start := 276817, 
                                                          stop := 276830 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 3, 10, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[]]);\n<immutable empty digraph with 1 vertex>\ngap> IsEul\
erianDigraph(D);\ntrue\ngap> D := Digraph([[2], []]);\n<immutable digraph with\
 2 vertices, 1 edge>\ngap> IsEulerianDigraph(D);\nfalse\ngap> D := Digraph([[3\
], [], [2]]);\n<immutable digraph with 3 vertices, 2 edges>\ngap> IsEulerianDi\
graph(D);\nfalse\ngap> D := Digraph([[2], [3], [1]]);\n<immutable digraph with\
 3 vertices, 3 edges>\ngap> IsEulerianDigraph(D);\ntrue\n", count := 
                                                                    [ 6, 3, 
                                                                      10, 6 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 10, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 277394, 
                                                          root := ~, 
                                                          start := 276932, 
                                                          stop := 277393 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 10, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 277411, root := ~, 
                                                  start := 276345, 
                                                  stop := 277410 ) ], 
                                          count := [ 6, 3, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 277425, root := ~, 
                                          start := 276231, stop := 277424 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 10, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsHamiltonianDi\
graph" ), content := 0, count := [ 6, 3, 11, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 277495, root := ~, 
                                                  start := 277446, 
                                                  stop := 277494 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 277518, 
                                                          root := ~, 
                                                          start := 277507, 
                                                          stop := 277517 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 277534, 
                                                          root := ~, 
                                                          start := 277522, 
                                                          stop := 277533 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 277545, root := ~, 
                                                  start := 277498, 
                                                  stop := 277544 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 277583, 
                                                          root := ~, 
                                                          start := 277569, 
                                                          stop := 277582 ), 
                                                      rec( 
                                                          content := " is Hami\
ltonian, then this property returns\n    ", count := [ 6, 3, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 277642, 
                                                          root := ~, 
                                                          start := 277631, 
                                                          stop := 277641 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 6, 3, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 277660, 
                                                          root := ~, 
                                                          start := 277648, 
                                                          stop := 277659 ), 
                                                      rec( 
                                                          content := " if it i\
s not. ", count := [ 6, 3, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 277679, 
                                                          root := ~, 
                                                          start := 277675, 
                                                          stop := 277678 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph with ", count := [ 6, 3, 11, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 3, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 277708, 
                                                          root := ~, 
                                                          start := 277700, 
                                                          stop := 277707 ), 
                                                      rec( 
                                                          content := " vertice\
s is ", count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
amiltonian", count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 277739, 
                                                          root := ~, 
                                                          start := 277721, 
                                                          stop := 277738 ), 
                                                      rec( 
                                                          content := " if it h\
as a\n    directed cycle of length ", count := [ 6, 3, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 6, 3, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 277789, 
                                                          root := ~, 
                                                          start := 277781, 
                                                          stop := 277788 ), 
                                                      rec( 
                                                          content := ". See Se\
ction ", count := [ 6, 3, 11, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Style := "Number\
", Subsect := "Definitions" ), content := 0, count := [ 6, 3, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 277852, 
                                                          root := ~, 
                                                          start := 277803, 
                                                          stop := 277851 ), 
                                                      rec( 
                                                          content := " for the\
 definition of a directed cycle.\n    Note the empty digraphs on 0 and 1 verti\
ces are considered to be\n    Hamiltonian.", count := [ 6, 3, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 277982, 
                                                          root := ~, 
                                                          start := 277978, 
                                                          stop := 277981 ), 
                                                      rec( 
                                                          content := "\n\n    \
The method used in this operation has the worst case complexity as\n    ", 
                                                          count := 
                                                            [ 6, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Monomorphism" ), content := 0, count := [ 6, 3, 11, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 278092, 
                                                          root := ~, 
                                                          start := 278059, 
                                                          stop := 278091 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 278102, 
                                                          root := ~, 
                                                          start := 278098, 
                                                          stop := 278101 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 278144, 
                                                          root := ~, 
                                                          start := 278130, 
                                                          stop := 278143 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> g := Digraph([[]]);\n<immutable empty digraph with 1 vertex>\ngap> IsHam\
iltonianDigraph(g);\ntrue\ngap> g := Digraph([[2], [1]]);\n<immutable digraph \
with 2 vertices, 2 edges>\ngap> IsHamiltonianDigraph(g);\ntrue\ngap> g := Digr\
aph([[3], [], [2]]);\n<immutable digraph with 3 vertices, 2 edges>\ngap> IsHam\
iltonianDigraph(g);\nfalse\ngap> g := Digraph([[2], [3], [1]]);\n<immutable di\
graph with 3 vertices, 3 edges>\ngap> IsHamiltonianDigraph(g);\ntrue\n", 
                                                                  count := 
                                                                    [ 6, 3, 
                                                                      11, 7 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 11, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 278720, 
                                                          root := ~, 
                                                          start := 278245, 
                                                          stop := 278719 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 11, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 278737, root := ~, 
                                                  start := 277548, 
                                                  stop := 278736 ) ], 
                                          count := [ 6, 3, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 278751, root := ~, 
                                          start := 277431, stop := 278750 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 3, 11, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsCycleDigraph"\
 ), content := 0, count := [ 6, 3, 12, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 278815, root := ~, 
                                                  start := 278772, 
                                                  stop := 278814 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 278838, 
                                                          root := ~, 
                                                          start := 278827, 
                                                          stop := 278837 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 278854, 
                                                          root := ~, 
                                                          start := 278842, 
                                                          stop := 278853 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 278865, root := ~, 
                                                  start := 278818, 
                                                  stop := 278864 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sCycleDigraph", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 278907, 
                                                          root := ~, 
                                                          start := 278886, 
                                                          stop := 278906 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 278927, 
                                                          root := ~, 
                                                          start := 278916, 
                                                          stop := 278926 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 278957, 
                                                          root := ~, 
                                                          start := 278943, 
                                                          stop := 278956 ), 
                                                      rec( 
                                                          content := " is\n   \
 isomorphic to the cycle digraph with the same number of vertices as\n    ", 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 279051, 
                                                          root := ~, 
                                                          start := 279037, 
                                                          stop := 279050 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 279069, 
                                                          root := ~, 
                                                          start := 279057, 
                                                          stop := 279068 ), 
                                                      rec( 
                                                          content := " if it i\
s not; see ", count := [ 6, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "CycleDi\
graph" ), content := 0, count := [ 6, 3, 12, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 279120, 
                                                          root := ~, 
                                                          start := 279088, 
                                                          stop := 279119 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 279125, 
                                                          root := ~, 
                                                          start := 279121, 
                                                          stop := 279124 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph is a ", count := [ 6, 3, 12, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ycle", count := [ 6, 3, 12, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 279158, 
                                                          root := ~, 
                                                          start := 279146, 
                                                          stop := 279157 ), 
                                                      rec( 
                                                          content := " if and \
only if it is strongly connected and has\n    the same number of edges as vert\
ices. \n    ", count := [ 6, 3, 12, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 3, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 279258, 
                                                          root := ~, 
                                                          start := 279254, 
                                                          stop := 279257 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 3, 12, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 3, 12, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 3, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 279300, 
                                                          root := ~, 
                                                          start := 279286, 
                                                          stop := 279299 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n", count := [ 6, 3, 12, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[1, 3], [2, 3], [3]]);\n<immutable digraph with 3 vertices\
, 5 edges>\ngap> IsCycleDigraph(D);\nfalse\ngap> D := CycleDigraph(5);\n<immut\
able cycle digraph with 5 vertices>\ngap> IsCycleDigraph(D);\ntrue\ngap> D := \
OnDigraphs(D, (1, 2, 3));\n<immutable digraph with 5 vertices, 5 edges>\ngap> \
D = CycleDigraph(5);\nfalse\ngap> IsCycleDigraph(D);\ntrue", count := 
                                                                    [ 6, 3, 
                                                                      12, 6 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 3, 12, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 279785, 
                                                          root := ~, 
                                                          start := 279397, 
                                                          stop := 279784 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 3, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 3, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 279802, root := ~, 
                                                  start := 278868, 
                                                  stop := 279801 ) ], 
                                          count := [ 6, 3, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 279816, root := ~, 
                                          start := 278757, stop := 279815 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 6, 3, 12, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 6, 3, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 279830, 
                                  root := ~, start := 262391, stop := 279829 )
                                , 
                              rec( content := "\n  \n  ", 
                                  count := [ 6, 3, 12, 7 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Planarity", 
                                                  count := [ 6, 4, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 6, 4, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 279873, 
                                          root := ~, start := 279845, 
                                          stop := 279872 ), 
                                      rec( content := "\n    ", 
                                          count := [ 6, 4, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsPlanarDigraph\
" ), content := 0, count := [ 6, 4, 1, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 279937, root := ~, 
                                                  start := 279893, 
                                                  stop := 279936 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 279960, 
                                                          root := ~, 
                                                          start := 279949, 
                                                          stop := 279959 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 279976, 
                                                          root := ~, 
                                                          start := 279964, 
                                                          stop := 279975 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 4, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 279987, root := ~, 
                                                  start := 279940, 
                                                  stop := 279986 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A "
                                                            , 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
lanar", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 280023, 
                                                          root := ~, 
                                                          start := 280010, 
                                                          stop := 280022 ), 
                                                      rec( 
                                                          content := " digraph\
 is a digraph that can be embedded in the plane in\n    such a way that its ed\
ges do not intersect. A digraph is planar if and only\n    if it does not have\
 a subdigraph that is homeomorphic to either the\n    complete graph on ", 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "5\
", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 280264, 
                                                          root := ~, 
                                                          start := 280256, 
                                                          stop := 280263 ), 
                                                      rec( 
                                                          content := " vertice\
s or the complete bipartite graph with\n    vertex sets of sizes ", 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 280344, 
                                                          root := ~, 
                                                          start := 280336, 
                                                          stop := 280343 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 6, 4, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 280357, 
                                                          root := ~, 
                                                          start := 280349, 
                                                          stop := 280356 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 4, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 280367, 
                                                          root := ~, 
                                                          start := 280363, 
                                                          stop := 280366 ), 
                                                      rec( 
                                                          content := "\n    \n\
    ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sPlanarDigraph", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 280399, 
                                                          root := ~, 
                                                          start := 280377, 
                                                          stop := 280398 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 280419, 
                                                          root := ~, 
                                                          start := 280408, 
                                                          stop := 280418 ), 
                                                      rec( 
                                                          content := " if the \
digraph ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 280449, 
                                                          root := ~, 
                                                          start := 280435, 
                                                          stop := 280448 ), 
                                                      rec( 
                                                          content := " is\n   \
 planar and ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 280480, 
                                                          root := ~, 
                                                          start := 280468, 
                                                          stop := 280479 ), 
                                                      rec( 
                                                          content := " if it i\
s not. The directions and multiplicities of\n    any edges in ", 
                                                          count := 
                                                            [ 6, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 280563, 
                                                          root := ~, 
                                                          start := 280549, 
                                                          stop := 280562 ), 
                                                      rec( 
                                                          content := " are ign\
ored by ", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sPlanarDigraph", count := [ 6, 4, 1, 4 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 280601, 
                                                          root := ~, 
                                                          start := 280579, 
                                                          stop := 280600 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 4, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 280611, 
                                                          root := ~, 
                                                          start := 280607, 
                                                          stop := 280610 ), 
                                                      rec( 
                                                          content := " \n\n   \
 See also ", count := [ 6, 4, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsOuter\
PlanarDigraph" ), content := 0, count := [ 6, 4, 1, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 280661, 
                                                          root := ~, 
                                                          start := 280627, 
                                                          stop := 280660 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 4, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 280671, 
                                                          root := ~, 
                                                          start := 280667, 
                                                          stop := 280670 ), 
                                                      rec( 
                                                          content := "\n\n    \
This method uses the reference implementation in\n    ", count := 
                                                            [ 6, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \
"https://github.com/graph-algorithms/edge-addition-planarity-suite", count := 
                                                                            [ \
6, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 6, 4, 
                                                                      1, 6 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], 
                                                          count := 
                                                            [ 6, 4, 1, 6 ], 
                                                          name := "Alt", 
                                                          next := 146, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 145 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "edge-addition-planarity-suite", count \
:= [ 6, 4, 1, 6 ], name := "PCDATA", root := ~ ) ], count := [ 6, 4, 1, 6 ], 
                                                                  name := "Pac\
kage", next := 218, root := ~, start := 170, stop := 217 ) ], 
                                                          count := 
                                                            [ 6, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 224, 
                                                          root := ~, 
                                                          start := 146, 
                                                          stop := 223 ), 
                                                      rec( 
                                                          content := " by John\
 Boyer of the algorithms described\n    in ", count := [ 6, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "BM06" ),
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 4, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 280829, 
                                                          root := ~, 
                                                          start := 280811, 
                                                          stop := 280828 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 6, 4, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> IsPlanarDigraph(CompleteDigraph(4));\ntrue\ngap> IsPlanarDigraph(Complet\
eDigraph(5));\nfalse\ngap> IsPlanarDigraph(CompleteBipartiteDigraph(2, 3));\nt\
rue\ngap> IsPlanarDigraph(CompleteBipartiteDigraph(3, 3));\nfalse\ngap> IsPlan\
arDigraph(CompleteDigraph(IsMutableDigraph, 4));\ntrue\ngap> IsPlanarDigraph(C\
ompleteDigraph(IsMutableDigraph, 5));\nfalse\ngap> IsPlanarDigraph(CompleteBip\
artiteDigraph(IsMutableDigraph, 2, 3));\ntrue\ngap> IsPlanarDigraph(CompleteBi\
partiteDigraph(IsMutableDigraph, 3, 3));\nfalse\n", count := [ 6, 4, 1, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 4, 1, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 281368, 
                                                          root := ~, 
                                                          start := 280836, 
                                                          stop := 281367 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 4, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 4, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 281385, root := ~, 
                                                  start := 279990, 
                                                  stop := 281384 ) ], 
                                          count := [ 6, 4, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 281399, root := ~, 
                                          start := 279878, stop := 281398 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 4, 1, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsOuterPlanarDi\
graph" ), content := 0, count := [ 6, 4, 2, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 281469, root := ~, 
                                                  start := 281420, 
                                                  stop := 281468 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 281492, 
                                                          root := ~, 
                                                          start := 281481, 
                                                          stop := 281491 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 281508, 
                                                          root := ~, 
                                                          start := 281496, 
                                                          stop := 281507 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 4, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 281519, root := ~, 
                                                  start := 281472, 
                                                  stop := 281518 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    An \
", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
uter planar", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 281562, 
                                                          root := ~, 
                                                          start := 281543, 
                                                          stop := 281561 ), 
                                                      rec( 
                                                          content := " digraph\
 is a digraph that can be embedded in the\n    plane in such a way that its ed\
ges do not intersect, and all vertices\n    belong to the unbounded face of th\
e embedding.  A digraph is outer planar\n    if and only if it does not have a\
 subdigraph that is homeomorphic to either\n    the complete graph on ", 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "4\
", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 281878, 
                                                          root := ~, 
                                                          start := 281870, 
                                                          stop := 281877 ), 
                                                      rec( 
                                                          content := " vertice\
s or the complete bipartite graph\n    with vertex sets of sizes ", 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 281958, 
                                                          root := ~, 
                                                          start := 281950, 
                                                          stop := 281957 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "3\
", count := [ 6, 4, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 281971, 
                                                          root := ~, 
                                                          start := 281963, 
                                                          stop := 281970 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 4, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 281981, 
                                                          root := ~, 
                                                          start := 281977, 
                                                          stop := 281980 ), 
                                                      rec( 
                                                          content := "\n    \n\
    ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sOuterPlanarDigraph", count := [ 6, 4, 2, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 4, 2, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 282018, 
                                                          root := ~, 
                                                          start := 281991, 
                                                          stop := 282017 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 282038, 
                                                          root := ~, 
                                                          start := 282027, 
                                                          stop := 282037 ), 
                                                      rec( 
                                                          content := " if the \
digraph\n    ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 282072, 
                                                          root := ~, 
                                                          start := 282058, 
                                                          stop := 282071 ), 
                                                      rec( 
                                                          content := " is oute\
r planar and ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 282105, 
                                                          root := ~, 
                                                          start := 282093, 
                                                          stop := 282104 ), 
                                                      rec( 
                                                          content := " if it i\
s not. The\n    directions and multiplicities of any edges in ", 
                                                          count := 
                                                            [ 6, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 282188, 
                                                          root := ~, 
                                                          start := 282174, 
                                                          stop := 282187 ), 
                                                      rec( 
                                                          content := " are ign\
ored by\n    ", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sPlanarDigraph", count := [ 6, 4, 2, 4 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 282230, 
                                                          root := ~, 
                                                          start := 282208, 
                                                          stop := 282229 ), 
                                                      rec( content := ".  ", 
                                                          count := 
                                                            [ 6, 4, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 4, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 282237, 
                                                          root := ~, 
                                                          start := 282233, 
                                                          stop := 282236 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 6, 4, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsPlana\
rDigraph" ), content := 0, count := [ 6, 4, 2, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 282281, 
                                                          root := ~, 
                                                          start := 282252, 
                                                          stop := 282280 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 This method uses the reference implementation in\n    ", count := 
                                                            [ 6, 4, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "edge-addition-planarity-suite" ), content := [ rec( content := \
"https://github.com/graph-algorithms/edge-addition-planarity-suite", count := 
                                                                            [ \
6, 4, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 6, 4, 
                                                                      2, 5 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 140, root := ~, start := 17, stop := 139 ) ], 
                                                          count := 
                                                            [ 6, 4, 2, 5 ], 
                                                          name := "Alt", 
                                                          next := 146, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 145 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "edge-addition-planarity-suite", count \
:= [ 6, 4, 2, 5 ], name := "PCDATA", root := ~ ) ], count := [ 6, 4, 2, 5 ], 
                                                                  name := "Pac\
kage", next := 218, root := ~, start := 170, stop := 217 ) ], 
                                                          count := 
                                                            [ 6, 4, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 224, 
                                                          root := ~, 
                                                          start := 146, 
                                                          stop := 223 ), 
                                                      rec( 
                                                          content := " by John\
 Boyer of the algorithms described\n    in ", count := [ 6, 4, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Key := "BM06" ),
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 4, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Cite", 
                                                          next := 282440, 
                                                          root := ~, 
                                                          start := 282422, 
                                                          stop := 282439 ), 
                                                      rec( content := ".\n\n",
                                                          count := 
                                                            [ 6, 4, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> IsOuterPlanarDigraph(CompleteDigraph(4));\nfalse\ngap> IsOuterPlanarDigr\
aph(CompleteDigraph(5));\nfalse\ngap> IsOuterPlanarDigraph(CompleteBipartiteDi\
graph(2, 3));\nfalse\ngap> IsOuterPlanarDigraph(CompleteBipartiteDigraph(3, 3)\
);\nfalse\ngap> IsOuterPlanarDigraph(CycleDigraph(10));\ntrue\ngap> IsOuterPla\
narDigraph(CompleteDigraph(IsMutableDigraph, 4));\nfalse\ngap> IsOuterPlanarDi\
graph(CompleteDigraph(IsMutableDigraph, 5));\nfalse\ngap> IsOuterPlanarDigraph\
(CompleteBipartiteDigraph(IsMutableDigraph,\n>                                \
                  2, 3));\nfalse\ngap> IsOuterPlanarDigraph(CompleteBipartiteD\
igraph(IsMutableDigraph,\n>                                                  3\
, 3));\nfalse\ngap> IsOuterPlanarDigraph(CycleDigraph(IsMutableDigraph, 10));\
\ntrue\n\n", count := [ 6, 4, 2, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 6, 4, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 283240, 
                                                          root := ~, 
                                                          start := 282443, 
                                                          stop := 283239 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 4, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 4, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 283257, root := ~, 
                                                  start := 281522, 
                                                  stop := 283256 ) ], 
                                          count := [ 6, 4, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 283271, root := ~, 
                                          start := 281405, stop := 283270 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 6, 4, 2, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 6, 4, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 283285, 
                                  root := ~, start := 279836, stop := 283284 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 6, 4, 2, 7 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Homomorphisms and\
 transformations", count := [ 6, 5, 0, 2 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 6, 5, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 283350, 
                                          root := ~, start := 283298, 
                                          stop := 283349 ), 
                                      rec( content := "\n    ", 
                                          count := [ 6, 5, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsDigraphCore" 
                                                     ), content := 0, 
                                                  count := [ 6, 5, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 283412, root := ~, 
                                                  start := 283370, 
                                                  stop := 283411 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 283435, 
                                                          root := ~, 
                                                          start := 283424, 
                                                          stop := 283434 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 283451, 
                                                          root := ~, 
                                                          start := 283439, 
                                                          stop := 283450 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 5, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 283462, root := ~, 
                                                  start := 283415, 
                                                  stop := 283461 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s property returns ", count := [ 6, 5, 1, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 283516, 
                                                          root := ~, 
                                                          start := 283505, 
                                                          stop := 283515 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 6, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 283534, 
                                                          root := ~, 
                                                          start := 283520, 
                                                          stop := 283533 ), 
                                                      rec( 
                                                          content := " is a co\
re,\n    and ", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 283566, 
                                                          root := ~, 
                                                          start := 283554, 
                                                          stop := 283565 ), 
                                                      rec( 
                                                          content := " if it i\
s not.", count := [ 6, 5, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 283584, 
                                                          root := ~, 
                                                          start := 283580, 
                                                          stop := 283583 ), 
                                                      rec( 
                                                          content := "\n\n    \
A digraph ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 283608, 
                                                          root := ~, 
                                                          start := 283600, 
                                                          stop := 283607 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ore", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 283625, 
                                                          root := ~, 
                                                          start := 283614, 
                                                          stop := 283624 ), 
                                                      rec( 
                                                          content := " if and \
only if it has no proper\n    subdigraphs ", count := [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 283682, 
                                                          root := ~, 
                                                          start := 283674, 
                                                          stop := 283681 ), 
                                                      rec( 
                                                          content := " such th\
at there exists a homomorphism from ", count := [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 283734, 
                                                          root := ~, 
                                                          start := 283726, 
                                                          stop := 283733 ), 
                                                      rec( 
                                                          content := "\n    to\
 ", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 283750, 
                                                          root := ~, 
                                                          start := 283742, 
                                                          stop := 283749 ), 
                                                      rec( 
                                                          content := ". In oth\
er words, a digraph ", count := [ 6, 5, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 283786, 
                                                          root := ~, 
                                                          start := 283778, 
                                                          stop := 283785 ), 
                                                      rec( 
                                                          content := " is a co\
re if and only if\n    every endomorphism on ", count := [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 283846, 
                                                          root := ~, 
                                                          start := 283838, 
                                                          stop := 283845 ), 
                                                      rec( 
                                                          content := " is an a\
utomorphism on ", count := [ 6, 5, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 6, 5, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 283877, 
                                                          root := ~, 
                                                          start := 283869, 
                                                          stop := 283876 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 6, 5, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 283887, 
                                                          root := ~, 
                                                          start := 283883, 
                                                          stop := 283886 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 5, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 5, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 283929, 
                                                          root := ~, 
                                                          start := 283915, 
                                                          stop := 283928 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 5, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(6);\n<immutable complete digraph with 6 vertices>\n\
gap> IsDigraphCore(D);\ntrue\ngap> D := DigraphSymmetricClosure(CycleDigraph(6\
));\n<immutable symmetric digraph with 6 vertices, 12 edges>\ngap> DigraphHomo\
morphism(D, CompleteDigraph(2));\nTransformation( [ 1, 2, 1, 2, 1, 2 ] )\ngap>\
 IsDigraphCore(D);\nfalse\n", count := [ 6, 5, 1, 6 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 284390, 
                                                          root := ~, 
                                                          start := 284030, 
                                                          stop := 284389 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 5, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 5, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 284407, root := ~, 
                                                  start := 283465, 
                                                  stop := 284406 ) ], 
                                          count := [ 6, 5, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 284421, root := ~, 
                                          start := 283355, stop := 284420 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 5, 1, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsEdgeTransitiv\
e" ), content := 0, count := [ 6, 5, 2, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 284487, root := ~, 
                                                  start := 284442, 
                                                  stop := 284486 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 284510, 
                                                          root := ~, 
                                                          start := 284499, 
                                                          stop := 284509 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 284526, 
                                                          root := ~, 
                                                          start := 284514, 
                                                          stop := 284525 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 5, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 284537, root := ~, 
                                                  start := 284490, 
                                                  stop := 284536 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 284575, 
                                                          root := ~, 
                                                          start := 284561, 
                                                          stop := 284574 ), 
                                                      rec( 
                                                          content := " is a di\
graph without multiple edges, then\n    ", count := [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sEdgeTransitive", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "C", 
                                                          next := 284645, 
                                                          root := ~, 
                                                          start := 284622, 
                                                          stop := 284644 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 284665, 
                                                          root := ~, 
                                                          start := 284654, 
                                                          stop := 284664 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 284683, 
                                                          root := ~, 
                                                          start := 284669, 
                                                          stop := 284682 ), 
                                                      rec( 
                                                          content := "\n    is\
 edge transitive, and ", count := [ 6, 5, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 284724, 
                                                          root := ~, 
                                                          start := 284712, 
                                                          stop := 284723 ), 
                                                      rec( 
                                                          content := " otherwi\
se. A digraph is\n    ", count := [ 6, 5, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge transitive", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 284775, 
                                                          root := ~, 
                                                          start := 284753, 
                                                          stop := 284774 ), 
                                                      rec( 
                                                          content := " if its \
automorphism group acts\n    transitively on its edges (via the action\n    ",
                                                          count := 
                                                            [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Func := "OnPairs" ), content := 0, count := [ 6, 5, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 284893, 
                                                          root := ~, 
                                                          start := 284857, 
                                                          stop := 284892 ), 
                                                      rec( 
                                                          content := ").\n    \
", count := [ 6, 5, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 284904, 
                                                          root := ~, 
                                                          start := 284900, 
                                                          stop := 284903 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 5, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 284946, 
                                                          root := ~, 
                                                          start := 284932, 
                                                          stop := 284945 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 5, 2, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> IsEdgeTransitive(CompleteDigraph(2));\ntrue\ngap> IsEdgeTransitive(Chain\
Digraph(3));\nfalse\ngap> IsEdgeTransitive(Digraph([[2], [3, 3, 3], []]));\nEr\
ror, the argument <D> must be a digraph with no multiple edges,\n", 
                                                                  count := 
                                                                    [ 6, 5, 
                                                                      2, 5 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 6, 5, 2, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 285293, 
                                                          root := ~, 
                                                          start := 285047, 
                                                          stop := 285292 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 5, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 5, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 285310, root := ~, 
                                                  start := 284540, 
                                                  stop := 285309 ) ], 
                                          count := [ 6, 5, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 285324, root := ~, 
                                          start := 284427, stop := 285323 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 6, 5, 2, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "IsVertexTransit\
ive" ), content := 0, count := [ 6, 5, 3, 2 ], mathmode := "Text", 
                                                  name := "Prop", 
                                                  next := 285392, root := ~, 
                                                  start := 285345, 
                                                  stop := 285391 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 285415, 
                                                          root := ~, 
                                                          start := 285404, 
                                                          stop := 285414 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 285431, 
                                                          root := ~, 
                                                          start := 285419, 
                                                          stop := 285430 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 5, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 285442, root := ~, 
                                                  start := 285395, 
                                                  stop := 285441 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 285480, 
                                                          root := ~, 
                                                          start := 285466, 
                                                          stop := 285479 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sVertexTransitive", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "C", 
                                                          next := 285525, 
                                                          root := ~, 
                                                          start := 285500, 
                                                          stop := 285524 ), 
                                                      rec( 
                                                          content := " returns\
\n    ", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 285549, 
                                                          root := ~, 
                                                          start := 285538, 
                                                          stop := 285548 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 285567, 
                                                          root := ~, 
                                                          start := 285553, 
                                                          stop := 285566 ), 
                                                      rec( 
                                                          content := " is vert\
ex transitive, and ", count := [ 6, 5, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 285606, 
                                                          root := ~, 
                                                          start := 285594, 
                                                          stop := 285605 ), 
                                                      rec( 
                                                          content := "\n    ot\
herwise. A digraph is ", count := [ 6, 5, 3, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex transitive", count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 6, 5, 3, 3 ], mathmode := "Text", name := "E", 
                                                          next := 285659, 
                                                          root := ~, 
                                                          start := 285635, 
                                                          stop := 285658 ), 
                                                      rec( 
                                                          content := " if its \
automorphism group\n    acts transitively on its vertices.\n    ", 
                                                          count := 
                                                            [ 6, 5, 3, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 6, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 285733, 
                                                          root := ~, 
                                                          start := 285729, 
                                                          stop := 285732 ), 
                                                      rec( 
                                                          content := "\n      \
\n    If the argument ", count := [ 6, 5, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 6, 5, 3, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 3, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 285775, 
                                                          root := ~, 
                                                          start := 285761, 
                                                          stop := 285774 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this property is recomputed every time it i\
s called. \n\n    ", count := [ 6, 5, 3, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> IsVertexTransitive(CompleteDigraph(2));\ntrue\ngap> IsVertexTransitive(C\
hainDigraph(3));\nfalse\n", count := [ 6, 5, 3, 5 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 6, 5, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 286006, 
                                                          root := ~, 
                                                          start := 285876, 
                                                          stop := 286005 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 6, 5, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 6, 5, 3, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 286023, root := ~, 
                                                  start := 285445, 
                                                  stop := 286022 ) ], 
                                          count := [ 6, 5, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 286037, root := ~, 
                                          start := 285330, stop := 286036 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 6, 5, 3, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 6, 5, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 286051, 
                                  root := ~, start := 283289, stop := 286050 )
                                , 
                              rec( content := "\n\n  \n", 
                                  count := [ 6, 5, 3, 6 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ) ], 
                          count := [ 6, 0, 0, 1 ], mathmode := "Text", 
                          name := "Chapter", next := 286066, root := ~, 
                          start := 238167, stop := 286065 ), 
                      rec( content := "\n ", count := [ 6, 5, 3, 6 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " properties ", count := [ 6, 5, 3, 6 ],
                          mathmode := "Text", name := "XMLCOMMENT", root := ~ 
                         ), 
                      rec( content := "\n  ", count := [ 6, 5, 3, 6 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Label := "Homomorphisms" ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Homomorphisms", 
                                          count := [ 7, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 7, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 286153, 
                                  root := ~, start := 286121, stop := 286152 )
                                , 
                              rec( content := "\n  ", count := [ 7, 0, 0, 3 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  content := "Let $E_a=(E_a^0,E_a^1,\\ra_a,\\s\
o_a)$ and $E_b=(E_b^0,E_b^1,\\ra_b,\\so_b)$ be two\ngraphs, and let $\\phi_0 :\
 E_a^0 \\to E_b^0$ and $\\phi_1 : E_a^1 \\to E_b^1$ be\nfunctions. Then the pa\
ir $\\phi = (\\phi_0, \\phi_1)$ is a \\emph{graph homomorphism\nfrom} $E_a$ \\\
emph{to} $E_b$ if $\\phi_0(\\so_a(e)) = \\so_b(\\phi_1(e))$ and\n$\\phi_0(\\ra\
_a(e)) = \\ra_b(\\phi_1(e))$ for every $e \\in E_a^1$. If $\\phi_0$ and\n$\\ph\
i_1$ are in addition bijective, then $\\phi$ is a \\emph{graph isomorphism\nfr\
om} $E_a$ \\emph{to} $E_b$. In this case we say that $E_a$ and $E_b$ are\n\\em\
ph{isomorphic} and write $E_a \\cong E_b$.", count := [ 7, 0, 0, 3 ], 
                                  mathmode := "Text", name := "XMLCOMMENT", 
                                  root := ~ ), 
                              rec( content := "\n\n  ", 
                                  count := [ 7, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Acting on digraph\
s", count := [ 7, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                 ) ], count := [ 7, 1, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 286797, 
                                          root := ~, start := 286760, 
                                          stop := 286796 ), 
                                      rec( content := "\n    ", 
                                          count := [ 7, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, perm", 
                                                      Label := "for a digraph \
and a perm", Name := "OnDigraphs" ), content := 0, count := [ 7, 1, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 286899, root := ~, 
                                                  start := 286817, 
                                                  stop := 286898 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, trans",
                                                      Label := "for a digraph \
and a transformation", Name := "OnDigraphs" ), content := 0, 
                                                  count := [ 7, 1, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 286995, root := ~, 
                                                  start := 286902, 
                                                  stop := 286994 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 7, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 287027, root := ~, 
                                                  start := 286998, 
                                                  stop := 287026 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287065, 
                                                          root := ~, 
                                                          start := 287051, 
                                                          stop := 287064 ), 
                                                      rec( 
                                                          content := " is a di\
graph, and the second argument ", count := [ 7, 1, 1, 5 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
erm", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287115, 
                                                          root := ~, 
                                                          start := 287104, 
                                                          stop := 287114 ), 
                                                      rec( 
                                                          content := " is a\n \
   ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
ermutation", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 287143, 
                                                          root := ~, 
                                                          start := 287125, 
                                                          stop := 287142 ), 
                                                      rec( 
                                                          content := " of the \
vertices of ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287177, 
                                                          root := ~, 
                                                          start := 287163, 
                                                          stop := 287176 ), 
                                                      rec( 
                                                          content := ", then t\
his operation\n    returns a digraph constructed by relabelling the vertices o\
f\n    ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287282, 
                                                          root := ~, 
                                                          start := 287268, 
                                                          stop := 287281 ), 
                                                      rec( 
                                                          content := " accordi\
ng to ", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
erm", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287307, 
                                                          root := ~, 
                                                          start := 287296, 
                                                          stop := 287306 ), 
                                                      rec( 
                                                          content := ".  Note \
that for an automorphism\n    ", count := [ 7, 1, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 287352, 
                                                          root := ~, 
                                                          start := 287344, 
                                                          stop := 287351 ), 
                                                      rec( 
                                                          content := " of a di\
graph, we have ", count := [ 7, 1, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
nDigraphs(", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "digraph", count := [ 7, 1, 1, 5 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], 
                                                                  mathmode := \
"Text", name := "A", next := 287403, root := ~, start := 287389, stop := 28740\
2 ), rec( content := ", f) =\n    ", count := [ 7, 1, 1, 5 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 287418, 
                                                          root := ~, 
                                                          start := 287375, 
                                                          stop := 287417 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287432, 
                                                          root := ~, 
                                                          start := 287418, 
                                                          stop := 287431 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 287442, 
                                                          root := ~, 
                                                          start := 287438, 
                                                          stop := 287441 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the second argument is a ", count := [ 7, 1, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
ransformation", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 287497, 
                                                          root := ~, 
                                                          start := 287476, 
                                                          stop := 287496 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287510, 
                                                          root := ~, 
                                                          start := 287498, 
                                                          stop := 287509 ), 
                                                      rec( 
                                                          content := " of the\\
n    vertices of ", count := [ 7, 1, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287548, 
                                                          root := ~, 
                                                          start := 287534, 
                                                          stop := 287547 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns a digraph\n    constructed by transforming the source an\
d range of each edge according to\n    ", count := [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287683, 
                                                          root := ~, 
                                                          start := 287671, 
                                                          stop := 287682 ), 
                                                      rec( 
                                                          content := ". Thus a\
 vertex which does not appear in the image of\n    ", count := [ 7, 1, 1, 6 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287753, 
                                                          root := ~, 
                                                          start := 287741, 
                                                          stop := 287752 ), 
                                                      rec( 
                                                          content := " will be\
 isolated in the returned digraph, and the returned\n    digraph may contain m\
ultiple edges, even if ", count := [ 7, 1, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287875, 
                                                          root := ~, 
                                                          start := 287861, 
                                                          stop := 287874 ), 
                                                      rec( 
                                                          content := " does no\
t.\n    If ", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 287905, 
                                                          root := ~, 
                                                          start := 287893, 
                                                          stop := 287904 ), 
                                                      rec( 
                                                          content := " is math\
ematically a permutation, then the result coincides\n    with ", 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
nDigraphs(", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "digraph", count := [ 7, 1, 1, 6 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 288002, root := ~, start := 287988, stop := 28800\
1 ), rec( content := ", AsPermutation(", count := [ 7, 1, 1, 6 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "trans", count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ) ], count := [ 7, 1, 1, 6 ], mathmode := "Text", name := "A", 
                                                                  next := 2880\
30, root := ~, start := 288018, stop := 288029 ), rec( content := "))", 
                                                                  count := 
                                                                    [ 7, 1, 
                                                                      1, 6 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 288036, 
                                                          root := ~, 
                                                          start := 287974, 
                                                          stop := 288035 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 288046, 
                                                          root := ~, 
                                                          start := 288042, 
                                                          stop := 288045 ), 
                                                      rec( 
                                                          content := "\n\n    \
The ", count := [ 7, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 7, 1, 1, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 288089, 
                                                          root := ~, 
                                                          start := 288056, 
                                                          stop := 288088 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 288107, 
                                                          root := ~, 
                                                          start := 288093, 
                                                          stop := 288106 ), 
                                                      rec( 
                                                          content := " will no\
t be retained\n    in the returned digraph. ", count := [ 7, 1, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 288162, 
                                                          root := ~, 
                                                          start := 288158, 
                                                          stop := 288161 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 288185, 
                                                          root := ~, 
                                                          start := 288171, 
                                                          stop := 288184 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 7, 1, 1, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 288227, 
                                                          root := ~, 
                                                          start := 288197, 
                                                          stop := 288226 ), 
                                                      rec( 
                                                          content := ", then\n\
    relabelling of the vertices is performed directly on ", 
                                                          count := 
                                                            [ 7, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 288305, 
                                                          root := ~, 
                                                          start := 288291, 
                                                          stop := 288304 ), 
                                                      rec( 
                                                          content := ".\n    I\
f ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 288328, 
                                                          root := ~, 
                                                          start := 288314, 
                                                          stop := 288327 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 7, 1, 1, 8 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 288372, 
                                                          root := ~, 
                                                          start := 288340, 
                                                          stop := 288371 ), 
                                                      rec( 
                                                          content := ", an imm\
utable\n    copy of ", count := [ 7, 1, 1, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 288413, 
                                                          root := ~, 
                                                          start := 288399, 
                                                          stop := 288412 ), 
                                                      rec( 
                                                          content := " with th\
e vertices relabelled is returned.", count := [ 7, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 1, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 288459, 
                                                          root := ~, 
                                                          start := 288455, 
                                                          stop := 288458 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 1, 1, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\n<immutable d\
igraph with 5 vertices, 11 edges>\ngap> new := OnDigraphs(D, (1, 2));\n<immuta\
ble digraph with 5 vertices, 11 edges>\ngap> OutNeighbours(new);\n[ [ 2, 3, 5 \
], [ 3 ], [ 2 ], [ 2, 1, 4 ], [ 1, 3, 5 ] ]\ngap> D := Digraph([[2], [], [2]])\
;\n<immutable digraph with 3 vertices, 2 edges>\ngap> t := Transformation([1, \
2, 1]);;\ngap> new := OnDigraphs(D, t);\n<immutable multidigraph with 3 vertic\
es, 2 edges>\ngap> OutNeighbours(new);\n[ [ 2, 2 ], [  ], [  ] ]\ngap> ForAll(\
DigraphEdges(D),\n>  e -> IsDigraphEdge(new, [e[1] ^ t, e[2] ^ t]));\ntrue\n",
                                                                  count := 
                                                                    [ 7, 1, 
                                                                      1, 10 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 1, 1, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 289102, 
                                                          root := ~, 
                                                          start := 288465, 
                                                          stop := 289101 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 1, 1, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 289119, root := ~, 
                                                  start := 287030, 
                                                  stop := 289118 ) ], 
                                          count := [ 7, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 289133, root := ~, 
                                          start := 286802, stop := 289132 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 1, 1, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, pair", 
                                                      Name := "OnMultiDigraphs\
" ), content := 0, count := [ 7, 1, 2, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 289204, root := ~, 
                                                  start := 289154, 
                                                  stop := 289203 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, perm1, \
perm2", Label := "for a digraph, perm, and perm", Name := "OnMultiDigraphs" ),
                                                  content := 0, 
                                                  count := [ 7, 1, 2, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 289307, root := ~, 
                                                  start := 289207, 
                                                  stop := 289306 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 7, 1, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 289339, root := ~, 
                                                  start := 289310, 
                                                  stop := 289338 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 289377, 
                                                          root := ~, 
                                                          start := 289363, 
                                                          stop := 289376 ), 
                                                      rec( 
                                                          content := " is a di\
graph, and ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
air", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 289407, 
                                                          root := ~, 
                                                          start := 289396, 
                                                          stop := 289406 ), 
                                                      rec( 
                                                          content := " is a pa\
ir consisting of a\n    permutation of the vertices and a permutation of the e\
dges of\n    ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 289518, 
                                                          root := ~, 
                                                          start := 289504, 
                                                          stop := 289517 ), 
                                                      rec( 
                                                          content := ", then t\
his operation returns a digraph\n    constructed by relabelling the vertices a\
nd edges of ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 289629, 
                                                          root := ~, 
                                                          start := 289615, 
                                                          stop := 289628 ), 
                                                      rec( 
                                                          content := "\n    ac\
cording to ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
erm[1]", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 289661, 
                                                          root := ~, 
                                                          start := 289647, 
                                                          stop := 289660 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
erm[2]", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 289680, 
                                                          root := ~, 
                                                          start := 289666, 
                                                          stop := 289679 ), 
                                                      rec( 
                                                          content := ", respec\
tively. ", count := [ 7, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 289700, 
                                                          root := ~, 
                                                          start := 289696, 
                                                          stop := 289699 ), 
                                                      rec( 
                                                          content := "\n\n    \
In its second form, ", count := [ 7, 1, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
nMultiDigraphs", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 289748, 
                                                          root := ~, 
                                                          start := 289726, 
                                                          stop := 289747 ), 
                                                      rec( 
                                                          content := " returns\
 a digraph with vertices\n    and edges permuted by ", count := [ 7, 1, 2, 6 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
erm1", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 289819, 
                                                          root := ~, 
                                                          start := 289807, 
                                                          stop := 289818 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
erm2", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 289836, 
                                                          root := ~, 
                                                          start := 289824, 
                                                          stop := 289835 ), 
                                                      rec( 
                                                          content := ", respec\
tively. ", count := [ 7, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 289856, 
                                                          root := ~, 
                                                          start := 289852, 
                                                          stop := 289855 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
nDigraphs(", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "digraph", count := [ 7, 1, 2, 7 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 1, 2, 7 ], 
                                                                  mathmode := \
"Text", name := "A", next := 289900, root := ~, start := 289886, stop := 28989\
9 ), rec( content := ",\n      perm)=OnMultiDigraphs(", count := [ 7, 1, 2, 7 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "A", 
                                                                  next := 2899\
44, root := ~, start := 289930, stop := 289943 ), rec( content := ", [perm, ()\
])", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 289961, 
                                                          root := ~, 
                                                          start := 289872, 
                                                          stop := 289960 ), 
                                                      rec( 
                                                          content := " where "
                                                            , 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
erm", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 289979, 
                                                          root := ~, 
                                                          start := 289968, 
                                                          stop := 289978 ), 
                                                      rec( 
                                                          content := " is\n   \
 a permutation of the vertices of ", count := [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 290034, 
                                                          root := ~, 
                                                          start := 290020, 
                                                          stop := 290033 ), 
                                                      rec( 
                                                          content := ". If you\
 are only interested\n    in the action of a permutation on the vertices of a \
digraph, then you can\n    use ", count := [ 7, 1, 2, 7 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
nDigraphs", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 290166, 
                                                          root := ~, 
                                                          start := 290149, 
                                                          stop := 290165 ), 
                                                      rec( 
                                                          content := " instead\
 of ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
nMultiDigraphs", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 290200, 
                                                          root := ~, 
                                                          start := 290178, 
                                                          stop := 290199 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 If ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 290224, 
                                                          root := ~, 
                                                          start := 290210, 
                                                          stop := 290223 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 7, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 290266, 
                                                          root := ~, 
                                                          start := 290236, 
                                                          stop := 290265 ), 
                                                      rec( 
                                                          content := ", then\n\
    relabelling of the vertices is performed directly on ", 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 290344, 
                                                          root := ~, 
                                                          start := 290330, 
                                                          stop := 290343 ), 
                                                      rec( 
                                                          content := ".\n    I\
f ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 290367, 
                                                          root := ~, 
                                                          start := 290353, 
                                                          stop := 290366 ), 
                                                      rec( 
                                                          content := " belongs\
 to ", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 7, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 290411, 
                                                          root := ~, 
                                                          start := 290379, 
                                                          stop := 290410 ), 
                                                      rec( 
                                                          content := ", an imm\
utable\n    copy of ", count := [ 7, 1, 2, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 290452, 
                                                          root := ~, 
                                                          start := 290438, 
                                                          stop := 290451 ), 
                                                      rec( 
                                                          content := " with th\
e vertices relabelled is returned.", count := [ 7, 1, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 1, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 290498, 
                                                          root := ~, 
                                                          start := 290494, 
                                                          stop := 290497 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D1 := Digraph([\n> [3, 6, 3], [], [3], [9, 10], [9], [],  [], [10, 4, 10\
], [], []]);\n<immutable multidigraph with 10 vertices, 10 edges>\ngap> p := B\
lissCanonicalLabelling(D1);\n[ (1,7)(3,6)(4,10)(5,9), () ]\ngap> D2 := OnMulti\
Digraphs(D1, p);\n<immutable multidigraph with 10 vertices, 10 edges>\ngap> Ou\
tNeighbours(D2);\n[ [  ], [  ], [  ], [  ], [  ], [ 6 ], [ 6, 3, 6 ], [ 4, 10,\
 4 ], \n  [ 5 ], [ 5, 4 ] ]", count := [ 7, 1, 2, 9 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 1, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 290943, 
                                                          root := ~, 
                                                          start := 290504, 
                                                          stop := 290942 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 1, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 1, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 290960, root := ~, 
                                                  start := 289342, 
                                                  stop := 290959 ) ], 
                                          count := [ 7, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 290974, root := ~, 
                                          start := 289139, stop := 290973 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 7, 1, 2, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 7, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 290988, 
                                  root := ~, start := 286751, stop := 290987 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 7, 1, 2, 10 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( 
                                      Label := "Isomorphisms and canonical lab\
ellings" ), content := [ rec( content := "\n    ", count := [ 7, 2, 0, 1 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Isomorphisms and \
canonical labellings", count := [ 7, 2, 0, 2 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 7, 2, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 291108, 
                                          root := ~, start := 291052, 
                                          stop := 291107 ), 
                                      rec( 
                                          content := "\n    From version 0.11.\
0 of ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 7, 2, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( 
                                          content := " it is possible to use e\
ither ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "bliss" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://ww\
w.tcs.tkk.fi/Software/bliss/", count := [ 7, 2, 0, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 81, 
                                                  root := ~, start := 17, 
                                                  stop := 80 ) ], 
                                          count := [ 7, 2, 0, 3 ], 
                                          name := "Alt", next := 87, 
                                          root := ~, start := 1, stop := 86 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "bliss", 
                                                          count := 
                                                            [ 7, 2, 0, 3 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  name := "Package", 
                                                  next := 131, root := ~, 
                                                  start := 107, stop := 130 ) 
                                             ], count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 137, root := ~, 
                                          start := 87, stop := 136 ), 
                                      rec( content := " or\n    ", 
                                          count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "nauty" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://pa\
llini.di.uniroma1.it/", count := [ 7, 2, 0, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 74, 
                                                  root := ~, start := 17, 
                                                  stop := 73 ) ], 
                                          count := [ 7, 2, 0, 3 ], 
                                          name := "Alt", next := 80, 
                                          root := ~, start := 1, stop := 79 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "nauty", 
                                                          count := 
                                                            [ 7, 2, 0, 3 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  name := "Package", 
                                                  next := 124, root := ~, 
                                                  start := 100, stop := 123 ) 
                                             ], count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 130, root := ~, 
                                          start := 80, stop := 129 ), 
                                      rec( content := " (via ", 
                                          count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Text := "NautyTracesInte\
rface" ), content := [ rec( content := "https://github.com/gap-packages/NautyT\
racesInterface", count := [ 7, 2, 0, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 111, 
                                                  root := ~, start := 17, 
                                                  stop := 110 ) ], 
                                          count := [ 7, 2, 0, 3 ], 
                                          name := "Alt", next := 117, 
                                          root := ~, start := 1, stop := 116 )
                                        , 
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "NautyTrac\
esInterface", count := [ 7, 2, 0, 3 ], name := "PCDATA", root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  name := "Package", 
                                                  next := 176, root := ~, 
                                                  start := 137, stop := 175 ) 
                                             ], count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 182, root := ~, 
                                          start := 117, stop := 181 ), 
                                      rec( 
                                          content := ") to calculate canonical\
 labellings and\n    automorphism groups of digraphs; see ", 
                                          count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Key := "JK07" ),
                                          content := 0, 
                                          count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Cite", 
                                          next := 291325, root := ~, 
                                          start := 291307, stop := 291324 ), 
                                      rec( content := " and ", 
                                          count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Key := "MP14" ),
                                          content := 0, 
                                          count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Cite", 
                                          next := 291354, root := ~, 
                                          start := 291330, stop := 291353 ), 
                                      rec( 
                                          content := " for more details about \
", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "bliss" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://ww\
w.tcs.tkk.fi/Software/bliss/", count := [ 7, 2, 0, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 81, 
                                                  root := ~, start := 17, 
                                                  stop := 80 ) ], 
                                          count := [ 7, 2, 0, 3 ], 
                                          name := "Alt", next := 87, 
                                          root := ~, start := 1, stop := 86 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "bliss", 
                                                          count := 
                                                            [ 7, 2, 0, 3 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  name := "Package", 
                                                  next := 131, root := ~, 
                                                  start := 107, stop := 130 ) 
                                             ], count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 137, root := ~, 
                                          start := 87, stop := 136 ), 
                                      rec( content := " and ", 
                                          count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec( Not := "Text" ),
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Text := "nauty" ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "http://pa\
llini.di.uniroma1.it/", count := [ 7, 2, 0, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "URL", next := 74, 
                                                  root := ~, start := 17, 
                                                  stop := 73 ) ], 
                                          count := [ 7, 2, 0, 3 ], 
                                          name := "Alt", next := 80, 
                                          root := ~, start := 1, stop := 79 ),
                                      rec( attributes := rec( Only := "Text" )
                                            , 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "nauty", 
                                                          count := 
                                                            [ 7, 2, 0, 3 ], 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 0, 3 ], 
                                                  name := "Package", 
                                                  next := 124, root := ~, 
                                                  start := 100, stop := 123 ) 
                                             ], count := [ 7, 2, 0, 3 ], 
                                          mathmode := "Text", name := "Alt", 
                                          next := 130, root := ~, 
                                          start := 80, stop := 129 ), 
                                      rec( 
                                          content := ",\n    respectively. \n\\
n    ", count := [ 7, 2, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "", 
                                                      Name := "DigraphsUseNaut\
y" ), content := 0, count := [ 7, 2, 1, 2 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 291476, root := ~, 
                                                  start := 291438, 
                                                  stop := 291475 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "", 
                                                      Name := "DigraphsUseBlis\
s" ), content := 0, count := [ 7, 2, 1, 4 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 291517, root := ~, 
                                                  start := 291479, 
                                                  stop := 291516 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Nothing."
                                                            , 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 291547, root := ~, 
                                                  start := 291520, 
                                                  stop := 291546 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
se functions can be used to specify whether ", count := [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 1, 5 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "URL", 
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 1, 5 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " should \
be\n    used by default by ", count := [ 7, 2, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 1, 5 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\
, 1, 5 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " is not \
available,\n    then these functions do nothing. Otherwise, by calling\n    ",
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphsUseNauty", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "C", 
                                                          next := 291809, 
                                                          root := ~, 
                                                          start := 291786, 
                                                          stop := 291808 ), 
                                                      rec( 
                                                          content := " subsequ\
ent computations will default to using\n    ", count := [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 1, 5 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " rather \
than ", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 1, 5 ], mathmode := "Text", name := "URL", 
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 1, 5 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 5 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := ", where \
possible.\n    ", count := [ 7, 2, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 291913, 
                                                          root := ~, 
                                                          start := 291909, 
                                                          stop := 291912 ), 
                                                      rec( 
                                                          content := "\n\n    \
You can call these functions at any point in a ", count := [ 7, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
AP", count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 23, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 22 ), 
                                                      rec( 
                                                          content := " session\
, as many\n    times as you like, it is guaranteed that existing digraphs rema\
in\n    valid, and that comparison of existing digraphs and newly created digr\
aphs\n    via\n    ", count := [ 7, 2, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs", Oper := "IsIsomorphicDigraph" ), content := 0, count := 
                                                            [ 7, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 292204, 
                                                          root := ~, 
                                                          start := 292150, 
                                                          stop := 292203 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs and homogeneous lists", Oper := "IsIsomorphicDigraph" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 292292, 
                                                          root := ~, 
                                                          start := 292210, 
                                                          stop := 292291 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := 
                                                            [ 7, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 292352, 
                                                          root := ~, 
                                                          start := 292298, 
                                                          stop := 292351 ), 
                                                      rec( 
                                                          content := ", and\n \
   ", count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 292444, 
                                                          root := ~, 
                                                          start := 292362, 
                                                          stop := 292443 ), 
                                                      rec( 
                                                          content := " are als\
o valid.", count := [ 7, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 292464, 
                                                          root := ~, 
                                                          start := 292460, 
                                                          stop := 292463 ), 
                                                      rec( 
                                                          content := "\n\n    \
It is also possible to compute the automorphism group of a specific digraph\n \
   using both ", count := [ 7, 2, 1, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 7 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 1, 7 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 7 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "URL", 
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 7 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 1, 7 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 1, 7 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " using "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "NautyAu\
tomorphismGroup" ), content := 0, count := [ 7, 2, 1, 7 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 292623, 
                                                          root := ~, 
                                                          start := 292587, 
                                                          stop := 292622 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "BlissAu\
tomorphismGroup", Label := "for a digraph" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 292690, 
                                                          root := ~, 
                                                          start := 292632, 
                                                          stop := 292689 ), 
                                                      rec( 
                                                          content := ", respec\
tively.\n  ", count := [ 7, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 292722, root := ~, 
                                                  start := 291550, 
                                                  stop := 292721 ) ], 
                                          count := [ 7, 2, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 292736, root := ~, 
                                          start := 291423, stop := 292735 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 1, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Label := "for a digraph"
                                                        , 
                                                      Name := "AutomorphismGro\
up" ), content := 0, count := [ 7, 2, 2, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 292825, root := ~, 
                                                  start := 292757, 
                                                  stop := 292824 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A permuta\
tion group.", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 292867, root := ~, 
                                                  start := 292828, 
                                                  stop := 292866 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 292905, 
                                                          root := ~, 
                                                          start := 292891, 
                                                          stop := 292904 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then this attribute contains the group of\n    automorphisms of ", 
                                                          count := 
                                                            [ 7, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 292997, 
                                                          root := ~, 
                                                          start := 292983, 
                                                          stop := 292996 ), 
                                                      rec( 
                                                          content := ".  An ",
                                                          count := 
                                                            [ 7, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
utomorphism", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 293022, 
                                                          root := ~, 
                                                          start := 293003, 
                                                          stop := 293021 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 293040, 
                                                          root := ~, 
                                                          start := 293026, 
                                                          stop := 293039 ), 
                                                      rec( 
                                                          content := "\n    is\
 an isomorphism from ", count := [ 7, 2, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 293082, 
                                                          root := ~, 
                                                          start := 293068, 
                                                          stop := 293081 ), 
                                                      rec( 
                                                          content := " to itse\
lf. See ", count := [ 7, 2, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := 
                                                            [ 7, 2, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 293159, 
                                                          root := ~, 
                                                          start := 293098, 
                                                          stop := 293158 ), 
                                                      rec( 
                                                          content := " for mor\
e information\n    about isomorphisms of digraphs. ", count := [ 7, 2, 2, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 293221, 
                                                          root := ~, 
                                                          start := 293217, 
                                                          stop := 293220 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 293244, 
                                                          root := ~, 
                                                          start := 293230, 
                                                          stop := 293243 ), 
                                                      rec( 
                                                          content := " is not \
a multidigraph then the automorphism group is\n    returned as a group of perm\
utations on the set of vertices of\n    ", count := [ 7, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 293382, 
                                                          root := ~, 
                                                          start := 293368, 
                                                          stop := 293381 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 2, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 293388, 
                                                          root := ~, 
                                                          start := 293384, 
                                                          stop := 293387 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 293411, 
                                                          root := ~, 
                                                          start := 293397, 
                                                          stop := 293410 ), 
                                                      rec( 
                                                          content := " is a mu\
ltidigraph then the automorphism group is returned\n    as the direct product \
of a group of permutations on the set of vertices of\n    ", 
                                                          count := 
                                                            [ 7, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 293567, 
                                                          root := ~, 
                                                          start := 293553, 
                                                          stop := 293566 ), 
                                                      rec( 
                                                          content := " with a \
group of permutations on the set of edges of\n    ", count := [ 7, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 293638, 
                                                          root := ~, 
                                                          start := 293624, 
                                                          stop := 293637 ), 
                                                      rec( 
                                                          content := ". These \
groups can be accessed using ", count := [ 7, 2, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Label := "for a domain and a positive integer", Oper := "Projection" ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 293764, 
                                                          root := ~, 
                                                          start := 293675, 
                                                          stop := 293763 ), 
                                                      rec( 
                                                          content := " on the\\
n    returned group.", count := [ 7, 2, 2, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 293795, 
                                                          root := ~, 
                                                          start := 293791, 
                                                          stop := 293794 ), 
                                                      rec( 
                                                          content := "\n\n    \
By default, the automorphism group is found using ", count := [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "URL", 
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 2, 6 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 6 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila\n    and Petteri Kaski. If ", count := [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 2, 6 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 6 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\
, 2, 6 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 6 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " is avai\
lable, then ", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 2, 6 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 2, 6 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by\n   \
 Brendan Mckay and Adolfo Piperno can be used instead; see\n    ", 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "BlissAu\
tomorphismGroup", Label := "for a digraph" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 294080, 
                                                          root := ~, 
                                                          start := 294022, 
                                                          stop := 294079 ), 
                                                      rec( 
                                                          content := ", \n    \
", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "NautyAu\
tomorphismGroup" ), content := 0, count := [ 7, 2, 2, 6 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 294123, 
                                                          root := ~, 
                                                          start := 294087, 
                                                          stop := 294122 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseBliss" ), content := 0, count := [ 7, 2, 2, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 294155, 
                                                          root := ~, 
                                                          start := 294125, 
                                                          stop := 294154 ), 
                                                      rec( 
                                                          content := ",\n    a\
nd ", count := [ 7, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseNauty" ), content := 0, count := [ 7, 2, 2, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 294195, 
                                                          root := ~, 
                                                          start := 294165, 
                                                          stop := 294194 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 294205, 
                                                          root := ~, 
                                                          start := 294201, 
                                                          stop := 294204 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the argument ", count := [ 7, 2, 2, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 294241, 
                                                          root := ~, 
                                                          start := 294227, 
                                                          stop := 294240 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this attribute is recomputed every time it \
is called. \n\n    ", count := [ 7, 2, 2, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> johnson := DigraphFromGraph6String(\"E}lw\");\n<immutable digraph with 6\
 vertices, 24 edges>\ngap> G := AutomorphismGroup(johnson);\nGroup([ (3,4), (2\
,3)(4,5), (1,2)(5,6) ])\ngap> cycle := CycleDigraph(9);\n<immutable cycle digr\
aph with 9 vertices>\ngap> G := AutomorphismGroup(cycle);\nGroup([ (1,2,3,4,5,\
6,7,8,9) ])\ngap> IsCyclic(G) and Size(G) = 9;\ntrue", count := [ 7, 2, 2, 8 ]
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 2, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 294727, 
                                                          root := ~, 
                                                          start := 294343, 
                                                          stop := 294726 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 7, 2, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 294746, root := ~, 
                                                  start := 292870, 
                                                  stop := 294745 ) ], 
                                          count := [ 7, 2, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 294762, root := ~, 
                                          start := 292742, stop := 294761 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 2, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Label := "for a digraph"
                                                        , 
                                                      Name := "BlissAutomorphi\
smGroup" ), content := 0, count := [ 7, 2, 3, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 294856, root := ~, 
                                                  start := 294783, 
                                                  stop := 294855 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex_\
colours", Label := "for a digraph and homogenous list", 
                                                      Name := "BlissAutomorphi\
smGroup" ), content := 0, count := [ 7, 2, 3, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 294973, root := ~, 
                                                  start := 294859, 
                                                  stop := 294972 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vertex_\
colours, edge_colours", Label := "for a digraph, homogenous list, and list", 
                                                      Name := "BlissAutomorphi\
smGroup" ), content := 0, count := [ 7, 2, 3, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 295111, root := ~, 
                                                  start := 294976, 
                                                  stop := 295110 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A permuta\
tion group.", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 3, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 295153, root := ~, 
                                                  start := 295114, 
                                                  stop := 295152 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 295191, 
                                                          root := ~, 
                                                          start := 295177, 
                                                          stop := 295190 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then this attribute contains the group of\n    automorphisms of ", 
                                                          count := 
                                                            [ 7, 2, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 295283, 
                                                          root := ~, 
                                                          start := 295269, 
                                                          stop := 295282 ), 
                                                      rec( 
                                                          content := " as calc\
ulated using ", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 3, 7 ], mathmode := "Text", name := "URL", 
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 3, 7 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 3, 7 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 7 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila\n    and Petteri Kaski. ", count := [ 7, 2, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 3, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 295357, 
                                                          root := ~, 
                                                          start := 295353, 
                                                          stop := 295356 ), 
                                                      rec( 
                                                          content := "\n\n    \
The attribute ", count := [ 7, 2, 3, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 3, 8 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 295430, 
                                                          root := ~, 
                                                          start := 295377, 
                                                          stop := 295429 ), 
                                                      rec( 
                                                          content := " and\n  \
  operation ", count := [ 7, 2, 3, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and a homogeneous list", Oper := "AutomorphismGroup" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 3, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 295532, 
                                                          root := ~, 
                                                          start := 295449, 
                                                          stop := 295531 ), 
                                                      rec( 
                                                          content := " returns\
\n    the value of either ", count := [ 7, 2, 3, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
lissAutomorphismGroup", count := [ 7, 2, 3, 8 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 3, 8 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 295594, 
                                                          root := ~, 
                                                          start := 295565, 
                                                          stop := 295593 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 7, 2, 3, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "NautyAu\
tomorphismGroup" ), content := 0, count := [ 7, 2, 3, 8 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 295640, 
                                                          root := ~, 
                                                          start := 295598, 
                                                          stop := 295639 ), 
                                                      rec( 
                                                          content := ". These \
groups are, of course, equal but\n    their generating sets may differ. ", 
                                                          count := 
                                                            [ 7, 2, 3, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 295723, 
                                                          root := ~, 
                                                          start := 295719, 
                                                          stop := 295722 ), 
                                                      rec( 
                                                          content := "\n    Th\
e attribute ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph, homogeneous list, and list" ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 295830, 
                                                          root := ~, 
                                                          start := 295742, 
                                                          stop := 295829 ), 
                                                      rec( 
                                                          content := " returns\
 the value of\n    ", count := [ 7, 2, 3, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
lissAutomorphismGroup", count := [ 7, 2, 3, 9 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 3, 9 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 295885, 
                                                          root := ~, 
                                                          start := 295856, 
                                                          stop := 295884 ), 
                                                      rec( 
                                                          content := " as it i\
s not implemented for ", count := [ 7, 2, 3, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 3, 9 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 3, 9 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 3, 9 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " The \n \
   requirements for the optional arguments ", count := [ 7, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ertex_colours", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 295993, 
                                                          root := ~, 
                                                          start := 295972, 
                                                          stop := 295992 ), 
                                                      rec( 
                                                          content := " and \n \
   ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge_colours", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 296022, 
                                                          root := ~, 
                                                          start := 296003, 
                                                          stop := 296021 ), 
                                                      rec( 
                                                          content := " are doc\
umented in ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph, homogeneous list, and list" ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 296129, 
                                                          root := ~, 
                                                          start := 296041, 
                                                          stop := 296128 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 See also ", count := [ 7, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseBliss" ), content := 0, count := [ 7, 2, 3, 9 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 296175, 
                                                          root := ~, 
                                                          start := 296145, 
                                                          stop := 296174 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 7, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseNauty" ), content := 0, count := [ 7, 2, 3, 9 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 296211, 
                                                          root := ~, 
                                                          start := 296181, 
                                                          stop := 296210 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 296221, 
                                                          root := ~, 
                                                          start := 296217, 
                                                          stop := 296220 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the argument ", count := [ 7, 2, 3, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 296257, 
                                                          root := ~, 
                                                          start := 296243, 
                                                          stop := 296256 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this attribute is recomputed every time it \
is called. \n\n    ", count := [ 7, 2, 3, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> G := BlissAutomorphismGroup(JohnsonDigraph(5, 2));;\ngap> IsSymmetricGro\
up(G);\ntrue\ngap> Size(G);\n120", count := [ 7, 2, 3, 11 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 3, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 296496, 
                                                          root := ~, 
                                                          start := 296359, 
                                                          stop := 296495 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 7, 2, 3, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 3, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 296515, root := ~, 
                                                  start := 295156, 
                                                  stop := 296514 ) ], 
                                          count := [ 7, 2, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 296531, root := ~, 
                                          start := 294768, stop := 296530 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 3, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, vert_c\
olours]", Name := "NautyAutomorphismGroup" ), content := 0, 
                                                  count := [ 7, 2, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 296619, root := ~, 
                                                  start := 296552, 
                                                  stop := 296618 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A permuta\
tion group.", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 296661, root := ~, 
                                                  start := 296622, 
                                                  stop := 296660 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 296699, 
                                                          root := ~, 
                                                          start := 296685, 
                                                          stop := 296698 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then this attribute contains the group of\n    automorphisms of ", 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 296791, 
                                                          root := ~, 
                                                          start := 296777, 
                                                          stop := 296790 ), 
                                                      rec( 
                                                          content := " as calc\
ulated using ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 4, 3 ], name \
:= "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by\n   \
 Brendan Mckay and Adolfo Piperno via ", count := [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 4, 3 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\
, 4, 3 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          content := " FIXME b\
e more explicit about what the second arg is ", count := [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "XMLCOMMENT"
                                                            , root := ~ ), 
                                                      rec( 
                                                          content := "\n\n    \
The attribute ", count := [ 7, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 4, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 297026, 
                                                          root := ~, 
                                                          start := 296973, 
                                                          stop := 297025 ), 
                                                      rec( 
                                                          content := " and\n  \
  operation ", count := [ 7, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and a homogeneous list", Oper := "AutomorphismGroup" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 297128, 
                                                          root := ~, 
                                                          start := 297045, 
                                                          stop := 297127 ), 
                                                      rec( 
                                                          content := " returns\
\n    the value of either ", count := [ 7, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "N\
autyAutomorphismGroup", count := [ 7, 2, 4, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 4, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 297190, 
                                                          root := ~, 
                                                          start := 297161, 
                                                          stop := 297189 ), 
                                                      rec( content := " or  ",
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "BlissAu\
tomorphismGroup", Label := "for a digraph" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 297259, 
                                                          root := ~, 
                                                          start := 297195, 
                                                          stop := 297258 ), 
                                                      rec( 
                                                          content := ".\n    T\
hese groups are, of course, equal but their generating sets may differ.", 
                                                          count := 
                                                            [ 7, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 297341, 
                                                          root := ~, 
                                                          start := 297337, 
                                                          stop := 297340 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 7, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseBliss" ), content := 0, count := [ 7, 2, 4, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 297386, 
                                                          root := ~, 
                                                          start := 297356, 
                                                          stop := 297385 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 7, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseNauty" ), content := 0, count := [ 7, 2, 4, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 297422, 
                                                          root := ~, 
                                                          start := 297392, 
                                                          stop := 297421 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 297432, 
                                                          root := ~, 
                                                          start := 297428, 
                                                          stop := 297431 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the argument ", count := [ 7, 2, 4, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 297468, 
                                                          root := ~, 
                                                          start := 297454, 
                                                          stop := 297467 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this attribute is recomputed every time it \
is called. \n\n    ", count := [ 7, 2, 4, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> NautyAutomorphismGroup(JohnsonDigraph(5, 2));\nGroup([ (3,4)(6,7)(8,9), \
(2,3)(5,6)(9,10), (2,5)(3,6)(4,7),\n (1,2)(6,8)(7,9) ])", count := [ 7, 2, 4, 
                                                                      6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 4, 6 ], mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 297724, 
                                                          root := ~, 
                                                          start := 297570, 
                                                          stop := 297723 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 7, 2, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 297743, root := ~, 
                                                  start := 296664, 
                                                  stop := 297742 ) ], 
                                          count := [ 7, 2, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 297759, root := ~, 
                                          start := 296537, stop := 297758 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 4, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vert_co\
lours", Label := "for a digraph and a homogeneous list", 
                                                      Name := "AutomorphismGro\
up" ), content := 0, count := [ 7, 2, 5, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 297889, root := ~, 
                                                  start := 297780, 
                                                  stop := 297888 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A permuta\
tion group.", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 297931, root := ~, 
                                                  start := 297892, 
                                                  stop := 297930 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\n    T\
his operation computes the automorphism group of a vertex-coloured digraph.\n \
   A vertex-coloured digraph can be specified by its underlying digraph\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 298121, 
                                                          root := ~, 
                                                          start := 298107, 
                                                          stop := 298120 ), 
                                                      rec( 
                                                          content := " and its\
 colouring ", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ert_colours", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 298159, 
                                                          root := ~, 
                                                          start := 298140, 
                                                          stop := 298158 ), 
                                                      rec( 
                                                          content := ". Let ",
                                                          count := 
                                                            [ 7, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 298173, 
                                                          root := ~, 
                                                          start := 298165, 
                                                          stop := 298172 ), 
                                                      rec( 
                                                          content := " be the\\
n    number of vertices of ", count := [ 7, 2, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 298221, 
                                                          root := ~, 
                                                          start := 298207, 
                                                          stop := 298220 ), 
                                                      rec( 
                                                          content := ". The co\
louring ", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ert_colours", count := [ 7, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 298256, 
                                                          root := ~, 
                                                          start := 298237, 
                                                          stop := 298255 ), 
                                                      rec( 
                                                          content := " may\n  \
  have one of the following two forms:\n\n    ", count := [ 7, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        a list of ", count := [ 7, 2\
, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 7, 2, 5, 5 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ], mathmode\
 := "Text", name := "C", next := 298353, root := ~, start := 298345, stop := 2\
98352 ), rec( content := " integers, where ", count := [ 7, 2, 5, 5 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conten\
t := [ rec( content := "vert_colours", count := [ 7, 2, 5, 5 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ], mathmode := "T\
ext", name := "A", next := 298389, root := ~, start := 298370, stop := 298388 
                                                                         ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[i]", count := [ 7, 2, 5, 5 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 298399, root := ~, start := 298389, stop \
:= 298398 ), rec( content := " is the\n        colour of vertex ", count := [ \
7, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := [ rec( content := "i", count := [ 7, 2, 5, 5 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ], math\
mode := "Text", name := "C", next := 298440, root := ~, start := 298432, stop \
:= 298439 ), rec( content := ", using the colours ", count := [ 7, 2, 5, 5 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "[1 .. m]", count := [ 7, 2, 5, 5 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 5 ], mathmode := "Tex\
t", name := "C", next := 298475, root := ~, start := 298460, stop := 298474 ),
                                                                      rec( 
                                                                          cont\
ent := " for some\n        ", count := [ 7, 2, 5, 5 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "m <= n", count := [ 7, 2, 5, 5 ], mathmode := "Text", name := "PCDATA",\
 root := ~ ) ], count := [ 7, 2, 5, 5 ], mathmode := "Text", name := "C", next\
 := 298509, root := ~, start := 298493, stop := 298508 ), rec( content := "; o\
r\n      ", count := [ 7, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 5, 5 ], name := "Item", next := 298527, 
                                                                  root := ~, 
                                                                  start := 298\
320, stop := 298526 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        a list of non-empty disjoint lists whose union is\n        ", 
                                                                          coun\
t := [ 7, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "DigraphVertices(", count := [\
 7, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "digraph", count := [ 7, 2, 5, 7 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 \
], mathmode := "Text", name := "A", next := 298640, root := ~, start := 298626\
, stop := 298639 ), rec( content := ")", count := [ 7, 2, 5, 7 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ], mathmode := \
"Text", name := "C", next := 298645, root := ~, start := 298607, stop := 29864\
4 ), rec( content := ", such that\n        ", count := [ 7, 2, 5, 7 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conten\
t := [ rec( content := "vert_colours", count := [ 7, 2, 5, 7 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ], mathmode := "T\
ext", name := "A", next := 298684, root := ~, start := 298665, stop := 298683 
                                                                         ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[i]", count := [ 7, 2, 5, 7 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 298694, root := ~, start := 298684, stop \
:= 298693 ), rec( content := " is the list of all vertices with colour\n      \
  ", count := [ 7, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "i", count := [ 7, 2, 5, 7 ], \
mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ], 
                                                                          math\
mode := "Text", name := "C", next := 298751, root := ~, start := 298743, stop \
:= 298750 ), rec( content := ".\n      ", count := [ 7, 2, 5, 7 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 7 ], 
                                                                  name := "Ite\
m", next := 298766, root := ~, start := 298534, stop := 298765 ) ], 
                                                          count := 
                                                            [ 7, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 298778, 
                                                          root := ~, 
                                                          start := 298307, 
                                                          stop := 298777 ), 
                                                      rec( 
                                                          content := "\n\n    \
The ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
utomorphism group", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "E", 
                                                          next := 298813, 
                                                          root := ~, 
                                                          start := 298788, 
                                                          stop := 298812 ), 
                                                      rec( 
                                                          content := " of a co\
loured digraph ", count := [ 7, 2, 5, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 298850, 
                                                          root := ~, 
                                                          start := 298836, 
                                                          stop := 298849 ), 
                                                      rec( 
                                                          content := " with\n \
   colouring ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ert_colours", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 298889, 
                                                          root := ~, 
                                                          start := 298870, 
                                                          stop := 298888 ), 
                                                      rec( 
                                                          content := " is the \
group consisting of its automorphisms; an\n    ", count := [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
utomorphism", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 298962, 
                                                          root := ~, 
                                                          start := 298943, 
                                                          stop := 298961 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 298980, 
                                                          root := ~, 
                                                          start := 298966, 
                                                          stop := 298979 ), 
                                                      rec( 
                                                          content := " is an i\
somorphism of coloured\n    digraphs from ", count := [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 299043, 
                                                          root := ~, 
                                                          start := 299029, 
                                                          stop := 299042 ), 
                                                      rec( 
                                                          content := " to itse\
lf.  This group is equal to the\n    subgroup of ", count := [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
utomorphismGroup(", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "di\
graph", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root :=\
 ~ ) ], count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "A", next := 2991\
34, root := ~, start := 299120, stop := 299133 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      5, 9 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 299139, 
                                                          root := ~, 
                                                          start := 299099, 
                                                          stop := 299138 ), 
                                                      rec( 
                                                          content := " consist\
ing of those\n    automorphisms that preserve the colouring specified by ", 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ert_colours", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 299238, 
                                                          root := ~, 
                                                          start := 299219, 
                                                          stop := 299237 ), 
                                                      rec( 
                                                          content := ". See\n \
   ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 2, 5, 9 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 299302, 
                                                          root := ~, 
                                                          start := 299248, 
                                                          stop := 299301 ), 
                                                      rec( 
                                                          content := ", and se\
e ", count := [ 7, 2, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 299395, 
                                                          root := ~, 
                                                          start := 299312, 
                                                          stop := 299394 ), 
                                                      rec( 
                                                          content := "\n    fo\
r more information about isomorphisms of coloured digraphs. ", 
                                                          count := 
                                                            [ 7, 2, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 299466, 
                                                          root := ~, 
                                                          start := 299462, 
                                                          stop := 299465 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 299489, 
                                                          root := ~, 
                                                          start := 299475, 
                                                          stop := 299488 ), 
                                                      rec( 
                                                          content := " is not \
a multidigraph then the automorphism group is\n    returned as a group of perm\
utations on the set of vertices of\n    ", count := [ 7, 2, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 299627, 
                                                          root := ~, 
                                                          start := 299613, 
                                                          stop := 299626 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 2, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 299633, 
                                                          root := ~, 
                                                          start := 299629, 
                                                          stop := 299632 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 299656, 
                                                          root := ~, 
                                                          start := 299642, 
                                                          stop := 299655 ), 
                                                      rec( 
                                                          content := " is a mu\
ltidigraph then the automorphism group is returned\n    as the direct product \
of a group of permutations on the set of vertices of\n    ", 
                                                          count := 
                                                            [ 7, 2, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 299812, 
                                                          root := ~, 
                                                          start := 299798, 
                                                          stop := 299811 ), 
                                                      rec( 
                                                          content := " with a \
group of permutations on the set of edges of\n    ", count := [ 7, 2, 5, 11 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 5, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 299883, 
                                                          root := ~, 
                                                          start := 299869, 
                                                          stop := 299882 ), 
                                                      rec( 
                                                          content := ". These \
groups can be accessed using ", count := [ 7, 2, 5, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Label := "for a domain and a positive integer", Oper := "Projection" ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 300009, 
                                                          root := ~, 
                                                          start := 299920, 
                                                          stop := 300008 ), 
                                                      rec( 
                                                          content := " on the\\
n    returned group.", count := [ 7, 2, 5, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 300040, 
                                                          root := ~, 
                                                          start := 300036, 
                                                          stop := 300039 ), 
                                                      rec( 
                                                          content := "\n\n    \
By default, the automorphism group is found using ", count := [ 7, 2, 5, 12 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "URL",
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 5, 12 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 12 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila\n    and Petteri Kaski. If ", count := [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 5, 12 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 12 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\
, 5, 12 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 12 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " is avai\
lable, then ", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 5, 12 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 5, 12 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by\n   \
 Brendan Mckay and Adolfo Piperno can be used instead; see\n    ", 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "BlissAu\
tomorphismGroup", Label := "for a digraph and homogenous list" ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 300351, 
                                                          root := ~, 
                                                          start := 300267, 
                                                          stop := 300350 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "NautyAu\
tomorphismGroup" ), content := 0, count := [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 300393, 
                                                          root := ~, 
                                                          start := 300357, 
                                                          stop := 300392 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseBliss" ), content := 0, count := [ 7, 2, 5, 12 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 300425, 
                                                          root := ~, 
                                                          start := 300395, 
                                                          stop := 300424 ), 
                                                      rec( 
                                                          content := ",\n    a\
nd ", count := [ 7, 2, 5, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseNauty" ), content := 0, count := [ 7, 2, 5, 12 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 300465, 
                                                          root := ~, 
                                                          start := 300435, 
                                                          stop := 300464 ), 
                                                      rec( 
                                                          content := ".\n\n  "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 5, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> cycle := CycleDigraph(9);\n<immutable cycle digraph with 9 vertices>\nga\
p> G := AutomorphismGroup(cycle);;\ngap> IsCyclic(G) and Size(G) = 9;\ntrue\ng\
ap> colours := [[1, 4, 7], [2, 5, 8], [3, 6, 9]];;\ngap> H := AutomorphismGrou\
p(cycle, colours);;\ngap> Size(H);\n3\ngap> H = AutomorphismGroup(cycle, [1, 2\
, 3, 1, 2, 3, 1, 2, 3]);\ntrue\ngap> H = SubgroupByProperty(G, p -> OnTuplesSe\
ts(colours, p) = colours);\ntrue\ngap> IsTrivial(AutomorphismGroup(cycle, [1, \
1, 2, 2, 2, 2, 2, 2, 2]));\ntrue", count := [ 7, 2, 5, 13 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 5, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 300987, 
                                                          root := ~, 
                                                          start := 300470, 
                                                          stop := 300986 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 5, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 301004, root := ~, 
                                                  start := 297934, 
                                                  stop := 301003 ) ], 
                                          count := [ 7, 2, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 301018, root := ~, 
                                          start := 297765, stop := 301017 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 5, 14 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vert_co\
lours, edge_colours", Label := "for a digraph, homogeneous list, and list", 
                                                      Name := "AutomorphismGro\
up" ), content := 0, count := [ 7, 2, 6, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 301171, root := ~, 
                                                  start := 301039, 
                                                  stop := 301170 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A permuta\
tion group.", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 301213, root := ~, 
                                                  start := 301174, 
                                                  stop := 301212 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n\n    T\
his operation computes the automorphism group of a vertex- and/or\n    edge-co\
loured digraph.\n    A coloured digraph can be specified by its underlying dig\
raph\n    ", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 301413, 
                                                          root := ~, 
                                                          start := 301399, 
                                                          stop := 301412 ), 
                                                      rec( 
                                                          content := " and col\
ourings ", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ert_colours", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 301448, 
                                                          root := ~, 
                                                          start := 301429, 
                                                          stop := 301447 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 7, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge_colours", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 301469, 
                                                          root := ~, 
                                                          start := 301450, 
                                                          stop := 301468 ), 
                                                      rec( 
                                                          content := ".\n    L\
et ", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 301487, 
                                                          root := ~, 
                                                          start := 301479, 
                                                          stop := 301486 ), 
                                                      rec( 
                                                          content := " be the \
number of vertices of ", count := [ 7, 2, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 301531, 
                                                          root := ~, 
                                                          start := 301517, 
                                                          stop := 301530 ), 
                                                      rec( 
                                                          content := ". The co\
lourings\n    must have the following forms:\n\n    ", count := [ 7, 2, 6, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 7, 2, 6, 5 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "vert_colours", count := [ 7, 2, 6, 5 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 5 ], mathmode := \
"Text", name := "A", next := 301635, root := ~, start := 301616, stop := 30163\
4 ), rec( content := " must be ", count := [ 7, 2, 6, 5 ], mathmode := "Text",
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "fail", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "K", next :\
= 301655, root := ~, start := 301644, stop := 301654 ), rec( content := " or a\
 list of ", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "n", count :\
= [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\
= [ 7, 2, 6, 5 ], mathmode := "Text", name := "C", next := 301677, root := ~, 
                                                                          star\
t := 301669, stop := 301676 ), rec( content := " integers,\n        where ", 
                                                                          coun\
t := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "vert_colours", count := [ 7, \
2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, \
2, 6, 5 ], mathmode := "Text", name := "A", next := 301721, root := ~, start :\
= 301702, stop := 301720 ), rec( attributes := rec(  ), content := [ rec( cont\
ent := "[i]", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "C", next :\
= 301731, root := ~, start := 301721, stop := 301730 ), rec( content := " is t\
he colour of vertex ", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "P\
CDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := \
"i", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ \
) ], count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "C", next := 301764,
                                                                          root\
 := ~, start := 301756, stop := 301763 ), rec( content := ",\n        using th\
e colours ", count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "[1 .. m]", \
count := [ 7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 7, 2, 6, 5 ], mathmode := "Text", name := "C", next := 301807, root := \
~, start := 301792, stop := 301806 ), rec( content := " for some ", count := 
                                                                            [ \
7, 2, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := [ rec( content := "m <= n", count := [ 7, 2, 6, 5 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 5 ],
                                                                          math\
mode := "Text", name := "C", next := 301833, root := ~, start := 301817, stop \
:= 301832 ), rec( content := ";\n      ", count := [ 7, 2, 6, 5 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 5 ], 
                                                                  name := "Ite\
m", next := 301848, root := ~, start := 301601, stop := 301847 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        ", count := [ 7, 2, 6, 7 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "edge_colours", count := [ 7, 2, 6, 7 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], mathmode := \
"Text", name := "A", next := 301889, root := ~, start := 301870, stop := 30188\
8 ), rec( content := " must be ", count := [ 7, 2, 6, 7 ], mathmode := "Text",
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "fail", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "K", next :\
= 301909, root := ~, start := 301898, stop := 301908 ), rec( content := " or a\
 list of ", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "n", count :\
= [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\
= [ 7, 2, 6, 7 ], mathmode := "Text", name := "C", next := 301931, root := ~, 
                                                                          star\
t := 301923, stop := 301930 ), rec( content := " lists of\n        integers of\
 the same shape as ", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PC\
DATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\
OutNeighbours(digraph)", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], mathmode := "Text", name := \
"C", next := 302008, root := ~, start := 301979, stop := 302007 ), rec( conten\
t := ", where\n        ", count := [ 7, 2, 6, 7 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "edge_colours", count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 2, 6, 7 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 302043, root := ~, start := 302024, stop := 302042 ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := "[i][j]", count := [ 7, 2, 6, 7 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], mathmod\
e := "Text", name := "C", next := 302056, root := ~, start := 302043, stop := \
302055 ), rec( content := " is the colour of the edge\n        ", count := [ 7\
, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\
s := rec(  ), content := [ rec( content := "OutNeighbours(digraph)[i][j]", cou\
nt := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 7, 2, 6, 7 ], mathmode := "Text", name := "C", next := 302126, root := \
~, start := 302091, stop := 302125 ), rec( content := ", using the colours ", 
                                                                          coun\
t := [ 7, 2, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[1 .. k]", count := [ 7, 2, 6\
, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6\
, 7 ], mathmode := "Text", name := "C", next := 302161, root := ~, start := 30\
2146, stop := 302160 ), rec( content := "\n        for some ", count := [ 7, 2\
, 6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( content := "k <= n", count := [ 7, 2, 6, 7 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], 
                                                                          math\
mode := "Text", name := "C", next := 302195, root := ~, start := 302179, stop \
:= 302194 ), rec( content := ";\n      ", count := [ 7, 2, 6, 7 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 7 ], 
                                                                  name := "Ite\
m", next := 302210, root := ~, start := 301855, stop := 302209 ) ], 
                                                          count := 
                                                            [ 7, 2, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 302222, 
                                                          root := ~, 
                                                          start := 301588, 
                                                          stop := 302221 ), 
                                                      rec( 
                                                          content := "\n\n    \
Giving ", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
ert_colours", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 302254, 
                                                          root := ~, 
                                                          start := 302235, 
                                                          stop := 302253 ), 
                                                      rec( content := " [", 
                                                          count := 
                                                            [ 7, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
dge_colours", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 302275, 
                                                          root := ~, 
                                                          start := 302256, 
                                                          stop := 302274 ), 
                                                      rec( content := "] as ",
                                                          count := 
                                                            [ 7, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 2, 6, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 302291, 
                                                          root := ~, 
                                                          start := 302280, 
                                                          stop := 302290 ), 
                                                      rec( 
                                                          content := " is\n   \
 equivalent to setting all vertices [edges] to be the same colour. ", 
                                                          count := 
                                                            [ 7, 2, 6, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 302369, 
                                                          root := ~, 
                                                          start := 302365, 
                                                          stop := 302368 ), 
                                                      rec( 
                                                          content := "\n\n    \
Unlike ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 302435, 
                                                          root := ~, 
                                                          start := 302382, 
                                                          stop := 302434 ), 
                                                      rec( 
                                                          content := ", it is\\
n    possible to obtain the automorphism group of an edge-coloured multidigrap\
h\n    (see ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsMulti\
Digraph" ), content := 0, count := [ 7, 2, 6, 10 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 302560, 
                                                          root := ~, 
                                                          start := 302531, 
                                                          stop := 302559 ), 
                                                      rec( 
                                                          content := ") when n\
o two edges share the same\n    source, range, and colour.\n\n    The ", 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
utomorphism group", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 302660, 
                                                          root := ~, 
                                                          start := 302635, 
                                                          stop := 302659 ), 
                                                      rec( 
                                                          content := " of a ve\
rtex/edge-coloured digraph\n    ", count := [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 302713, 
                                                          root := ~, 
                                                          start := 302699, 
                                                          stop := 302712 ), 
                                                      rec( 
                                                          content := " with co\
louring ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 302737, 
                                                          root := ~, 
                                                          start := 302729, 
                                                          stop := 302736 ), 
                                                      rec( 
                                                          content := " is the \
group consisting of its\n    vertex/edge-colour preserving automorphisms; an\n\
    ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
utomorphism", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 302844, 
                                                          root := ~, 
                                                          start := 302825, 
                                                          stop := 302843 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 302862, 
                                                          root := ~, 
                                                          start := 302848, 
                                                          stop := 302861 ), 
                                                      rec( 
                                                          content := " is an i\
somorphism of vertex/edge-coloured\n    digraphs from ", count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 302937, 
                                                          root := ~, 
                                                          start := 302923, 
                                                          stop := 302936 ), 
                                                      rec( 
                                                          content := " to itse\
lf.  This group is equal to the\n    subgroup of ", count := [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
utomorphismGroup(", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "d\
igraph", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "A", 
                                                                  next := 3030\
28, root := ~, start := 303014, stop := 303027 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      6, 10 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 303033, 
                                                          root := ~, 
                                                          start := 302993, 
                                                          stop := 303032 ), 
                                                      rec( 
                                                          content := " consist\
ing of those\n    automorphisms that preserve the colouring specified by ", 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 303127, 
                                                          root := ~, 
                                                          start := 303113, 
                                                          stop := 303126 ), 
                                                      rec( 
                                                          content := ". See\n \
   ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 303191, 
                                                          root := ~, 
                                                          start := 303137, 
                                                          stop := 303190 ), 
                                                      rec( 
                                                          content := ", and se\
e ", count := [ 7, 2, 6, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 303284, 
                                                          root := ~, 
                                                          start := 303201, 
                                                          stop := 303283 ), 
                                                      rec( 
                                                          content := "\n    fo\
r more information about isomorphisms of coloured digraphs. ", 
                                                          count := 
                                                            [ 7, 2, 6, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 6, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 303355, 
                                                          root := ~, 
                                                          start := 303351, 
                                                          stop := 303354 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 303378, 
                                                          root := ~, 
                                                          start := 303364, 
                                                          stop := 303377 ), 
                                                      rec( 
                                                          content := " is not \
a multidigraph then the automorphism group is\n    returned as a group of perm\
utations on the set of vertices of\n    ", count := [ 7, 2, 6, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 303516, 
                                                          root := ~, 
                                                          start := 303502, 
                                                          stop := 303515 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 2, 6, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 6, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 303522, 
                                                          root := ~, 
                                                          start := 303518, 
                                                          stop := 303521 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 303545, 
                                                          root := ~, 
                                                          start := 303531, 
                                                          stop := 303544 ), 
                                                      rec( 
                                                          content := " is a mu\
ltidigraph then the automorphism group is returned\n    as the direct product \
of a group of permutations on the set of vertices of\n    ", 
                                                          count := 
                                                            [ 7, 2, 6, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 303701, 
                                                          root := ~, 
                                                          start := 303687, 
                                                          stop := 303700 ), 
                                                      rec( 
                                                          content := " with a \
group of permutations on the set of edges of\n    ", count := [ 7, 2, 6, 12 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 6, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 6, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 303772, 
                                                          root := ~, 
                                                          start := 303758, 
                                                          stop := 303771 ), 
                                                      rec( 
                                                          content := ". These \
groups can be accessed using ", count := [ 7, 2, 6, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Label := "for a domain and a positive integer", Oper := "Projection" ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 6, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 303898, 
                                                          root := ~, 
                                                          start := 303809, 
                                                          stop := 303897 ), 
                                                      rec( 
                                                          content := " on the\\
n    returned group.", count := [ 7, 2, 6, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 303929, 
                                                          root := ~, 
                                                          start := 303925, 
                                                          stop := 303928 ), 
                                                      rec( 
                                                          content := "\n\n    \
By default, the automorphism group is found using ", count := [ 7, 2, 6, 13 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "URL",
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 6, 13 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 13 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila\n    and Petteri Kaski. If ", count := [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 6, 13 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 13 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\
, 6, 13 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 13 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " is avai\
lable, then ", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 6, 13 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 6, 13 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by\n   \
 Brendan Mckay and Adolfo Piperno can be used instead; see\n     ", 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "BlissAu\
tomorphismGroup", Label := "for a digraph, homogenous list, and list" ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 304249, 
                                                          root := ~, 
                                                          start := 304157, 
                                                          stop := 304248 ), 
                                                      rec( 
                                                          content := ",\n     \
", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "NautyAu\
tomorphismGroup" ), content := 0, count := [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 304292, 
                                                          root := ~, 
                                                          start := 304256, 
                                                          stop := 304291 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseBliss" ), content := 0, count := [ 7, 2, 6, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 304324, 
                                                          root := ~, 
                                                          start := 304294, 
                                                          stop := 304323 ), 
                                                      rec( 
                                                          content := ", and\n \
    ", count := [ 7, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseNauty" ), content := 0, count := [ 7, 2, 6, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 304365, 
                                                          root := ~, 
                                                          start := 304335, 
                                                          stop := 304364 ), 
                                                      rec( 
                                                          content := ".\n\n  "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 6, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> cycle := CycleDigraph(12);\n<immutable cycle digraph with 12 vertices>\n\
gap> vert_colours := List([1 .. 12], x -> x mod 3 + 1);;\ngap> edge_colours :=\
 List([1 .. 12], x -> [x mod 2 + 1]);;\ngap> Size(AutomorphismGroup(cycle));\n\
12\ngap> Size(AutomorphismGroup(cycle, vert_colours));\n4\ngap> Size(Automorph\
ismGroup(cycle, fail, edge_colours));\n6\ngap> Size(AutomorphismGroup(cycle, v\
ert_colours, edge_colours));\n2\ngap> IsTrivial(AutomorphismGroup(cycle,\n> ve\
rt_colours, List([1 .. 12], x -> [x mod 4 + 1])));\ntrue\n", count := 
                                                                    [ 7, 2, 
                                                                      6, 14 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 6, 14 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 304912, 
                                                          root := ~, 
                                                          start := 304370, 
                                                          stop := 304911 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 6, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 304929, root := ~, 
                                                  start := 301216, 
                                                  stop := 304928 ) ], 
                                          count := [ 7, 2, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 304943, root := ~, 
                                          start := 301024, stop := 304942 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 6, 15 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Label := "for a digraph"
                                                        , 
                                                      Name := "BlissCanonicalL\
abelling" ), content := 0, count := [ 7, 2, 7, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 305038, root := ~, 
                                                  start := 304964, 
                                                  stop := 305037 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Label := "for a digraph"
                                                        , 
                                                      Name := "NautyCanonicalL\
abelling" ), content := 0, count := [ 7, 2, 7, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 305115, root := ~, 
                                                  start := 305041, 
                                                  stop := 305114 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A permuta\
tion, or a list of two permutations.", count := [ 7, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 7, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 305182, root := ~, 
                                                  start := 305118, 
                                                  stop := 305181 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A f\
unction ", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\rho", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 305225, 
                                                          root := ~, 
                                                          start := 305214, 
                                                          stop := 305224 ), 
                                                      rec( 
                                                          content := " that ma\
ps a digraph to a digraph is a ", count := [ 7, 2, 7, 5 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
anonical\n      representative map", count := [ 7, 2, 7, 5 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 305305, 
                                                          root := ~, 
                                                          start := 305264, 
                                                          stop := 305304 ), 
                                                      rec( 
                                                          content := " if the \
following two conditions hold for all\n    digraphs ", count := [ 7, 2, 7, 5 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 305372, 
                                                          root := ~, 
                                                          start := 305364, 
                                                          stop := 305371 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
", count := [ 7, 2, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 305385, 
                                                          root := ~, 
                                                          start := 305377, 
                                                          stop := 305384 ), 
                                                      rec( content := ": ", 
                                                          count := 
                                                            [ 7, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 305391, 
                                                          root := ~, 
                                                          start := 305387, 
                                                          stop := 305390 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 7, 2, 7, 8 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "\\rho(G)", count := [ 7, 2, 7, 8 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 8 ], mathmode := "Tex\
t", name := "M", next := 305439, root := ~, start := 305425, stop := 305438 ),
                                                                      rec( 
                                                                          cont\
ent := " and ", count := [ 7, 2, 7, 8 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "G", count :\
= [ 7, 2, 7, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\
= [ 7, 2, 7, 8 ], mathmode := "Text", name := "M", next := 305452, root := ~, 
                                                                          star\
t := 305444, stop := 305451 ), rec( content := " are isomorphic as digraphs; a\
nd\n      ", count := [ 7, 2, 7, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 7, 8 ], name := "Item", next := 305498, 
                                                                  root := ~, 
                                                                  start := 305\
410, stop := 305497 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        ", count := [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\\rho(G)=\\\
rho(H)", count := [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 7, 10 ], mathmode := "Text", name := "M", next := 3\
05542, root := ~, start := 305520, stop := 305541 ), rec( content := " if and \
only if ", count := [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "G", count :\
= [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \
:= [ 7, 2, 7, 10 ], mathmode := "Text", name := "M", next := 305566, root := ~
                                                                            , 
                                                                          star\
t := 305558, stop := 305565 ), rec( content := " and ", count := [ 7, 2, 7, 10\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
  ), content := [ rec( content := "H", count := [ 7, 2, 7, 10 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 10 ], mathmode := \
"Text", name := "M", next := 305579, root := ~, start := 305571, stop := 30557\
8 ), rec( content := " are\n        isomorphic as digraphs.\n      ", count :=\
 [ 7, 2, 7, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      7, 10 ],
                                                                  name := "Ite\
m", next := 305629, root := ~, start := 305505, stop := 305628 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 305641, 
                                                          root := ~, 
                                                          start := 305397, 
                                                          stop := 305640 ), 
                                                      rec( 
                                                          content := "\n\n    \
A ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
anonical labelling", count := [ 7, 2, 7, 12 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 7, 12 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 305675, 
                                                          root := ~, 
                                                          start := 305649, 
                                                          stop := 305674 ), 
                                                      rec( 
                                                          content := " of a di\
graph ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 305697, 
                                                          root := ~, 
                                                          start := 305689, 
                                                          stop := 305696 ), 
                                                      rec( 
                                                          content := " (under \
", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\rho", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 305716, 
                                                          root := ~, 
                                                          start := 305705, 
                                                          stop := 305715 ), 
                                                      rec( 
                                                          content := ") is an\\
n    isomorphism of ", count := [ 7, 2, 7, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 305751, 
                                                          root := ~, 
                                                          start := 305743, 
                                                          stop := 305750 ), 
                                                      rec( 
                                                          content := " onto it\
s ", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
anonical representative", count := [ 7, 2, 7, 12 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 7, 12 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 305792, 
                                                          root := ~, 
                                                          start := 305761, 
                                                          stop := 305791 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\rho(G)", count := [ 7, 2, 7, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 305812, 
                                                          root := ~, 
                                                          start := 305798, 
                                                          stop := 305811 ), 
                                                      rec( 
                                                          content := ".  See "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := 
                                                            [ 7, 2, 7, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 305874, 
                                                          root := ~, 
                                                          start := 305819, 
                                                          stop := 305873 ), 
                                                      rec( 
                                                          content := "\n    fo\
r more information about isomorphisms of digraphs. ", count := [ 7, 2, 7, 12 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 305936, 
                                                          root := ~, 
                                                          start := 305932, 
                                                          stop := 305935 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
lissCanonicalLabelling", count := [ 7, 2, 7, 13 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 305972, 
                                                          root := ~, 
                                                          start := 305942, 
                                                          stop := 305971 ), 
                                                      rec( 
                                                          content := " returns\
 a canonical labelling of the digraph\n    ", count := [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 306036, 
                                                          root := ~, 
                                                          start := 306022, 
                                                          stop := 306035 ), 
                                                      rec( 
                                                          content := " found u\
sing ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "URL",
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 7, 13 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila and Petteri Kaski.\n    ", count := [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "N\
autyCanonicalLabelling", count := [ 7, 2, 7, 13 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 306128, 
                                                          root := ~, 
                                                          start := 306098, 
                                                          stop := 306127 ), 
                                                      rec( 
                                                          content := " returns\
 a canonical labelling of the digraph\n    ", count := [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 306192, 
                                                          root := ~, 
                                                          start := 306178, 
                                                          stop := 306191 ), 
                                                      rec( 
                                                          content := " found u\
sing ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 7, 13 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by Bren\
dan McKay and Adolfo Piperno.\n    Note that the canonical labellings returned\
 by ", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "URL",
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 7, 13 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 2, 7, 13 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 7, 13 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 7, 13 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " are not\
\n    usually the same (and may depend of the version used).", 
                                                          count := 
                                                            [ 7, 2, 7, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 7, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 306391, 
                                                          root := ~, 
                                                          start := 306387, 
                                                          stop := 306390 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
lissCanonicalLabelling", count := [ 7, 2, 7, 14 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 7, 14 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 306427, 
                                                          root := ~, 
                                                          start := 306397, 
                                                          stop := 306426 ), 
                                                      rec( 
                                                          content := " can onl\
y be computed if ", count := [ 7, 2, 7, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 7, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 7, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 306466, 
                                                          root := ~, 
                                                          start := 306452, 
                                                          stop := 306465 ), 
                                                      rec( 
                                                          content := " has\n  \
  no multiple edges; see ", count := [ 7, 2, 7, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsMulti\
Digraph" ), content := 0, count := [ 7, 2, 7, 14 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 306527, 
                                                          root := ~, 
                                                          start := 306498, 
                                                          stop := 306526 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 2, 7, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 7, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 306533, 
                                                          root := ~, 
                                                          start := 306529, 
                                                          stop := 306532 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 7, 15 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph1 := DigraphFromDiSparse6String(\".ImNS_AiB?qRN\");\n<immutable d\
igraph with 10 vertices, 8 edges>\ngap> BlissCanonicalLabelling(digraph1);\n(1\
,9,5,7)(3,6,4,10)\ngap> p := (1, 2, 7, 5)(3, 9)(6, 10, 8);;\ngap> digraph2 := \
OnDigraphs(digraph1, p);\n<immutable digraph with 10 vertices, 8 edges>\ngap> \
digraph1 = digraph2;\nfalse\ngap> OnDigraphs(digraph1, BlissCanonicalLabelling\
(digraph1)) =\n>    OnDigraphs(digraph2, BlissCanonicalLabelling(digraph2));\n\
true", count := [ 7, 2, 7, 16 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 7, 2, 7, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 307029, 
                                                          root := ~, 
                                                          start := 306539, 
                                                          stop := 307028 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 7, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 7, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 307046, root := ~, 
                                                  start := 305185, 
                                                  stop := 307045 ) ], 
                                          count := [ 7, 2, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 307060, root := ~, 
                                          start := 304949, stop := 307059 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 7, 17 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, colours\
", Label := "for a digraph and a list", Name := "BlissCanonicalLabelling" ), 
                                                  content := 0, 
                                                  count := [ 7, 2, 8, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 307179, root := ~, 
                                                  start := 307081, 
                                                  stop := 307178 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, colours\
", Label := "for a digraph and a list", Name := "NautyCanonicalLabelling" ), 
                                                  content := 0, 
                                                  count := [ 7, 2, 8, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 307280, root := ~, 
                                                  start := 307182, 
                                                  stop := 307279 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A permuta\
tion.", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 8, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 307316, root := ~, 
                                                  start := 307283, 
                                                  stop := 307315 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A f\
unction ", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\rho", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 307359, 
                                                          root := ~, 
                                                          start := 307348, 
                                                          stop := 307358 ), 
                                                      rec( 
                                                          content := " that ma\
ps a coloured digraph to a coloured digraph is\n    a ", count := 
                                                            [ 7, 2, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
anonical representative map", count := [ 7, 2, 8, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 8, 5 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 307455, 
                                                          root := ~, 
                                                          start := 307420, 
                                                          stop := 307454 ), 
                                                      rec( 
                                                          content := " if the \
following two conditions hold\n    for all coloured digraphs ", 
                                                          count := 
                                                            [ 7, 2, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 307531, 
                                                          root := ~, 
                                                          start := 307523, 
                                                          stop := 307530 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 307544, 
                                                          root := ~, 
                                                          start := 307536, 
                                                          stop := 307543 ), 
                                                      rec( 
                                                          content := ":\n\n   \
 ", count := [ 7, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 7, 2, 8, 7 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "\\rho(G)", count := [ 7, 2, 8, 7 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 7 ], mathmode := "Tex\
t", name := "M", next := 307593, root := ~, start := 307579, stop := 307592 ),
                                                                      rec( 
                                                                          cont\
ent := " and ", count := [ 7, 2, 8, 7 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "G", count :\
= [ 7, 2, 8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\
= [ 7, 2, 8, 7 ], mathmode := "Text", name := "M", next := 307606, root := ~, 
                                                                          star\
t := 307598, stop := 307605 ), rec( content := " are isomorphic as coloured di\
graphs; and\n      ", count := [ 7, 2, 8, 7 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ 7, 2, 8, 7 ], name := "Item", next := 307661,
                                                                  root := ~, 
                                                                  start := 307\
564, stop := 307660 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        ", count := [ 7, 2, 8, 9 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\\rho(G)=\\\
rho(H)", count := [ 7, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ) ], count := [ 7, 2, 8, 9 ], mathmode := "Text", name := "M", next := 307\
705, root := ~, start := 307683, stop := 307704 ), rec( content := " if and on\
ly if ", count := [ 7, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ), rec( attributes := rec(  ), content := [ rec( content := "G", count := \
[ 7, 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                            [ \
7, 2, 8, 9 ], mathmode := "Text", name := "M", next := 307729, root := ~, star\
t := 307721, stop := 307728 ), rec( content := " and ", count := [ 7, 2, 8, 9 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "H", count := [ 7, 2, 8, 9 ], mathmode := "Text", nam\
e := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 9 ], mathmode := "Text", 
                                                                          name\
 := "M", next := 307742, root := ~, start := 307734, stop := 307741 ), 
                                                                      rec( 
                                                                          cont\
ent := " are\n        isomorphic as coloured digraphs.\n      ", count := [ 7,\
 2, 8, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 7, 2, 
                                                                      8, 9 ], 
                                                                  name := "Ite\
m", next := 307801, root := ~, start := 307668, stop := 307800 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 307813, 
                                                          root := ~, 
                                                          start := 307551, 
                                                          stop := 307812 ), 
                                                      rec( 
                                                          content := "\n\n    \
A ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
anonical labelling", count := [ 7, 2, 8, 11 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 8, 11 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 307847, 
                                                          root := ~, 
                                                          start := 307821, 
                                                          stop := 307846 ), 
                                                      rec( 
                                                          content := " of a co\
loured digraph ", count := [ 7, 2, 8, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 307878, 
                                                          root := ~, 
                                                          start := 307870, 
                                                          stop := 307877 ), 
                                                      rec( 
                                                          content := " (under\\
n    ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\rho", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 307901, 
                                                          root := ~, 
                                                          start := 307890, 
                                                          stop := 307900 ), 
                                                      rec( 
                                                          content := ") is an \
isomorphism of ", count := [ 7, 2, 8, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 307932, 
                                                          root := ~, 
                                                          start := 307924, 
                                                          stop := 307931 ), 
                                                      rec( 
                                                          content := " onto it\
s ", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
anonical\n      representative", count := [ 7, 2, 8, 11 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 8, 11 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 307979, 
                                                          root := ~, 
                                                          start := 307942, 
                                                          stop := 307978 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 7, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
\rho(G)", count := [ 7, 2, 8, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 307995, 
                                                          root := ~, 
                                                          start := 307981, 
                                                          stop := 307994 ), 
                                                      rec( 
                                                          content := ".  See "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 308085, 
                                                          root := ~, 
                                                          start := 308002, 
                                                          stop := 308084 ), 
                                                      rec( 
                                                          content := " for mor\
e information about\n    isomorphisms of coloured digraphs. ", 
                                                          count := 
                                                            [ 7, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 308156, 
                                                          root := ~, 
                                                          start := 308152, 
                                                          stop := 308155 ), 
                                                      rec( 
                                                          content := "\n\n    \
A coloured digraph can be specified by its underlying digraph ", 
                                                          count := 
                                                            [ 7, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 308238, 
                                                          root := ~, 
                                                          start := 308224, 
                                                          stop := 308237 ), 
                                                      rec( 
                                                          content := "\n    an\
d its colouring ", count := [ 7, 2, 8, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 308275, 
                                                          root := ~, 
                                                          start := 308261, 
                                                          stop := 308274 ), 
                                                      rec( 
                                                          content := ".  Let "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 308290, 
                                                          root := ~, 
                                                          start := 308282, 
                                                          stop := 308289 ), 
                                                      rec( 
                                                          content := " be the \
number of vertices of\n    ", count := [ 7, 2, 8, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 308338, 
                                                          root := ~, 
                                                          start := 308324, 
                                                          stop := 308337 ), 
                                                      rec( 
                                                          content := ". The co\
louring ", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours", count := [ 7, 2, 8, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 308368, 
                                                          root := ~, 
                                                          start := 308354, 
                                                          stop := 308367 ), 
                                                      rec( 
                                                          content := " may hav\
e one of the following\n    two forms: ", count := [ 7, 2, 8, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 8, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 308418, 
                                                          root := ~, 
                                                          start := 308414, 
                                                          stop := 308417 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 8, 13 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        a list of ", count := [ 7, 2\
, 8, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \
:= rec(  ), content := [ rec( content := "n", count := [ 7, 2, 8, 15 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15 ], mathm\
ode := "Text", name := "C", next := 308470, root := ~, start := 308462, stop :\
= 308469 ), rec( content := " integers, where ", count := [ 7, 2, 8, 15 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "colours", count := [ 7, 2, 8, 15 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15 ], mathmode := "Te\
xt", name := "A", next := 308501, root := ~, start := 308487, stop := 308500 )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[i]", count := [ 7, 2, 8, 15 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15\
 ], mathmode := "Text", name := "C", next := 308511, root := ~, start := 30850\
1, stop := 308510 ), rec( content := " is the\n        colour of vertex ", 
                                                                          coun\
t := [ 7, 2, 8, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "i", count := [ 7, 2, 8, 15 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 308552, root := ~, start := 308544, stop \
:= 308551 ), rec( content := ", using the colours ", count := [ 7, 2, 8, 15 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "[1 .. m]", count := [ 7, 2, 8, 15 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 15 ], mathmode := "T\
ext", name := "C", next := 308587, root := ~, start := 308572, stop := 308586 
                                                                         ), 
                                                                      rec( 
                                                                          cont\
ent := " for some\n        ", count := [ 7, 2, 8, 15 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "m <= n", count := [ 7, 2, 8, 15 ], mathmode := "Text", name := "PCDATA"\
, root := ~ ) ], count := [ 7, 2, 8, 15 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 308621, root := ~, start := 308605, stop := 308620 ), rec( content := "; o\
r\n      ", count := [ 7, 2, 8, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 8, 15 ], name := "Item", next := 308639, 
                                                                  root := ~, 
                                                                  start := 308\
437, stop := 308638 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        a list of non-empty disjoint lists whose union is\n        ", 
                                                                          coun\
t := [ 7, 2, 8, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "DigraphVertices(", count := [\
 7, 2, 8, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\
utes := rec(  ), content := [ rec( content := "digraph", count := [ 7, 2, 8, 1\
7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, \
17 ], mathmode := "Text", name := "A", next := 308752, root := ~, start := 308\
738, stop := 308751 ), rec( content := ")", count := [ 7, 2, 8, 17 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 17 ], mathmod\
e := "Text", name := "C", next := 308757, root := ~, start := 308719, stop := \
308756 ), rec( content := ", such that\n        ", count := [ 7, 2, 8, 17 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "colours", count := [ 7, 2, 8, 17 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 17 ], mathmode := "Te\
xt", name := "A", next := 308791, root := ~, start := 308777, stop := 308790 )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[i]", count := [ 7, 2, 8, 17 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 17\
 ], mathmode := "Text", name := "C", next := 308801, root := ~, start := 30879\
1, stop := 308800 ), rec( content := " is the list of all vertices with colour\
\n        ", count := [ 7, 2, 8, 17 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "i", count :\
= [ 7, 2, 8, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \
:= [ 7, 2, 8, 17 ], mathmode := "Text", name := "C", next := 308858, root := ~
                                                                            , 
                                                                          star\
t := 308850, stop := 308857 ), rec( content := ".\n      ", count := [ 7, 2, 8\
, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 7, 2, 
                                                                      8, 17 ],
                                                                  name := "Ite\
m", next := 308873, root := ~, start := 308646, stop := 308872 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 308885, 
                                                          root := ~, 
                                                          start := 308424, 
                                                          stop := 308884 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 308908, 
                                                          root := ~, 
                                                          start := 308894, 
                                                          stop := 308907 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 308927, 
                                                          root := ~, 
                                                          start := 308913, 
                                                          stop := 308926 ), 
                                                      rec( 
                                                          content := " togethe\
r form a coloured digraph,\n    ", count := [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
lissCanonicalLabelling", count := [ 7, 2, 8, 19 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 308996, 
                                                          root := ~, 
                                                          start := 308966, 
                                                          stop := 308995 ), 
                                                      rec( 
                                                          content := " returns\
 a canonical labelling of the digraph\n    ", count := [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 309060, 
                                                          root := ~, 
                                                          start := 309046, 
                                                          stop := 309059 ), 
                                                      rec( 
                                                          content := " found u\
sing ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "URL",
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 8, 19 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila and Petteri Kaski.\n    Similarly, ", count := [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "N\
autyCanonicalLabelling", count := [ 7, 2, 8, 19 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 309163, 
                                                          root := ~, 
                                                          start := 309133, 
                                                          stop := 309162 ), 
                                                      rec( 
                                                          content := " returns\
 a canonical labelling of\n    the digraph ", count := [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 309227, 
                                                          root := ~, 
                                                          start := 309213, 
                                                          stop := 309226 ), 
                                                      rec( 
                                                          content := " found u\
sing ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 8, 19 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by Bren\
dan McKay and Adolfo\n    Piperno.  Note that the canonical labellings returne\
d by ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "URL",
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 8, 19 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 2, 8, 19 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 8, 19 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 8, 19 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " are not\
 usually the same (and may depend of the version used).", count := 
                                                            [ 7, 2, 8, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 8, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 309427, 
                                                          root := ~, 
                                                          start := 309423, 
                                                          stop := 309426 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
lissCanonicalLabelling", count := [ 7, 2, 8, 20 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 8, 20 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 309463, 
                                                          root := ~, 
                                                          start := 309433, 
                                                          stop := 309462 ), 
                                                      rec( 
                                                          content := " can onl\
y be computed if ", count := [ 7, 2, 8, 20 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 309502, 
                                                          root := ~, 
                                                          start := 309488, 
                                                          stop := 309501 ), 
                                                      rec( 
                                                          content := " has\n  \
  no multiple edges; see ", count := [ 7, 2, 8, 20 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsMulti\
Digraph" ), content := 0, count := [ 7, 2, 8, 20 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 309563, 
                                                          root := ~, 
                                                          start := 309534, 
                                                          stop := 309562 ), 
                                                      rec( 
                                                          content := ". The ca\
nonical\n    labelling of ", count := [ 7, 2, 8, 20 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 309610, 
                                                          root := ~, 
                                                          start := 309596, 
                                                          stop := 309609 ), 
                                                      rec( 
                                                          content := " is give\
n as a permutation of its vertices.\n    The canonical representative of ", 
                                                          count := 
                                                            [ 7, 2, 8, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 309704, 
                                                          root := ~, 
                                                          start := 309690, 
                                                          stop := 309703 ), 
                                                      rec( 
                                                          content := " can be \
created from\n    ", count := [ 7, 2, 8, 20 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 309743, 
                                                          root := ~, 
                                                          start := 309729, 
                                                          stop := 309742 ), 
                                                      rec( 
                                                          content := " and its\
 canonical labelling ", count := [ 7, 2, 8, 20 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 7, 2, 8, 20 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 309780, 
                                                          root := ~, 
                                                          start := 309772, 
                                                          stop := 309779 ), 
                                                      rec( 
                                                          content := " by usin\
g the\n    operation ", count := [ 7, 2, 8, 20 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and a perm", Oper := "OnDigraphs" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 8, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 309866, 
                                                          root := ~, 
                                                          start := 309808, 
                                                          stop := 309865 ), 
                                                      rec( 
                                                          content := ":\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 8, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ap> OnDigraphs(digraph, p);", count := [ 7, 2, 8, 21 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 309911, 
                                                          root := ~, 
                                                          start := 309872, 
                                                          stop := 309910 ), 
                                                      rec( 
                                                          content := "\n\n    \
The colouring of the canonical representative can easily be\n    constructed. \
A vertex ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 310011, 
                                                          root := ~, 
                                                          start := 310003, 
                                                          stop := 310010 ), 
                                                      rec( content := " (in ",
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 310030, 
                                                          root := ~, 
                                                          start := 310016, 
                                                          stop := 310029 ), 
                                                      rec( 
                                                          content := ") has co\
lour ", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 310051, 
                                                          root := ~, 
                                                          start := 310043, 
                                                          stop := 310050 ), 
                                                      rec( 
                                                          content := " if\n   \
 and only if the vertex ", count := [ 7, 2, 8, 22 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
 ^ p", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 310094, 
                                                          root := ~, 
                                                          start := 310082, 
                                                          stop := 310093 ), 
                                                      rec( 
                                                          content := " (in the\
 canonical representative) has\n    colour ", count := [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 310152, 
                                                          root := ~, 
                                                          start := 310144, 
                                                          stop := 310151 ), 
                                                      rec( 
                                                          content := ", where \
", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 310168, 
                                                          root := ~, 
                                                          start := 310160, 
                                                          stop := 310167 ), 
                                                      rec( 
                                                          content := " is the \
permutation of the canonical\n    labelling that acts on the vertices of ", 
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 310262, 
                                                          root := ~, 
                                                          start := 310248, 
                                                          stop := 310261 ), 
                                                      rec( 
                                                          content := ". In par\
ticular, if\n    ", count := [ 7, 2, 8, 22 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours", count := [ 7, 2, 8, 22 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 310300, 
                                                          root := ~, 
                                                          start := 310286, 
                                                          stop := 310299 ), 
                                                      rec( 
                                                          content := " has the\
 first form that is described above, then the\n    colouring of the canonical \
representative is given by:\n\n    ", count := [ 7, 2, 8, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ap> List(DigraphVertices(digraph), i -> colours[i / p]);", count := [ 7, 2, 
                                                                      8, 23 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 8, 23 ], mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 310486, 
                                                          root := ~, 
                                                          start := 310418, 
                                                          stop := 310485 ), 
                                                      rec( 
                                                          content := "\n\n    \
On the other hand, if ", count := [ 7, 2, 8, 24 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours", count := [ 7, 2, 8, 24 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 24 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 310528, 
                                                          root := ~, 
                                                          start := 310514, 
                                                          stop := 310527 ), 
                                                      rec( 
                                                          content := " has the\
 second form above, then the\n    canonical representative has colouring:\n\n \
   ", count := [ 7, 2, 8, 24 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
ap> OnTuplesSets(colours, p);", count := [ 7, 2, 8, 25 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 8, 25 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 310655, 
                                                          root := ~, 
                                                          start := 310614, 
                                                          stop := 310654 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 8, 26 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 8, 27 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 310665, 
                                                          root := ~, 
                                                          start := 310661, 
                                                          stop := 310664 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 8, 27 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph := DigraphFromDiSparse6String(\".ImNS_AiB?qRN\");\n<immutable di\
graph with 10 vertices, 8 edges>\ngap> colours := [[1, 2, 8, 9, 10], [3, 4, 5,\
 6, 7]];;\ngap> p := BlissCanonicalLabelling(digraph, colours);\n(1,5,8,4,10,3\
,9)(6,7)\ngap> OnDigraphs(digraph, p);\n<immutable digraph with 10 vertices, 8\
 edges>\ngap> OnTuplesSets(colours, p);\n[ [ 1, 2, 3, 4, 5 ], [ 6, 7, 8, 9, 10\
 ] ]\ngap> colours := [1, 1, 1, 1, 2, 3, 1, 3, 2, 1];;\ngap> p := BlissCanonic\
alLabelling(digraph, colours);\n(1,6,9,7)(3,4,5,8,10)\ngap> OnDigraphs(digraph\
, p);\n<immutable digraph with 10 vertices, 8 edges>\ngap> List(DigraphVertice\
s(digraph), i -> colours[i / p]);\n[ 1, 1, 1, 1, 1, 1, 2, 2, 3, 3 ]", 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      8, 28 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 8, 28 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 311376, 
                                                          root := ~, 
                                                          start := 310671, 
                                                          stop := 311375 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 8, 29 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 8, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 311393, root := ~, 
                                                  start := 307319, 
                                                  stop := 311392 ) ], 
                                          count := [ 7, 2, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 311407, root := ~, 
                                          start := 307066, stop := 311406 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 8, 29 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "BlissCanonicalD\
igraph" ), content := 0, count := [ 7, 2, 9, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 311478, root := ~, 
                                                  start := 311428, 
                                                  stop := 311477 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "NautyCanonicalD\
igraph" ), content := 0, count := [ 7, 2, 9, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 311531, root := ~, 
                                                  start := 311481, 
                                                  stop := 311530 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 7, 2, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 311563, root := ~, 
                                                  start := 311534, 
                                                  stop := 311562 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
 attribute ", count := [ 7, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
lissCanonicalLabelling", count := [ 7, 2, 9, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 9, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 311628, 
                                                          root := ~, 
                                                          start := 311598, 
                                                          stop := 311627 ), 
                                                      rec( 
                                                          content := " returns\
 the canonical\n    representative found by applying ", count := 
                                                            [ 7, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "BlissCa\
nonicalLabelling", Label := "for a digraph" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 311753, 
                                                          root := ~, 
                                                          start := 311688, 
                                                          stop := 311752 ), 
                                                      rec( 
                                                          content := ". The di\
graph returned is canonical in the sense\n    that\n\n    ", 
                                                          count := 
                                                            [ 7, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 7, 2, 9, 7 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "BlissCanonicalDigraph(", count := [ 7, 2, 9, 7 ], ma\
thmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), c\
ontent := [ rec( content := "digraph", count := [ 7, 2, 9, 7 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 7 ], mathmode := "T\
ext", name := "A", next := 311883, root := ~, start := 311869, stop := 311882 \
), rec( content := ")", count := [ 7, 2, 9, 7 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ 7, 2, 9, 7 ], mathmode := "Text", name := "\
C", next := 311888, root := ~, start := 311844, stop := 311887 ), rec( content\
 := " and ", count := [ 7, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "digraph", c\
ount := [ 7, 2, 9, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 7, 2, 9, 7 ], mathmode := "Text", name := "A", next := 311907, root := \
~, start := 311893, stop := 311906 ), rec( content := " are\n        isomorphi\
c as digraphs; and\n      ", count := [ 7, 2, 9, 7 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 7 ], name := "Item", 
                                                                  next := 3119\
61, root := ~, start := 311829, stop := 311960 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n        If ", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :=\
 "gr", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := \
~ ) ], count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "C", next := 31199\
5, root := ~, start := 311986, stop := 311994 ), rec( content := " is any digr\
aph then ", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "BlissCanoni\
calDigraph(gr)", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA"\
, root := ~ ) ], count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 312048, root := ~, start := 312016, stop := 312047 ), rec( content := "\n \
       and ", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "BlissCanoni\
calDigraph(", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ), rec( attributes := rec(  ), content := [ rec( content := "digraph"\
, count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ]\
, count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "A", next := 312100, ro\
ot := ~, start := 312086, stop := 312099 ), rec( content := ")", count := [ 7,\
 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7,\
 2, 9, 9 ], mathmode := "Text", name := "C", next := 312105, root := ~, start \
:= 312061, stop := 312104 ), rec( content := " are equal if and only\n        \
if ", count := [ 7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~\
 ), rec( attributes := rec(  ), content := [ rec( content := "gr", count := [ \
7, 2, 9, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \
7, 2, 9, 9 ], mathmode := "Text", name := "C", next := 312148, root := ~, star\
t := 312139, stop := 312147 ), rec( content := " and ", count := [ 7, 2, 9, 9 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "digraph", count := [ 7, 2, 9, 9 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 9 ], mathmode := "Text\
", name := "A", next := 312167, root := ~, start := 312153, stop := 312166 ), 
                                                                      rec( 
                                                                          cont\
ent := " are isomorphic as digraphs.\n      ", count := [ 7, 2, 9, 9 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 9, 9 ], 
                                                                  name := "Ite\
m", next := 312209, root := ~, start := 311968, stop := 312208 ) ], 
                                                          count := 
                                                            [ 7, 2, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 312221, 
                                                          root := ~, 
                                                          start := 311816, 
                                                          stop := 312220 ), 
                                                      rec( 
                                                          content := "\n\n    \
Analogously, the attribute ", count := [ 7, 2, 9, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "N\
autyCanonicalLabelling", count := [ 7, 2, 9, 11 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 9, 11 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 312284, 
                                                          root := ~, 
                                                          start := 312254, 
                                                          stop := 312283 ), 
                                                      rec( 
                                                          content := " returns\
 the\n    canonical representative found by applying ", count := 
                                                            [ 7, 2, 9, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "NautyCa\
nonicalLabelling", Label := "for a digraph" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 9, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 312409, 
                                                          root := ~, 
                                                          start := 312344, 
                                                          stop := 312408 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 9, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 9, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 312419, 
                                                          root := ~, 
                                                          start := 312415, 
                                                          stop := 312418 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the argument ", count := [ 7, 2, 9, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 9, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 9, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 312455, 
                                                          root := ~, 
                                                          start := 312441, 
                                                          stop := 312454 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the return value of\n    this attribute is recomputed every time it \
is called. \n\n    ", count := [ 7, 2, 9, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph := Digraph([[1], [2, 3], [3], [1, 2, 3]]);\n<immutable digraph w\
ith 4 vertices, 7 edges>\ngap> canon := BlissCanonicalDigraph(digraph);\n<immu\
table digraph with 4 vertices, 7 edges>\ngap> OutNeighbours(canon);\n[ [ 1 ], \
[ 2 ], [ 3, 2 ], [ 1, 3, 2 ] ]\n", count := [ 7, 2, 9, 13 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 9, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 312848, 
                                                          root := ~, 
                                                          start := 312557, 
                                                          stop := 312847 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 9, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 312865, root := ~, 
                                                  start := 311566, 
                                                  stop := 312864 ) ], 
                                          count := [ 7, 2, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 312879, root := ~, 
                                          start := 311413, stop := 312878 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 9, 14 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphGroup" )
                                                    , content := 0, 
                                                  count := [ 7, 2, 10, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 312941, root := ~, 
                                                  start := 312900, 
                                                  stop := 312940 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A permuta\
tion group.", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 312983, root := ~, 
                                                  start := 312944, 
                                                  stop := 312982 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 313021, 
                                                          root := ~, 
                                                          start := 313007, 
                                                          stop := 313020 ), 
                                                      rec( 
                                                          content := " is immu\
table and was created knowing a subgroup of\n    its automorphism group, then \
this group is stored in the attribute\n    ", count := [ 7, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphGroup", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 313167, 
                                                          root := ~, 
                                                          start := 313148, 
                                                          stop := 313166 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 7, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 313186, 
                                                          root := ~, 
                                                          start := 313172, 
                                                          stop := 313185 ), 
                                                      rec( 
                                                          content := " is muta\
ble, or was not created\n    knowing a subgroup of its automorphism group, the\
n ", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphGroup", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 313292, 
                                                          root := ~, 
                                                          start := 313273, 
                                                          stop := 313291 ), 
                                                      rec( 
                                                          content := "\n    re\
turns the entire automorphism group of ", count := [ 7, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 313352, 
                                                          root := ~, 
                                                          start := 313338, 
                                                          stop := 313351 ), 
                                                      rec( 
                                                          content := ".    \n \
   Note that if ", count := [ 7, 2, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 313389, 
                                                          root := ~, 
                                                          start := 313375, 
                                                          stop := 313388 ), 
                                                      rec( 
                                                          content := " is muta\
ble, then the automorphism group is\n    recomputed every time this function i\
s called.\n    ", count := [ 7, 2, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 313492, 
                                                          root := ~, 
                                                          start := 313488, 
                                                          stop := 313491 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that certain other constructor operations such as  ", 
                                                          count := 
                                                            [ 7, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "CayleyD\
igraph" ), content := 0, count := [ 7, 2, 10, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 313587, 
                                                          root := ~, 
                                                          start := 313554, 
                                                          stop := 313586 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 7, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Biparti\
teDoubleDigraph" ), content := 0, count := [ 7, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 313625, 
                                                          root := ~, 
                                                          start := 313589, 
                                                          stop := 313624 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 7, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "DoubleD\
igraph" ), content := 0, count := [ 7, 2, 10, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 313664, 
                                                          root := ~, 
                                                          start := 313631, 
                                                          stop := 313663 ), 
                                                      rec( 
                                                          content := ", may no\
t require a group as one of the arguments,\n    but use the standard construct\
or method using a group, and hence set the\n    ", count := [ 7, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphGroup", count := [ 7, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 313815, 
                                                          root := ~, 
                                                          start := 313796, 
                                                          stop := 313814 ), 
                                                      rec( 
                                                          content := " attribu\
te for the resulting digraph.\n\n    ", count := [ 7, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> n := 4;;\ngap> adj := function(x, y)\n>      return (((x - y) mod n) = 1\
) or (((x - y) mod n) = n - 1);\n>    end;;\ngap> group := CyclicGroup(IsPermG\
roup, n);\nGroup([ (1,2,3,4) ])\ngap> D := Digraph(IsMutableDigraph, group, [1\
 .. n], \\^, adj);\n<mutable digraph with 4 vertices, 8 edges>\ngap> HasDigrap\
hGroup(D);\nfalse\ngap> DigraphGroup(D);\nGroup([ (2,4), (1,2)(3,4) ])\ngap> A\
utomorphismGroup(D);\nGroup([ (2,4), (1,2)(3,4) ])\ngap> D := Digraph(group, [\
1 .. n], \\^, adj);\n<immutable digraph with 4 vertices, 8 edges>\ngap> HasDig\
raphGroup(D);\ntrue\ngap> DigraphGroup(D);\nGroup([ (1,2,3,4) ])\ngap> D := Do\
ubleDigraph(D);\n<immutable digraph with 8 vertices, 32 edges>\ngap> HasDigrap\
hGroup(D);\ntrue\ngap> DigraphGroup(D);\nGroup([ (1,2,3,4)(5,6,7,8), (1,5)(2,6\
)(3,7)(4,8) ])\ngap> AutomorphismGroup(D) =\n> Group([(6, 8), (5, 7), (4, 6), \
(3, 5), (2, 4),\n>        (1, 2)(3, 4)(5, 6)(7, 8)]);\ntrue\ngap> D := Digraph\
([[2, 3], [], []]);\n<immutable digraph with 3 vertices, 2 edges>\ngap> HasDig\
raphGroup(D);\nfalse\ngap> HasAutomorphismGroup(D);\nfalse\ngap> DigraphGroup(\
D);\nGroup([ (2,3) ])\ngap> HasAutomorphismGroup(D);\ntrue\ngap> group := Dihe\
dralGroup(8);\n<pc group of size 8 with 3 generators>\ngap> D := CayleyDigraph\
(group);\n<immutable digraph with 8 vertices, 24 edges>\ngap> HasDigraphGroup(\
D);\ntrue\ngap> GeneratorsOfGroup(DigraphGroup(D));\n[ (1,2)(3,5)(4,6)(7,8), (\
1,7,4,3)(2,5,6,8), (1,4)(2,6)(3,7)(5,8) ]", count := [ 7, 2, 10, 5 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 10, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 315285, 
                                                          root := ~, 
                                                          start := 313858, 
                                                          stop := 315284 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 315302, root := ~, 
                                                  start := 312986, 
                                                  stop := 315301 ) ], 
                                          count := [ 7, 2, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 315316, root := ~, 
                                          start := 312885, stop := 315315 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 10, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphOrbits" 
                                                     ), content := 0, 
                                                  count := [ 7, 2, 11, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 315379, root := ~, 
                                                  start := 315337, 
                                                  stop := 315378 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    An \
immutable list of lists of integers.\n  ", count := [ 7, 2, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 315448, root := ~, 
                                                  start := 315382, 
                                                  stop := 315447 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 2, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphOrbits", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 315489, 
                                                          root := ~, 
                                                          start := 315469, 
                                                          stop := 315488 ), 
                                                      rec( 
                                                          content := " returns\
 the orbits of the action of the\n    ", count := [ 7, 2, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Group" ), content := 0, count := [ 7, 2, 11, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 315560, 
                                                          root := ~, 
                                                          start := 315534, 
                                                          stop := 315559 ), 
                                                      rec( 
                                                          content := " on the \
set of vertices of ", count := [ 7, 2, 11, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 315601, 
                                                          root := ~, 
                                                          start := 315587, 
                                                          stop := 315600 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> G := Group([(2, 3)(7, 8, 9), (1, 2, 3)(4, 5, 6)(8, 9)]);;\ngap> D := Edg\
eOrbitsDigraph(G, [1, 2]);\n<immutable digraph with 9 vertices, 6 edges>\ngap>\
 DigraphOrbits(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]\ngap> D := Digra\
phMutableCopy(D);\n<mutable digraph with 9 vertices, 6 edges>\ngap> DigraphOrb\
its(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6, 7, 8, 9 ] ]\n", count := [ 7, 2, 11, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 11, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 315990, 
                                                          root := ~, 
                                                          start := 315608, 
                                                          stop := 315989 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 316007, root := ~, 
                                                  start := 315451, 
                                                  stop := 316006 ) ], 
                                          count := [ 7, 2, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 316021, root := ~, 
                                          start := 315322, stop := 316020 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 11, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphOrbitRep\
s" ), content := 0, count := [ 7, 2, 12, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 316087, root := ~, 
                                                  start := 316042, 
                                                  stop := 316086 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    An \
immutable list of integers.\n  ", count := [ 7, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 316147, root := ~, 
                                                  start := 316090, 
                                                  stop := 316146 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphOrbitReps", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "C", 
                                                          next := 316191, 
                                                          root := ~, 
                                                          start := 316168, 
                                                          stop := 316190 ), 
                                                      rec( 
                                                          content := " returns\
 a list of orbit representatives\n    of the action of the ", 
                                                          count := 
                                                            [ 7, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Group" ), content := 0, count := [ 7, 2, 12, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 316283, 
                                                          root := ~, 
                                                          start := 316257, 
                                                          stop := 316282 ), 
                                                      rec( 
                                                          content := " on the \
set of vertices of\n    ", count := [ 7, 2, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 316328, 
                                                          root := ~, 
                                                          start := 316314, 
                                                          stop := 316327 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 2, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CayleyDigraph(AlternatingGroup(4));\n<immutable digraph with 12 ver\
tices, 24 edges>\ngap> DigraphOrbitReps(D);\n[ 1 ]\ngap> D := DigraphMutableCo\
py(D);\n<mutable digraph with 12 vertices, 24 edges>\ngap> DigraphOrbitReps(D)\
;\n[ 1 ]\ngap> D := DigraphFromDigraph6String(\"&IGO??S?`?_@?a?CK?O\");\n<immu\
table digraph with 10 vertices, 14 edges>\ngap> DigraphOrbitReps(D);\n[ 1, 2, \
3, 4, 5, 6, 7, 8, 9, 10 ]\ngap> DigraphOrbitReps(DigraphMutableCopy(D));\n[ 1,\
 2, 3, 4, 5, 6, 7, 8, 9, 10 ]\n", count := [ 7, 2, 12, 4 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 316849, 
                                                          root := ~, 
                                                          start := 316335, 
                                                          stop := 316848 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 316866, root := ~, 
                                                  start := 316150, 
                                                  stop := 316865 ) ], 
                                          count := [ 7, 2, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 316880, root := ~, 
                                          start := 316027, stop := 316879 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 12, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphSchreier\
Vector" ), content := 0, count := [ 7, 2, 13, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 316951, root := ~, 
                                                  start := 316901, 
                                                  stop := 316950 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    An \
immutable list of integers.\n  ", count := [ 7, 2, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 13, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 317011, root := ~, 
                                                  start := 316954, 
                                                  stop := 317010 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 2, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphSchreierVector", count := [ 7, 2, 13, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 317060, 
                                                          root := ~, 
                                                          start := 317032, 
                                                          stop := 317059 ), 
                                                      rec( 
                                                          content := " returns\
 the so-called ", count := [ 7, 2, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
chreier vector", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "E", 
                                                          next := 317105, 
                                                          root := ~, 
                                                          start := 317083, 
                                                          stop := 317104 ), 
                                                      rec( 
                                                          content := "\n    of\
 the action of the ", count := [ 7, 2, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Group" ), content := 0, count := [ 7, 2, 13, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 317157, 
                                                          root := ~, 
                                                          start := 317131, 
                                                          stop := 317156 ), 
                                                      rec( 
                                                          content := " on the \
set of vertices of\n    ", count := [ 7, 2, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 317202, 
                                                          root := ~, 
                                                          start := 317188, 
                                                          stop := 317201 ), 
                                                      rec( 
                                                          content := ". The Sc\
hreier vector is a list ", count := [ 7, 2, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ch", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 317244, 
                                                          root := ~, 
                                                          start := 317234, 
                                                          stop := 317243 ), 
                                                      rec( 
                                                          content := " of inte\
gers with\n    length ", count := [ 7, 2, 13, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphNrVertices(", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "d\
igraph", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "A", 
                                                                  next := 3173\
08, root := ~, start := 317294, stop := 317307 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      13, 3 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 317313, 
                                                          root := ~, 
                                                          start := 317273, 
                                                          stop := 317312 ), 
                                                      rec( 
                                                          content := " where:\\
n    ", count := [ 7, 2, 13, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content :\
= "sch[i] < 0:", count := [ 7, 2, 13, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 13, 4 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 317365, root := ~, start := 317344, stop := 317364 ) ], count := 
                                                                    [ 7, 2, 
                                                                      13, 4 ],
                                                                  name := "Mar\
k", next := 317372, root := ~, start := 317338, stop := 317371 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        implies that ", count := [ \
7, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "i", count := [ 7, 2, 13, 5 ], ma\
thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 5 ], 
                                                                          math\
mode := "Text", name := "C", next := 317415, root := ~, start := 317407, stop \
:= 317414 ), rec( content := " is an orbit representative and\n        ", coun\
t := [ 7, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "DigraphOrbitReps(", count := \
[ 7, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attri\
butes := rec(  ), content := [ rec( content := "digraph", count := [ 7, 2, 13,\
 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13\
, 5 ], mathmode := "Text", name := "A", next := 317489, root := ~, start := 31\
7475, stop := 317488 ), rec( content := ")[-sch[i]] = i", count := [ 7, 2, 13,\
 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13\
, 5 ], mathmode := "Text", name := "C", next := 317507, root := ~, start := 31\
7455, stop := 317506 ), rec( content := ".\n      ", count := [ 7, 2, 13, 5 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 5 ], 
                                                                  name := "Ite\
m", next := 317522, root := ~, start := 317379, stop := 317521 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "sch[i] > 0:", count := [ 7, 2, 13, 6 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 2, 13, 6 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 317557, root := ~, start := 317536, stop := 317556 ) ], count := 
                                                                    [ 7, 2, 
                                                                      13, 6 ],
                                                                  name := "Mar\
k", next := 317564, root := ~, start := 317530, stop := 317563 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        implies that ", count := [ \
7, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "i / gens[sch[i]]", count := [ 7,\
 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7\
, 2, 13, 7 ], mathmode := "Text", name := "C", next := 317622, root := ~, star\
t := 317599, stop := 317621 ), rec( content := "\n        is one step closer t\
o the root (or representative) of the tree, where\n        ", count := [ 7, 2,\
 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( content := "gens", count := [ 7, 2, 13, 7 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 7 ], 
                                                                          math\
mode := "Text", name := "C", next := 317720, root := ~, start := 317709, stop \
:= 317719 ), rec( content := " is the generators of ", count := [ 7, 2, 13, 7 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "DigraphGroup(", count := [ 7, 2, 13, 7 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :\
= [ rec( content := "digraph", count := [ 7, 2, 13, 7 ], mathmode := "Text", n\
ame := "PCDATA", root := ~ ) ], count := [ 7, 2, 13, 7 ], mathmode := "Text", \
name := "A", next := 317772, root := ~, start := 317758, stop := 317771 ), rec\
( content := ")", count := [ 7, 2, 13, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 2, 13, 7 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 317777, root := ~, start := 317742, stop := 317776 ), rec( content := ".\n\
      ", count := [ 7, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 2, 13, 7 ], name := "Item", next := 317792, 
                                                                  root := ~, 
                                                                  start := 317\
571, stop := 317791 ) ], count := [ 7, 2, 13, 4 ], mathmode := "Text", 
                                                          name := "List", 
                                                          next := 317804, 
                                                          root := ~, 
                                                          start := 317325, 
                                                          stop := 317803 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 13, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> n := 4;;\ngap> adj := function(x, y)\n>      return (((x - y) mod n) = 1\
) or (((x - y) mod n) = n - 1);\n>    end;;\ngap> group := CyclicGroup(IsPermG\
roup, n);\nGroup([ (1,2,3,4) ])\ngap> D := Digraph(IsMutableDigraph, group, [1\
 .. n], \\^, adj);\n<mutable digraph with 4 vertices, 8 edges>\ngap> sch := Di\
graphSchreierVector(D);\n[ -1, 2, 2, 1 ]\ngap> D := CayleyDigraph(AlternatingG\
roup(4));\n<immutable digraph with 12 vertices, 24 edges>\ngap> sch := Digraph\
SchreierVector(D);\n[ -1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1 ]\ngap> DigraphOrbit\
Reps(D);\n[ 1 ]\ngap> gens := GeneratorsOfGroup(DigraphGroup(D));\n[ (1,7,5)(2\
,10,9)(3,4,11)(6,8,12), (1,3,2)(4,5,6)(7,9,8)(10,11,12) ]\ngap> 10 / gens[sch[\
10]];\n2\ngap> 7 / gens[sch[7]];\n1\ngap> 5 / gens[sch[5]];\n7", count := 
                                                                    [ 7, 2, 
                                                                      13, 10 ]
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 13, 10 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 318581, 
                                                          root := ~, 
                                                          start := 317810, 
                                                          stop := 318580 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 13, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 13, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 318598, root := ~, 
                                                  start := 317014, 
                                                  stop := 318597 ) ], 
                                          count := [ 7, 2, 13, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 318612, root := ~, 
                                          start := 316886, stop := 318611 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 13, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, v", 
                                                      Name := "DigraphStabiliz\
er" ), content := 0, count := [ 7, 2, 14, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 318682, root := ~, 
                                                  start := 318633, 
                                                  stop := 318681 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A p\
ermutation group.\n  ", count := [ 7, 2, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 318732, root := ~, 
                                                  start := 318685, 
                                                  stop := 318731 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 2, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphStabilizer", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 7, 2, 14, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 318777, 
                                                          root := ~, 
                                                          start := 318753, 
                                                          stop := 318776 ), 
                                                      rec( 
                                                          content := " returns\
 the stabilizer of the vertex ", count := [ 7, 2, 14, 3 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 318823, 
                                                          root := ~, 
                                                          start := 318815, 
                                                          stop := 318822 ), 
                                                      rec( 
                                                          content := "\n    un\
der of the action of the ", count := [ 7, 2, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Group" ), content := 0, count := [ 7, 2, 14, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 318881, 
                                                          root := ~, 
                                                          start := 318855, 
                                                          stop := 318880 ), 
                                                      rec( 
                                                          content := " on the \
set of\n    vertices of ", count := [ 7, 2, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 318926, 
                                                          root := ~, 
                                                          start := 318912, 
                                                          stop := 318925 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 2, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphFromDigraph6String(\"&GYHPQgWTIIPW\");\n<immutable digraph w\
ith 8 vertices, 24 edges>\ngap> DigraphStabilizer(D, 8);\nGroup(())\ngap> Digr\
aphStabilizer(D, 2);\nGroup(())\ngap> D := DigraphMutableCopy(D);\n<mutable di\
graph with 8 vertices, 24 edges>\ngap> DigraphStabilizer(D, 8);\nGroup(())\nga\
p> DigraphStabilizer(D, 2);\nGroup(())\n", count := [ 7, 2, 14, 4 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 14, 4 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 319302, 
                                                          root := ~, 
                                                          start := 318933, 
                                                          stop := 319301 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 319319, root := ~, 
                                                  start := 318735, 
                                                  stop := 319318 ) ], 
                                          count := [ 7, 2, 14, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 319333, root := ~, 
                                          start := 318618, stop := 319332 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 14, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Label := "for digraphs", Name := "IsIsomorphicDigraph" ), content := 0, 
                                                  count := [ 7, 2, 15, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 319434, root := ~, 
                                                  start := 319354, 
                                                  stop := 319433 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 319457, 
                                                          root := ~, 
                                                          start := 319446, 
                                                          stop := 319456 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 319473, 
                                                          root := ~, 
                                                          start := 319461, 
                                                          stop := 319472 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 15, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 319484, root := ~, 
                                                  start := 319437, 
                                                  stop := 319483 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns ", count := [ 7, 2, 15, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 319539, 
                                                          root := ~, 
                                                          start := 319528, 
                                                          stop := 319538 ), 
                                                      rec( 
                                                          content := " if ther\
e exists an isomorphism from the\n    digraph ", count := [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 319607, 
                                                          root := ~, 
                                                          start := 319592, 
                                                          stop := 319606 ), 
                                                      rec( 
                                                          content := " to the \
digraph ", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 2, 15, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 319638, 
                                                          root := ~, 
                                                          start := 319623, 
                                                          stop := 319637 ), 
                                                      rec( 
                                                          content := ".  See "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := 
                                                            [ 7, 2, 15, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 319706, 
                                                          root := ~, 
                                                          start := 319645, 
                                                          stop := 319705 ), 
                                                      rec( 
                                                          content := " for mor\
e information\n    about isomorphisms of digraphs. ", count := [ 7, 2, 15, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 319768, 
                                                          root := ~, 
                                                          start := 319764, 
                                                          stop := 319767 ), 
                                                      rec( 
                                                          content := "\n\n    \
By default, an isomorphism is found using the canonical labellings of the\n   \
 digraphs obtained from ", count := [ 7, 2, 15, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "URL",
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 15, 4 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 15, 4 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 4 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila\n    and Petteri Kaski. If ", count := [ 7, 2, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 15, 4 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 4 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 7, 2, 15, 4 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\
, 15, 4 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 4 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 7, 2, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " is avai\
lable, then ", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 15, 4 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 15, 4 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 15, 4 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by\n   \
 Brendan Mckay and Adolfo Piperno can be used instead; see\n    ", 
                                                          count := 
                                                            [ 7, 2, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseBliss" ), content := 0, count := [ 7, 2, 15, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 320076, 
                                                          root := ~, 
                                                          start := 320046, 
                                                          stop := 320075 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 7, 2, 15, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseNauty" ), content := 0, count := [ 7, 2, 15, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 320112, 
                                                          root := ~, 
                                                          start := 320082, 
                                                          stop := 320111 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 2, 15, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph1 := CycleDigraph(4);\n<immutable cycle digraph with 4 vertices>\
\ngap> digraph2 := CycleDigraph(5);\n<immutable cycle digraph with 5 vertices>\
\ngap> IsIsomorphicDigraph(digraph1, digraph2);\nfalse\ngap> digraph2 := Digra\
phReverse(digraph1);\n<immutable digraph with 4 vertices, 4 edges>\ngap> IsIso\
morphicDigraph(digraph1, digraph2);\ntrue\ngap> digraph1 := Digraph([[3], [], \
[]]);\n<immutable digraph with 3 vertices, 1 edge>\ngap> digraph2 := Digraph([\
[], [], [2]]);\n<immutable digraph with 3 vertices, 1 edge>\ngap> IsIsomorphic\
Digraph(digraph1, digraph2);\ntrue", count := [ 7, 2, 15, 5 ], name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 15, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 320714, 
                                                          root := ~, 
                                                          start := 320119, 
                                                          stop := 320713 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 15, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 15, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 320731, root := ~, 
                                                  start := 319487, 
                                                  stop := 320730 ) ], 
                                          count := [ 7, 2, 15, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 320745, root := ~, 
                                          start := 319339, stop := 320744 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 15, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2, colours1, colours2", Label := "for digraphs and homogeneous lists", 
                                                      Name := "IsIsomorphicDig\
raph" ), content := 0, count := [ 7, 2, 16, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 320892, root := ~, 
                                                  start := 320766, 
                                                  stop := 320891 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 320915, 
                                                          root := ~, 
                                                          start := 320904, 
                                                          stop := 320914 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 320931, 
                                                          root := ~, 
                                                          start := 320919, 
                                                          stop := 320930 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 16, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 320942, root := ~, 
                                                  start := 320895, 
                                                  stop := 320941 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation tests for isomorphism of coloured digraphs.  A coloured\n    digra\
ph can be specified by its underlying digraph ", count := [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321104, 
                                                          root := ~, 
                                                          start := 321089, 
                                                          stop := 321103 ), 
                                                      rec( 
                                                          content := " and its\
\n    colouring ", count := [ 7, 2, 16, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours1", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321142, 
                                                          root := ~, 
                                                          start := 321127, 
                                                          stop := 321141 ), 
                                                      rec( 
                                                          content := ".  Let "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 321157, 
                                                          root := ~, 
                                                          start := 321149, 
                                                          stop := 321156 ), 
                                                      rec( 
                                                          content := " be the \
number of vertices of\n    ", count := [ 7, 2, 16, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321206, 
                                                          root := ~, 
                                                          start := 321191, 
                                                          stop := 321205 ), 
                                                      rec( 
                                                          content := ". The co\
louring ", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours1", count := [ 7, 2, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321237, 
                                                          root := ~, 
                                                          start := 321222, 
                                                          stop := 321236 ), 
                                                      rec( 
                                                          content := " may hav\
e one of the following\n    two forms:\n\n    ", count := [ 7, 2, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        a list of ", count := [ 7, 2\
, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \
:= rec(  ), content := [ rec( content := "n", count := [ 7, 2, 16, 5 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5 ], mathm\
ode := "Text", name := "C", next := 321334, root := ~, start := 321326, stop :\
= 321333 ), rec( content := " integers, where ", count := [ 7, 2, 16, 5 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "colours", count := [ 7, 2, 16, 5 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5 ], mathmode := "Te\
xt", name := "A", next := 321365, root := ~, start := 321351, stop := 321364 )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[i]", count := [ 7, 2, 16, 5 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5\
 ], mathmode := "Text", name := "C", next := 321375, root := ~, start := 32136\
5, stop := 321374 ), rec( content := " is the\n        colour of vertex ", 
                                                                          coun\
t := [ 7, 2, 16, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "i", count := [ 7, 2, 16, 5 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 321416, root := ~, start := 321408, stop \
:= 321415 ), rec( content := ", using the colours ", count := [ 7, 2, 16, 5 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "[1 .. m]", count := [ 7, 2, 16, 5 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 5 ], mathmode := "T\
ext", name := "C", next := 321451, root := ~, start := 321436, stop := 321450 
                                                                         ), 
                                                                      rec( 
                                                                          cont\
ent := " for some\n        ", count := [ 7, 2, 16, 5 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "m <= n", count := [ 7, 2, 16, 5 ], mathmode := "Text", name := "PCDATA"\
, root := ~ ) ], count := [ 7, 2, 16, 5 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 321485, root := ~, start := 321469, stop := 321484 ), rec( content := "; o\
r\n      ", count := [ 7, 2, 16, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 16, 5 ], name := "Item", next := 321503, 
                                                                  root := ~, 
                                                                  start := 321\
301, stop := 321502 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        a list of non-empty disjoint lists whose union is\n        ", 
                                                                          coun\
t := [ 7, 2, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "DigraphVertices(", count := [\
 7, 2, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\
utes := rec(  ), content := [ rec( content := "digraph", count := [ 7, 2, 16, \
7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16,\
 7 ], mathmode := "Text", name := "A", next := 321616, root := ~, start := 321\
602, stop := 321615 ), rec( content := ")", count := [ 7, 2, 16, 7 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 7 ], mathmod\
e := "Text", name := "C", next := 321621, root := ~, start := 321583, stop := \
321620 ), rec( content := ", such that\n        ", count := [ 7, 2, 16, 7 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "colours", count := [ 7, 2, 16, 7 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 7 ], mathmode := "Te\
xt", name := "A", next := 321655, root := ~, start := 321641, stop := 321654 )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[i]", count := [ 7, 2, 16, 7 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 7\
 ], mathmode := "Text", name := "C", next := 321665, root := ~, start := 32165\
5, stop := 321664 ), rec( content := " is the list of all vertices with colour\
\n        ", count := [ 7, 2, 16, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "i", count :\
= [ 7, 2, 16, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \
:= [ 7, 2, 16, 7 ], mathmode := "Text", name := "C", next := 321722, root := ~
                                                                            , 
                                                                          star\
t := 321714, stop := 321721 ), rec( content := ".\n      ", count := [ 7, 2, 1\
6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 7, 2, 
                                                                      16, 7 ],
                                                                  name := "Ite\
m", next := 321737, root := ~, start := 321510, stop := 321736 ) ], 
                                                          count := 
                                                            [ 7, 2, 16, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 321749, 
                                                          root := ~, 
                                                          start := 321288, 
                                                          stop := 321748 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321773, 
                                                          root := ~, 
                                                          start := 321758, 
                                                          stop := 321772 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321793, 
                                                          root := ~, 
                                                          start := 321778, 
                                                          stop := 321792 ), 
                                                      rec( 
                                                          content := " are dig\
raphs without multiple edges,\n    and ", count := [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours1", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321854, 
                                                          root := ~, 
                                                          start := 321839, 
                                                          stop := 321853 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours2", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321874, 
                                                          root := ~, 
                                                          start := 321859, 
                                                          stop := 321873 ), 
                                                      rec( 
                                                          content := " are col\
ourings of ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321908, 
                                                          root := ~, 
                                                          start := 321893, 
                                                          stop := 321907 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 321932, 
                                                          root := ~, 
                                                          start := 321917, 
                                                          stop := 321931 ), 
                                                      rec( 
                                                          content := ", respec\
tively, then this operation returns ", count := [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 2, 16, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 321987, 
                                                          root := ~, 
                                                          start := 321976, 
                                                          stop := 321986 ), 
                                                      rec( 
                                                          content := "\n    if\
 there exists an isomorphism between these two coloured digraphs.  See\n    ",
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs and homogeneous lists", Oper := "IsomorphismDigraphs" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 322152, 
                                                          root := ~, 
                                                          start := 322069, 
                                                          stop := 322151 ), 
                                                      rec( 
                                                          content := " for mor\
e information about isomorphisms of coloured digraphs. ", count := 
                                                            [ 7, 2, 16, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 322219, 
                                                          root := ~, 
                                                          start := 322215, 
                                                          stop := 322218 ), 
                                                      rec( 
                                                          content := "\n\n    \
By default, an isomorphism is found using the canonical labellings of the\n   \
 digraphs obtained from ", count := [ 7, 2, 16, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "URL\
", next := 81, root := ~, start := 17, stop := 80 ) ], count := 
                                                            [ 7, 2, 16, 10 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 16, 10 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 10 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila\n    and Petteri Kaski. If ", count := [ 7, 2, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 16, 10 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 10 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 7, 2, 16, 10 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\
, 16, 10 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 10 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 7, 2, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " is avai\
lable, then ", count := [ 7, 2, 16, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 16, 10 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 16, 10 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 16, 10 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by\n   \
 Brendan Mckay and Adolfo Piperno can be used instead; see\n    ", 
                                                          count := 
                                                            [ 7, 2, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseBliss" ), content := 0, count := [ 7, 2, 16, 10 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 322527, 
                                                          root := ~, 
                                                          start := 322497, 
                                                          stop := 322526 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 7, 2, 16, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseNauty" ), content := 0, count := [ 7, 2, 16, 10 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 322563, 
                                                          root := ~, 
                                                          start := 322533, 
                                                          stop := 322562 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 2, 16, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph1 := ChainDigraph(4);\n<immutable chain digraph with 4 vertices>\
\ngap> digraph2 := ChainDigraph(3);\n<immutable chain digraph with 3 vertices>\
\ngap> IsIsomorphicDigraph(digraph1, digraph2,\n>  [[1, 4], [2, 3]], [[1, 2], \
[3]]);\nfalse\ngap> digraph2 := DigraphReverse(digraph1);\n<immutable digraph \
with 4 vertices, 3 edges>\ngap> IsIsomorphicDigraph(digraph1, digraph2,\n>  [1\
, 1, 1, 1], [1, 1, 1, 1]);\ntrue\ngap> IsIsomorphicDigraph(digraph1, digraph2,\
\n>  [1, 2, 2, 1], [1, 2, 2, 1]);\ntrue\ngap> IsIsomorphicDigraph(digraph1, di\
graph2,\n>  [1, 1, 2, 2], [1, 1, 2, 2]);\nfalse", count := [ 7, 2, 16, 11 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 16, 11 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 323176, 
                                                          root := ~, 
                                                          start := 322570, 
                                                          stop := 323175 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 16, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 16, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 323193, root := ~, 
                                                  start := 320945, 
                                                  stop := 323192 ) ], 
                                          count := [ 7, 2, 16, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 323207, root := ~, 
                                          start := 320751, stop := 323206 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 16, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Label := "for digraphs", Name := "IsomorphismDigraphs" ), content := 0, 
                                                  count := [ 7, 2, 17, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 323308, root := ~, 
                                                  start := 323228, 
                                                  stop := 323307 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A permut\
ation, or a pair of permutations, or ", count := [ 7, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 323377, 
                                                          root := ~, 
                                                          start := 323366, 
                                                          stop := 323376 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 323388, root := ~, 
                                                  start := 323311, 
                                                  stop := 323387 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation returns an isomorphism between the digraphs ", 
                                                          count := 
                                                            [ 7, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 323483, 
                                                          root := ~, 
                                                          start := 323468, 
                                                          stop := 323482 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 323507, 
                                                          root := ~, 
                                                          start := 323492, 
                                                          stop := 323506 ), 
                                                      rec( 
                                                          content := " if one \
exists, else this operation returns ", count := [ 7, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 2, 17, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 323562, 
                                                          root := ~, 
                                                          start := 323551, 
                                                          stop := 323561 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 323572, 
                                                          root := ~, 
                                                          start := 323568, 
                                                          stop := 323571 ), 
                                                      rec( 
                                                          content := "\n\n    \
An ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
somorphism", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 323599, 
                                                          root := ~, 
                                                          start := 323581, 
                                                          stop := 323598 ), 
                                                      rec( 
                                                          content := " from a \
digraph ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 323630, 
                                                          root := ~, 
                                                          start := 323615, 
                                                          stop := 323629 ), 
                                                      rec( 
                                                          content := " to a di\
graph\n    ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 323663, 
                                                          root := ~, 
                                                          start := 323648, 
                                                          stop := 323662 ), 
                                                      rec( 
                                                          content := " is a bi\
jection ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 323687, 
                                                          root := ~, 
                                                          start := 323679, 
                                                          stop := 323686 ), 
                                                      rec( 
                                                          content := " from th\
e vertices of\n    ", count := [ 7, 2, 17, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 323728, 
                                                          root := ~, 
                                                          start := 323713, 
                                                          stop := 323727 ), 
                                                      rec( 
                                                          content := " to the \
vertices of ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 323763, 
                                                          root := ~, 
                                                          start := 323748, 
                                                          stop := 323762 ), 
                                                      rec( 
                                                          content := " with th\
e following\n    property: for all vertices ", count := [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 323822, 
                                                          root := ~, 
                                                          start := 323814, 
                                                          stop := 323821 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 323835, 
                                                          root := ~, 
                                                          start := 323827, 
                                                          stop := 323834 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 323854, 
                                                          root := ~, 
                                                          start := 323839, 
                                                          stop := 323853 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i, j]", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 323873, 
                                                          root := ~, 
                                                          start := 323860, 
                                                          stop := 323872 ), 
                                                      rec( 
                                                          content := " is an e\
dge of ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 323903, 
                                                          root := ~, 
                                                          start := 323888, 
                                                          stop := 323902 ), 
                                                      rec( 
                                                          content := " if and \
only if ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i ^ p, j\n      ^ p]", count := [ 7, 2, 17, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 17, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 323946, 
                                                          root := ~, 
                                                          start := 323919, 
                                                          stop := 323945 ), 
                                                      rec( 
                                                          content := " is an e\
dge of ", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 2, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 323976, 
                                                          root := ~, 
                                                          start := 323961, 
                                                          stop := 323975 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 2, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 323982, 
                                                          root := ~, 
                                                          start := 323978, 
                                                          stop := 323981 ), 
                                                      rec( 
                                                          content := "\n\n    \
If there exists such an isomorphism, then this operation returns one.\n    The\
 form of this isomorphism is a permutation ", count := [ 7, 2, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 324116, 
                                                          root := ~, 
                                                          start := 324108, 
                                                          stop := 324115 ), 
                                                      rec( 
                                                          content := " of the \
vertices of\n    ", count := [ 7, 2, 17, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 17, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 324155, 
                                                          root := ~, 
                                                          start := 324140, 
                                                          stop := 324154 ), 
                                                      rec( 
                                                          content := " such th\
at ", count := [ 7, 2, 17, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 324170, 
                                                          root := ~, 
                                                          start := 324166, 
                                                          stop := 324169 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
nDigraphs(", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "digraph1", count := [ 7, 2, 17, 6 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 324205, root := ~, start := 324190, stop := 32420\
4 ), rec( content := ", p) = digraph2", count := [ 7, 2, 17, 6 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 324224, 
                                                          root := ~, 
                                                          start := 324176, 
                                                          stop := 324223 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 By default, an isomorphism is found using the canonical labellings of the\n  \
  digraphs obtained from ", count := [ 7, 2, 17, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "URL",
                                                                  next := 81, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 80 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 6 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 17, 6 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila\n    and Petteri Kaski. If ", count := [ 7, 2, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 17, 6 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 6 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\
, 17, 6 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " is avai\
lable, then ", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 6 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 17, 6 ], name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 17, 6 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by\n   \
 Brendan Mckay and Adolfo Piperno can be used instead; see\n    ", 
                                                          count := 
                                                            [ 7, 2, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseBliss" ), content := 0, count := [ 7, 2, 17, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 324533, 
                                                          root := ~, 
                                                          start := 324503, 
                                                          stop := 324532 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 7, 2, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseNauty" ), content := 0, count := [ 7, 2, 17, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 324569, 
                                                          root := ~, 
                                                          start := 324539, 
                                                          stop := 324568 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 2, 17, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph1 := CycleDigraph(4);\n<immutable cycle digraph with 4 vertices>\
\ngap> digraph2 := CycleDigraph(5);\n<immutable cycle digraph with 5 vertices>\
\ngap> IsomorphismDigraphs(digraph1, digraph2);\nfail\ngap> digraph1 := Comple\
teBipartiteDigraph(10, 5);\n<immutable complete bipartite digraph with bicompo\
nent sizes 10 and 5>\ngap> digraph2 := CompleteBipartiteDigraph(5, 10);\n<immu\
table complete bipartite digraph with bicomponent sizes 5 and 10>\ngap> p := I\
somorphismDigraphs(digraph1, digraph2);\n(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10\
,15)\ngap> OnDigraphs(digraph1, p) = digraph2;\ntrue\n", count := [ 7, 2, 17, 
                                                                      7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 17, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 325192, 
                                                          root := ~, 
                                                          start := 324576, 
                                                          stop := 325191 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 17, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 325209, root := ~, 
                                                  start := 323391, 
                                                  stop := 325208 ) ], 
                                          count := [ 7, 2, 17, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 325223, root := ~, 
                                          start := 323213, stop := 325222 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 17, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2, colours1, colours2", Label := "for digraphs and homogeneous lists", 
                                                      Name := "IsomorphismDigr\
aphs" ), content := 0, count := [ 7, 2, 18, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 325370, root := ~, 
                                                  start := 325244, 
                                                  stop := 325369 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A permut\
ation, or ", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 325412, 
                                                          root := ~, 
                                                          start := 325401, 
                                                          stop := 325411 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 325423, root := ~, 
                                                  start := 325373, 
                                                  stop := 325422 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s operation searches for an isomorphism between coloured digraphs.  A\n    col\
oured digraph can be specified by its underlying digraph ", 
                                                          count := 
                                                            [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 325596, 
                                                          root := ~, 
                                                          start := 325581, 
                                                          stop := 325595 ), 
                                                      rec( 
                                                          content := "\n    an\
d its colouring ", count := [ 7, 2, 18, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours1", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 325634, 
                                                          root := ~, 
                                                          start := 325619, 
                                                          stop := 325633 ), 
                                                      rec( 
                                                          content := ".  Let "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 325649, 
                                                          root := ~, 
                                                          start := 325641, 
                                                          stop := 325648 ), 
                                                      rec( 
                                                          content := " be the \
number of vertices\n    of ", count := [ 7, 2, 18, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 325698, 
                                                          root := ~, 
                                                          start := 325683, 
                                                          stop := 325697 ), 
                                                      rec( 
                                                          content := ". The co\
louring ", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours1", count := [ 7, 2, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 325729, 
                                                          root := ~, 
                                                          start := 325714, 
                                                          stop := 325728 ), 
                                                      rec( 
                                                          content := " may hav\
e one of the\n    following two forms:\n\n    ", count := [ 7, 2, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        a list of ", count := [ 7, 2\
, 18, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \
:= rec(  ), content := [ rec( content := "n", count := [ 7, 2, 18, 5 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5 ], mathm\
ode := "Text", name := "C", next := 325826, root := ~, start := 325818, stop :\
= 325825 ), rec( content := " integers, where ", count := [ 7, 2, 18, 5 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "colours", count := [ 7, 2, 18, 5 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5 ], mathmode := "Te\
xt", name := "A", next := 325857, root := ~, start := 325843, stop := 325856 )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[i]", count := [ 7, 2, 18, 5 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5\
 ], mathmode := "Text", name := "C", next := 325867, root := ~, start := 32585\
7, stop := 325866 ), rec( content := " is the\n        colour of vertex ", 
                                                                          coun\
t := [ 7, 2, 18, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "i", count := [ 7, 2, 18, 5 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 325908, root := ~, start := 325900, stop \
:= 325907 ), rec( content := ", using the colours ", count := [ 7, 2, 18, 5 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "[1 .. m]", count := [ 7, 2, 18, 5 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 5 ], mathmode := "T\
ext", name := "C", next := 325943, root := ~, start := 325928, stop := 325942 
                                                                         ), 
                                                                      rec( 
                                                                          cont\
ent := " for some\n        ", count := [ 7, 2, 18, 5 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "m <= n", count := [ 7, 2, 18, 5 ], mathmode := "Text", name := "PCDATA"\
, root := ~ ) ], count := [ 7, 2, 18, 5 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 325977, root := ~, start := 325961, stop := 325976 ), rec( content := "; o\
r\n      ", count := [ 7, 2, 18, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 18, 5 ], name := "Item", next := 325995, 
                                                                  root := ~, 
                                                                  start := 325\
793, stop := 325994 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        a list of non-empty disjoint lists whose union is\n        ", 
                                                                          coun\
t := [ 7, 2, 18, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "DigraphVertices(", count := [\
 7, 2, 18, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\
utes := rec(  ), content := [ rec( content := "digraph", count := [ 7, 2, 18, \
7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18,\
 7 ], mathmode := "Text", name := "A", next := 326108, root := ~, start := 326\
094, stop := 326107 ), rec( content := ")", count := [ 7, 2, 18, 7 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 7 ], mathmod\
e := "Text", name := "C", next := 326113, root := ~, start := 326075, stop := \
326112 ), rec( content := ", such that\n        ", count := [ 7, 2, 18, 7 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "colours", count := [ 7, 2, 18, 7 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 7 ], mathmode := "Te\
xt", name := "A", next := 326147, root := ~, start := 326133, stop := 326146 )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[i]", count := [ 7, 2, 18, 7 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 7\
 ], mathmode := "Text", name := "C", next := 326157, root := ~, start := 32614\
7, stop := 326156 ), rec( content := " is the list of all vertices with colour\
\n        ", count := [ 7, 2, 18, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "i", count :\
= [ 7, 2, 18, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count \
:= [ 7, 2, 18, 7 ], mathmode := "Text", name := "C", next := 326214, root := ~
                                                                            , 
                                                                          star\
t := 326206, stop := 326213 ), rec( content := ".\n      ", count := [ 7, 2, 1\
8, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 7, 2, 
                                                                      18, 7 ],
                                                                  name := "Ite\
m", next := 326229, root := ~, start := 326002, stop := 326228 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 326241, 
                                                          root := ~, 
                                                          start := 325780, 
                                                          stop := 326240 ), 
                                                      rec( 
                                                          content := "\n\n    \
An ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
somorphism", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 326268, 
                                                          root := ~, 
                                                          start := 326250, 
                                                          stop := 326267 ), 
                                                      rec( 
                                                          content := " between\
 coloured digraphs is an isomorphism between\n    the underlying digraphs that\
 preserves the colourings.  See ", count := [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 326445, 
                                                          root := ~, 
                                                          start := 326385, 
                                                          stop := 326444 ), 
                                                      rec( 
                                                          content := " for mor\
e information\n    about isomorphisms of digraphs. More precisely, let ", 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 326531, 
                                                          root := ~, 
                                                          start := 326523, 
                                                          stop := 326530 ), 
                                                      rec( 
                                                          content := " be an\n\
    isomorphism of digraphs from the digraph ", count := [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 326598, 
                                                          root := ~, 
                                                          start := 326583, 
                                                          stop := 326597 ), 
                                                      rec( 
                                                          content := " (with c\
olouring\n    ", count := [ 7, 2, 18, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 326634, 
                                                          root := ~, 
                                                          start := 326619, 
                                                          stop := 326633 ), 
                                                      rec( 
                                                          content := ") to the\
 digraph ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 326666, 
                                                          root := ~, 
                                                          start := 326651, 
                                                          stop := 326665 ), 
                                                      rec( 
                                                          content := " (with c\
olouring\n    ", count := [ 7, 2, 18, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olours2", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 326702, 
                                                          root := ~, 
                                                          start := 326687, 
                                                          stop := 326701 ), 
                                                      rec( 
                                                          content := "), and l\
et ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 326721, 
                                                          root := ~, 
                                                          start := 326713, 
                                                          stop := 326720 ), 
                                                      rec( 
                                                          content := " be the \
permutation of the vertices of\n    ", count := [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 326779, 
                                                          root := ~, 
                                                          start := 326764, 
                                                          stop := 326778 ), 
                                                      rec( 
                                                          content := " that co\
rresponds to ", count := [ 7, 2, 18, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 326808, 
                                                          root := ~, 
                                                          start := 326800, 
                                                          stop := 326807 ), 
                                                      rec( 
                                                          content := ".  Then \
", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 326824, 
                                                          root := ~, 
                                                          start := 326816, 
                                                          stop := 326823 ), 
                                                      rec( 
                                                          content := " preserv\
es the\n    colourings of ", count := [ 7, 2, 18, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 326872, 
                                                          root := ~, 
                                                          start := 326857, 
                                                          stop := 326871 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 326892, 
                                                          root := ~, 
                                                          start := 326877, 
                                                          stop := 326891 ), 
                                                      rec( 
                                                          content := " – and\
 hence is an\n    isomorphism of coloured digraphs – if ", 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "colours1", count := [ 7, 2, 18, 9 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], 
                                                                  mathmode := \
"Text", name := "A", next := 326975, root := ~, start := 326960, stop := 32697\
4 ), rec( content := "[i] =\n      ", count := [ 7, 2, 18, 9 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          conte\
nt := "colours2", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "A", 
                                                                  next := 3270\
02, root := ~, start := 326987, stop := 327001 ), rec( content := "[i ^ p]", 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      18, 9 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 327013, 
                                                          root := ~, 
                                                          start := 326957, 
                                                          stop := 327012 ), 
                                                      rec( 
                                                          content := " for all\
 vertices ", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 327039, 
                                                          root := ~, 
                                                          start := 327031, 
                                                          stop := 327038 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 2, 18, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 327058, 
                                                          root := ~, 
                                                          start := 327043, 
                                                          stop := 327057 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 18, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 18, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 327068, 
                                                          root := ~, 
                                                          start := 327064, 
                                                          stop := 327067 ), 
                                                      rec( 
                                                          content := "\n\n    \
This operation returns such an isomorphism if one exists, else it returns\n   \
 ", count := [ 7, 2, 18, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 2, 18, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 18, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 327163, 
                                                          root := ~, 
                                                          start := 327152, 
                                                          stop := 327162 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 2, 18, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 18, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 327169, 
                                                          root := ~, 
                                                          start := 327165, 
                                                          stop := 327168 ), 
                                                      rec( 
                                                          content := "\n\n    \
By default, an isomorphism is found using the canonical labellings of the\n   \
 digraphs obtained from ", count := [ 7, 2, 18, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "bliss" ), content := [ rec( content := "http://www.tcs.tkk.fi/S\
oftware/bliss/", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "URL\
", next := 81, root := ~, start := 17, stop := 80 ) ], count := 
                                                            [ 7, 2, 18, 11 ], 
                                                          name := "Alt", 
                                                          next := 87, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 86 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "bliss", count := [ 7, 2, 18, 11 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 11 ], name := "Package", 
                                                                  next := 131,
                                                                  root := ~, 
                                                                  start := 107
                                                                    , 
                                                                  stop := 130 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 137, 
                                                          root := ~, 
                                                          start := 87, 
                                                          stop := 136 ), 
                                                      rec( 
                                                          content := " by Tomm\
i Junttila\n    and Petteri Kaski. If ", count := [ 7, 2, 18, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "NautyTracesInterface" ), content := [ rec( content := "https://\
github.com/gap-packages/NautyTracesInterface", count := [ 7, 2, 18, 11 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 11 ], 
                                                                  mathmode := \
"Text", name := "URL", next := 111, root := ~, start := 17, stop := 110 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 11 ], 
                                                          name := "Alt", 
                                                          next := 117, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 116 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "NautyTracesInterface", count := [ 7, 2\
, 18, 11 ], name := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 11 ], 
                                                                  name := "Pac\
kage", next := 176, root := ~, start := 137, stop := 175 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 182, 
                                                          root := ~, 
                                                          start := 117, 
                                                          stop := 181 ), 
                                                      rec( 
                                                          content := " is avai\
lable, then ", count := [ 7, 2, 18, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "nauty" ), content := [ rec( content := "http://pallini.di.uniro\
ma1.it/", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "URL", 
                                                                  next := 74, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 73 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 11 ], 
                                                          name := "Alt", 
                                                          next := 80, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 79 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "nauty", count := [ 7, 2, 18, 11 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 7, 2, 18, 11 ], name := "Package", 
                                                                  next := 124,
                                                                  root := ~, 
                                                                  start := 100
                                                                    , 
                                                                  stop := 123 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 18, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 130, 
                                                          root := ~, 
                                                          start := 80, 
                                                          stop := 129 ), 
                                                      rec( 
                                                          content := " by\n   \
 Brendan Mckay and Adolfo Piperno can be used instead; see\n    ", 
                                                          count := 
                                                            [ 7, 2, 18, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseBliss" ), content := 0, count := [ 7, 2, 18, 11 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 327477, 
                                                          root := ~, 
                                                          start := 327447, 
                                                          stop := 327476 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 7, 2, 18, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
sUseNauty" ), content := 0, count := [ 7, 2, 18, 11 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 327513, 
                                                          root := ~, 
                                                          start := 327483, 
                                                          stop := 327512 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 2, 18, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph1 := ChainDigraph(4);\n<immutable chain digraph with 4 vertices>\
\ngap> digraph2 := ChainDigraph(3);\n<immutable chain digraph with 3 vertices>\
\ngap> IsomorphismDigraphs(digraph1, digraph2,\n>  [[1, 4], [2, 3]], [[1, 2], \
[3]]);\nfail\ngap> digraph2 := DigraphReverse(digraph1);\n<immutable digraph w\
ith 4 vertices, 3 edges>\ngap> colours1 := [1, 1, 1, 1];;\ngap> colours2 := [1\
, 1, 1, 1];;\ngap> p := IsomorphismDigraphs(digraph1, digraph2, colours1, colo\
urs2);\n(1,4)(2,3)\ngap> OnDigraphs(digraph1, p) = digraph2;\ntrue\ngap> List(\
DigraphVertices(digraph1), i -> colours1[i ^ p]) = colours2;\ntrue\ngap> colou\
rs1 := [1, 1, 2, 2];;\ngap> colours2 := [2, 2, 1, 1];;\ngap> p := IsomorphismD\
igraphs(digraph1, digraph2, colours1, colours2);\n(1,4)(2,3)\ngap> OnDigraphs(\
digraph1, p) = digraph2;\ntrue\ngap> List(DigraphVertices(digraph1), i -> colo\
urs1[i ^ p]) = colours2;\ntrue\ngap> IsomorphismDigraphs(digraph1, digraph2,\n\
>  [1, 1, 2, 2], [1, 1, 2, 2]);\nfail", count := [ 7, 2, 18, 12 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 18, 12 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 328496, 
                                                          root := ~, 
                                                          start := 327520, 
                                                          stop := 328495 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 18, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 328513, root := ~, 
                                                  start := 325426, 
                                                  stop := 328512 ) ], 
                                          count := [ 7, 2, 18, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 328527, root := ~, 
                                          start := 325229, stop := 328526 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 18, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "RepresentativeO\
utNeighbours" ), content := 0, count := [ 7, 2, 19, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 328604, root := ~, 
                                                  start := 328548, 
                                                  stop := 328603 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An immuta\
ble list of lists.", count := [ 7, 2, 19, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 19, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 328653, root := ~, 
                                                  start := 328607, 
                                                  stop := 328652 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function returns the list ", count := [ 7, 2, 19, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 328715, 
                                                          root := ~, 
                                                          start := 328705, 
                                                          stop := 328714 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 2, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut-neighbours", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 328740, 
                                                          root := ~, 
                                                          start := 328719, 
                                                          stop := 328739 ), 
                                                      rec( 
                                                          content := " of each\
\n    representative of the orbits of the action of ", count := 
                                                            [ 7, 2, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Group" ), content := 0, count := [ 7, 2, 19, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 328825, 
                                                          root := ~, 
                                                          start := 328799, 
                                                          stop := 328824 ), 
                                                      rec( 
                                                          content := " on\n   \
 the vertex set of the digraph ", count := [ 7, 2, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 19, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 328877, 
                                                          root := ~, 
                                                          start := 328863, 
                                                          stop := 328876 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 2, 19, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 328883, 
                                                          root := ~, 
                                                          start := 328879, 
                                                          stop := 328882 ), 
                                                      rec( 
                                                          content := "\n\n    \
More specifically, if ", count := [ 7, 2, 19, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
eps", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 328922, 
                                                          root := ~, 
                                                          start := 328911, 
                                                          stop := 328921 ), 
                                                      rec( 
                                                          content := " is the \
list of orbit representatives,\n    then a vertex ", count := [ 7, 2, 19, 4 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 328987, 
                                                          root := ~, 
                                                          start := 328979, 
                                                          stop := 328986 ), 
                                                      rec( 
                                                          content := " appears\
 in ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ut[i]", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 329012, 
                                                          root := ~, 
                                                          start := 328999, 
                                                          stop := 329011 ), 
                                                      rec( 
                                                          content := " each ti\
me\n    there exists an edge with source ", count := [ 7, 2, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
eps[i]", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 329074, 
                                                          root := ~, 
                                                          start := 329060, 
                                                          stop := 329073 ), 
                                                      rec( 
                                                          content := " and ran\
ge ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 329093, 
                                                          root := ~, 
                                                          start := 329085, 
                                                          stop := 329092 ), 
                                                      rec( 
                                                          content := " in\n   \
 ", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 19, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 329115, 
                                                          root := ~, 
                                                          start := 329101, 
                                                          stop := 329114 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 19, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 19, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 329125, 
                                                          root := ~, 
                                                          start := 329121, 
                                                          stop := 329124 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 2, 19, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Group" ), content := 0, count := [ 7, 2, 19, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 329160, 
                                                          root := ~, 
                                                          start := 329134, 
                                                          stop := 329159 ), 
                                                      rec( 
                                                          content := " is triv\
ial, then ", count := [ 7, 2, 19, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "OutNeig\
hbours" ), content := 0, count := [ 7, 2, 19, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 329205, 
                                                          root := ~, 
                                                          start := 329178, 
                                                          stop := 329204 ), 
                                                      rec( 
                                                          content := "\n    is\
 returned.\n\n    ", count := [ 7, 2, 19, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\n>  [2, 1, 3, 4, 5], [3, 5], [2], [1, 2, 3, 5], [1, 2, 3,\
 4]]);\n<immutable digraph with 5 vertices, 16 edges>\ngap> DigraphGroup(D);\n\
Group(())\ngap> RepresentativeOutNeighbours(D);\n[ [ 2, 1, 3, 4, 5 ], [ 3, 5 ]\
, [ 2 ], [ 1, 2, 3, 5 ], [ 1, 2, 3, 4 ] ]\ngap> D := Digraph(IsMutableDigraph,\
 [\n>  [2, 1, 3, 4, 5], [3, 5], [2], [1, 2, 3, 5], [1, 2, 3, 4]]);\n<mutable d\
igraph with 5 vertices, 16 edges>\ngap> DigraphGroup(D);\nGroup(())\ngap> Repr\
esentativeOutNeighbours(D);\n[ [ 2, 1, 3, 4, 5 ], [ 3, 5 ], [ 2 ], [ 1, 2, 3, \
5 ], [ 1, 2, 3, 4 ] ]\ngap> D := DigraphFromDigraph6String(\"&GYHPQgWTIIPW\");\
\n<immutable digraph with 8 vertices, 24 edges>\ngap> G := DigraphGroup(D);;\n\
gap> GeneratorsOfGroup(G);\n[ (1,2)(3,4)(5,6)(7,8), (1,3,2,4)(5,7,6,8), (1,5)(\
2,6)(3,8)(4,7) ]\ngap> Set(RepresentativeOutNeighbours(D), Set);\n[ [ 2, 3, 5 \
] ]", count := [ 7, 2, 19, 6 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 7, 2, 19, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 330098, 
                                                          root := ~, 
                                                          start := 329228, 
                                                          stop := 330097 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 19, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 19, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 330115, root := ~, 
                                                  start := 328656, 
                                                  stop := 330114 ) ], 
                                          count := [ 7, 2, 19, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 330129, root := ~, 
                                          start := 328533, stop := 330128 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 2, 19, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "src, ran, x",
                                                      Label := "for digraphs a\
nd transformation or permutation", Name := "IsDigraphIsomorphism" ), 
                                                  content := 0, 
                                                  count := [ 7, 2, 20, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 330267, root := ~, 
                                                  start := 330150, 
                                                  stop := 330266 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "src, ran, x, col\
1, col2", Name := "IsDigraphIsomorphism" ), content := 0, 
                                                  count := [ 7, 2, 20, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 330335, root := ~, 
                                                  start := 330270, 
                                                  stop := 330334 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, x", 
                                                      Label := "for a digraph \
and a transformation or permutation", Name := "IsDigraphAutomorphism" ), 
                                                  content := 0, 
                                                  count := [ 7, 2, 20, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 330458, root := ~, 
                                                  start := 330338, 
                                                  stop := 330457 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, x, col"
                                                        , 
                                                      Name := "IsDigraphAutomo\
rphism" ), content := 0, count := [ 7, 2, 20, 8 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 330519, root := ~, 
                                                  start := 330461, 
                                                  stop := 330518 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 330542, 
                                                          root := ~, 
                                                          start := 330531, 
                                                          stop := 330541 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 330558, 
                                                          root := ~, 
                                                          start := 330546, 
                                                          stop := 330557 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 20, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 330569, root := ~, 
                                                  start := 330522, 
                                                  stop := 330568 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphIsomorphism", count := [ 7, 2, 20, 9 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 20, 9 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 330617, 
                                                          root := ~, 
                                                          start := 330590, 
                                                          stop := 330616 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 330637, 
                                                          root := ~, 
                                                          start := 330626, 
                                                          stop := 330636 ), 
                                                      rec( 
                                                          content := " if the \
permutation or\n    transformation ", count := [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 330687, 
                                                          root := ~, 
                                                          start := 330679, 
                                                          stop := 330686 ), 
                                                      rec( 
                                                          content := " is an i\
somorphism from the digraph ", count := [ 7, 2, 20, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 330733, 
                                                          root := ~, 
                                                          start := 330723, 
                                                          stop := 330732 ), 
                                                      rec( 
                                                          content := " to\n   \
 the digraph ", count := [ 7, 2, 20, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 2, 20, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 330763, 
                                                          root := ~, 
                                                          start := 330753, 
                                                          stop := 330762 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 20, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 20, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 330773, 
                                                          root := ~, 
                                                          start := 330769, 
                                                          stop := 330772 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphAutomorphism", count := [ 7, 2, 20, 10 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 20, 10 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 330807, 
                                                          root := ~, 
                                                          start := 330779, 
                                                          stop := 330806 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 330827, 
                                                          root := ~, 
                                                          start := 330816, 
                                                          stop := 330826 ), 
                                                      rec( 
                                                          content := " if the \
permutation or\n    transformation ", count := [ 7, 2, 20, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 20, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 330877, 
                                                          root := ~, 
                                                          start := 330869, 
                                                          stop := 330876 ), 
                                                      rec( 
                                                          content := " is an a\
utomorphism of the digraph ", count := [ 7, 2, 20, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 20, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 330926, 
                                                          root := ~, 
                                                          start := 330912, 
                                                          stop := 330925 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 20, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 20, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 330936, 
                                                          root := ~, 
                                                          start := 330932, 
                                                          stop := 330935 ), 
                                                      rec( 
                                                          content := "\n\n    \
A permutation or transformation ", count := [ 7, 2, 20, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 20, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 330982, 
                                                          root := ~, 
                                                          start := 330974, 
                                                          stop := 330981 ), 
                                                      rec( 
                                                          content := " is an "
                                                            , 
                                                          count := 
                                                            [ 7, 2, 20, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
somorphism", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 331007, 
                                                          root := ~, 
                                                          start := 330989, 
                                                          stop := 331006 ), 
                                                      rec( 
                                                          content := " from a\\
n    digraph ", count := [ 7, 2, 20, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 331037, 
                                                          root := ~, 
                                                          start := 331027, 
                                                          stop := 331036 ), 
                                                      rec( 
                                                          content := " to a di\
graph ", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 2, 20, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 331061, 
                                                          root := ~, 
                                                          start := 331051, 
                                                          stop := 331060 ), 
                                                      rec( 
                                                          content := " if the \
following hold:\n    ", count := [ 7, 2, 20, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 7, 2, 20, 13 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "x", count := [ 7, 2, 20, 13 ], mathmode := "Text", n\
ame := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 13 ], mathmode := "Text",
                                                                          name\
 := "A", next := 331125, root := ~, start := 331117, stop := 331124 ), 
                                                                      rec( 
                                                                          cont\
ent := " is a bijection from the vertices of ", count := [ 7, 2, 20, 13 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "src", count := [ 7, 2, 20, 13 ], mathmode := "Text",\
 name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 13 ], mathmode := "Text\
", name := "A", next := 331172, root := ~, start := 331162, stop := 331171 ), 
                                                                      rec( 
                                                                          cont\
ent := " to those of\n        ", count := [ 7, 2, 20, 13 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "ran", count := [ 7, 2, 20, 13 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 7, 2, 20, 13 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 331203, root := ~, start := 331193, stop := 331202 ), rec( content := ";\n\
      ", count := [ 7, 2, 20, 13 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 2, 20, 13 ], name := "Item", next := 331218, 
                                                                  root := ~, 
                                                                  start := 331\
102, stop := 331217 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA\
", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "[u ^\
 ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA", root := ~\
 ), rec( attributes := rec(  ), content := [ rec( content := "x", count := [ 7\
, 2, 20, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [\
 7, 2, 20, 15 ], mathmode := "Text", name := "A", next := 331256, root := ~, s\
tart := 331248, stop := 331255 ), rec( content := ", v ^ ", count := [ 7, 2, 2\
0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\
 rec(  ), content := [ rec( content := "x", count := [ 7, 2, 20, 15 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 15 ], mathm\
ode := "Text", name := "A", next := 331270, root := ~, start := 331262, stop :\
= 331269 ), rec( content := "]", count := [ 7, 2, 20, 15 ], mathmode := "Text"\
, name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 15 ], mathmode := "Tex\
t", name := "C", next := 331275, root := ~, start := 331240, stop := 331274 ),
                                                                      rec( 
                                                                          cont\
ent := " is an edge of\n        ", count := [ 7, 2, 20, 15 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ re\
c( content := "ran", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 7, 2, 20, 15 ], mathmode := "Text", name := \
"A", next := 331308, root := ~, start := 331298, stop := 331307 ), rec( conten\
t := " if and only if ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content\
 := "[u, v]", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA",\
 root := ~ ) ], count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 331337, root := ~, start := 331324, stop := 331336 ), rec( content := " is\
 an\n        edge of ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "src", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "A", next :\
= 331370, root := ~, start := 331360, stop := 331369 ), rec( content := "; and\
\n      ", count := [ 7, 2, 20, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 7, 2, 20, 15 ], name := "Item", next := 331389, 
                                                                  root := ~, 
                                                                  start := 331\
225, stop := 331388 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        ", count := [ 7, 2, 20, 17 ], mathmode := "Text", name := "PCDATA\
", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "x", \
count := [ 7, 2, 20, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ]
                                                                            , 
                                                                          coun\
t := [ 7, 2, 20, 17 ], mathmode := "Text", name := "A", next := 331419, root :\
= ~, start := 331411, stop := 331418 ), rec( content := " fixes every ", count\
 := [ 7, 2, 20, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "i", count := [ 7, 2, 20, 17 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 17\
 ], mathmode := "Text", name := "C", next := 331440, root := ~, start := 33143\
2, stop := 331439 ), rec( content := " which is not a vertex of ", count := [ \
7, 2, 20, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\
utes := rec(  ), content := [ rec( content := "src", count := [ 7, 2, 20, 17 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 17\
 ], mathmode := "Text", name := "A", next := 331476, root := ~, start := 33146\
6, stop := 331475 ), rec( content := ".\n      ", count := [ 7, 2, 20, 17 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 17 ], 
                                                                  name := "Ite\
m", next := 331491, root := ~, start := 331396, stop := 331490 ) ], 
                                                          count := 
                                                            [ 7, 2, 20, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 331503, 
                                                          root := ~, 
                                                          start := 331089, 
                                                          stop := 331502 ), 
                                                      rec( 
                                                          content := "\n    Se\
e also ", count := [ 7, 2, 20, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := 
                                                            [ 7, 2, 20, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 331577, 
                                                          root := ~, 
                                                          start := 331517, 
                                                          stop := 331576 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 2, 20, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 20, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 331582, 
                                                          root := ~, 
                                                          start := 331578, 
                                                          stop := 331581 ), 
                                                      rec( 
                                                          content := "\n    \n\
    If ", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol1", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 331606, 
                                                          root := ~, 
                                                          start := 331595, 
                                                          stop := 331605 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 20, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol2", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 331622, 
                                                          root := ~, 
                                                          start := 331611, 
                                                          stop := 331621 ), 
                                                      rec( content := ", or ",
                                                          count := 
                                                            [ 7, 2, 20, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol", count := [ 7, 2, 20, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 331637, 
                                                          root := ~, 
                                                          start := 331627, 
                                                          stop := 331636 ), 
                                                      rec( 
                                                          content := ", are gi\
ven, then they must\n    represent vertex colourings; see \n    ", 
                                                          count := 
                                                            [ 7, 2, 20, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and a homogeneous list", Oper := "AutomorphismGroup" ), content := 0, 
                                                          count := 
                                                            [ 7, 2, 20, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 331783, 
                                                          root := ~, 
                                                          start := 331707, 
                                                          stop := 331782 ), 
                                                      rec( 
                                                          content := " \n    f\
or details of the permissible values for\n    these arguments. The homomorphis\
m must then also have the property:\n  \n    ", count := [ 7, 2, 20, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 7, 2, 20, 22 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "col1[i] = col2[i ^ x]", count := [ 7, 2, 20, 22 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 22 ],
                                                                          math\
mode := "Text", name := "C", next := 331966, root := ~, start := 331938, stop \
:= 331965 ), rec( content := " for all vertices ", count := [ 7, 2, 20, 22 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "i", count := [ 7, 2, 20, 22 ], mathmode := "Text", n\
ame := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 22 ], mathmode := "Text",
                                                                          name\
 := "C", next := 331992, root := ~, start := 331984, stop := 331991 ), 
                                                                      rec( 
                                                                          cont\
ent := " of ", count := [ 7, 2, 20, 22 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "src", count\
 := [ 7, 2, 20, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 7, 2, 20, 22 ], mathmode := "Text", name := "A", next := 332006, root :\
= ~, start := 331996, stop := 332005 ), rec( content := ",\n        for ", 
                                                                          coun\
t := [ 7, 2, 20, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "IsDigraphIsomorphism", count \
:= [ 7, 2, 20, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 7, 2, 20, 22 ], mathmode := "Text", name := "C", next := 332047, root :\
= ~, start := 332020, stop := 332046 ), rec( content := ". ", count := [ 7, 2,\
 20, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 7, 2, 
                                                                      20, 22 ]
                                                                    , 
                                                                  name := "Ite\
m", next := 332056, root := ~, start := 331923, stop := 332055 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        ", count := [ 7, 2, 20, 24 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "col[i] = col[i ^ x]", count := [ 7, 2, 20, 24 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 24 ], 
                                                                          math\
mode := "Text", name := "C", next := 332104, root := ~, start := 332078, stop \
:= 332103 ), rec( content := " for all vertices ", count := [ 7, 2, 20, 24 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "i", count := [ 7, 2, 20, 24 ], mathmode := "Text", n\
ame := "PCDATA", root := ~ ) ], count := [ 7, 2, 20, 24 ], mathmode := "Text",
                                                                          name\
 := "C", next := 332130, root := ~, start := 332122, stop := 332129 ), 
                                                                      rec( 
                                                                          cont\
ent := " of ", count := [ 7, 2, 20, 24 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "digraph", c\
ount := [ 7, 2, 20, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ],
                                                                          coun\
t := [ 7, 2, 20, 24 ], mathmode := "Text", name := "A", next := 332148, root :\
= ~, start := 332134, stop := 332147 ), rec( content := ",\n        for ", 
                                                                          coun\
t := [ 7, 2, 20, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "IsDigraphAutomorphism", count\
 := [ 7, 2, 20, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 7, 2, 20, 24 ], mathmode := "Text", name := "C", next := 332190, root :\
= ~, start := 332162, stop := 332189 ), rec( content := ". ", count := [ 7, 2,\
 20, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 7, 2, 
                                                                      20, 24 ]
                                                                    , 
                                                                  name := "Ite\
m", next := 332199, root := ~, start := 332063, stop := 332198 ) ], 
                                                          count := 
                                                            [ 7, 2, 20, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 332211, 
                                                          root := ~, 
                                                          start := 331910, 
                                                          stop := 332210 ), 
                                                      rec( 
                                                          content := "\n\n    \
For some digraphs, it can be faster to use ", count := [ 7, 2, 20, 26 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphAutomorphism", count := [ 7, 2, 20, 26 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 20, 26 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 332288, 
                                                          root := ~, 
                                                          start := 332260, 
                                                          stop := 332287 ), 
                                                      rec( 
                                                          content := "\n    th\
an to test membership in the automorphism group of ", count := 
                                                            [ 7, 2, 20, 26 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 20, 26 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 20, 26 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 332360, 
                                                          root := ~, 
                                                          start := 332346, 
                                                          stop := 332359 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 2, 20, 26 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> src := Digraph([[1], [1, 2], [1, 3]]);\n<immutable digraph with 3 vertic\
es, 5 edges>\ngap> IsDigraphAutomorphism(src, (1, 2, 3));\nfalse\ngap> IsDigra\
phAutomorphism(src, (2, 3));\ntrue\ngap> IsDigraphAutomorphism(src, (2, 3), [2\
, 1, 1]);\ntrue\ngap> IsDigraphAutomorphism(src, (2, 3), [2, 2, 1]);\nfalse\ng\
ap> IsDigraphAutomorphism(src, (2, 3)(4, 5));\nfalse\ngap> IsDigraphAutomorphi\
sm(src, (1, 4));\nfalse\ngap> IsDigraphAutomorphism(src, ());\ntrue\ngap> ran \
:= Digraph([[2, 1], [2], [2, 3]]);\n<immutable digraph with 3 vertices, 5 edge\
s>\ngap> IsDigraphIsomorphism(src, ran, (1, 2));\ntrue\ngap> IsDigraphIsomorph\
ism(ran, src, (1, 2));\ntrue\ngap> IsDigraphIsomorphism(ran, src, (1, 2));\ntr\
ue\ngap> IsDigraphIsomorphism(src, Digraph([[3], [1, 3], [2]]), (1, 2, 3));\nf\
alse\ngap> IsDigraphIsomorphism(src, ran, (1, 2), [1, 2, 3], [2, 1, 3]);\ntrue\
\ngap> IsDigraphIsomorphism(src, ran, (1, 2), [1, 2, 2], [2, 1, 3]);\nfalse\n"
                                                                    , 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      20, 27 ]
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 20, 27 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 333303, 
                                                          root := ~, 
                                                          start := 332367, 
                                                          stop := 333302 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 2, 20, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 20, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 333320, root := ~, 
                                                  start := 330572, 
                                                  stop := 333319 ) ], 
                                          count := [ 7, 2, 20, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 333334, root := ~, 
                                          start := 330135, stop := 333333 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 7, 2, 20, 28 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, list", 
                                                      Name := "IsDigraphColour\
ing" ), content := 0, count := [ 7, 2, 21, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 333412, root := ~, 
                                                  start := 333359, 
                                                  stop := 333411 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, t", 
                                                      Label := "for a transfor\
mation", Name := "IsDigraphColouring" ), content := 0, 
                                                  count := [ 7, 2, 21, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 333503, root := ~, 
                                                  start := 333417, 
                                                  stop := 333502 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 7, 2, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 333529, 
                                                          root := ~, 
                                                          start := 333518, 
                                                          stop := 333528 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 7, 2, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 333545, 
                                                          root := ~, 
                                                          start := 333533, 
                                                          stop := 333544 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 2, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 21, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 333557, root := ~, 
                                                  start := 333508, 
                                                  stop := 333556 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      T\
he operation ", count := [ 7, 2, 21, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphColouring", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 7, 2, 21, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 333621, 
                                                          root := ~, 
                                                          start := 333596, 
                                                          stop := 333620 ), 
                                                      rec( 
                                                          content := " verifie\
s whether or not \n      the list ", count := [ 7, 2, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 333673, 
                                                          root := ~, 
                                                          start := 333662, 
                                                          stop := 333672 ), 
                                                      rec( 
                                                          content := " describ\
es a proper colouring of the digraph \n      ", count := [ 7, 2, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 333739, 
                                                          root := ~, 
                                                          start := 333725, 
                                                          stop := 333738 ), 
                                                      rec( 
                                                          content := ". \n    \
  ", count := [ 7, 2, 21, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 333752, 
                                                          root := ~, 
                                                          start := 333748, 
                                                          stop := 333751 ), 
                                                      rec( 
                                                          content := "\n\n    \
  A list ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 333778, 
                                                          root := ~, 
                                                          start := 333767, 
                                                          stop := 333777 ), 
                                                      rec( 
                                                          content := " describ\
es a ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roper colouring", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "E", 
                                                          next := 333814, 
                                                          root := ~, 
                                                          start := 333791, 
                                                          stop := 333813 ), 
                                                      rec( 
                                                          content := " of a di\
graph\n      ", count := [ 7, 2, 21, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 333848, 
                                                          root := ~, 
                                                          start := 333834, 
                                                          stop := 333847 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 333863, 
                                                          root := ~, 
                                                          start := 333852, 
                                                          stop := 333862 ), 
                                                      rec( 
                                                          content := " consist\
s of positive integers, the length of\n      ", count := [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
ist", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 333926, 
                                                          root := ~, 
                                                          start := 333915, 
                                                          stop := 333925 ), 
                                                      rec( 
                                                          content := " equals \
the number of vertices in ", count := [ 7, 2, 21, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 333974, 
                                                          root := ~, 
                                                          start := 333960, 
                                                          stop := 333973 ), 
                                                      rec( 
                                                          content := ", and fo\
r any\n      vertices ", count := [ 7, 2, 21, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
, v", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 334014, 
                                                          root := ~, 
                                                          start := 334003, 
                                                          stop := 334013 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 334032, 
                                                          root := ~, 
                                                          start := 334018, 
                                                          stop := 334031 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 334044, 
                                                          root := ~, 
                                                          start := 334036, 
                                                          stop := 334043 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 334057, 
                                                          root := ~, 
                                                          start := 334049, 
                                                          stop := 334056 ), 
                                                      rec( 
                                                          content := " are adj\
acent,\n      then ", count := [ 7, 2, 21, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "list", count := [ 7, 2, 21, 6 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], 
                                                                  mathmode := \
"Text", name := "A", next := 334097, root := ~, start := 334086, stop := 33409\
6 ), rec( content := "[u] >< ", count := [ 7, 2, 21, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "l\
ist", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := \
~ ) ], count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "A", next := 3341\
21, root := ~, start := 334110, stop := 334120 ), rec( content := "[v]", 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      21, 6 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 334128, 
                                                          root := ~, 
                                                          start := 334083, 
                                                          stop := 334127 ), 
                                                      rec( 
                                                          content := ".\n     \
 ", count := [ 7, 2, 21, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 334140, 
                                                          root := ~, 
                                                          start := 334136, 
                                                          stop := 334139 ), 
                                                      rec( 
                                                          content := "\n\n    \
  A transformation ", count := [ 7, 2, 21, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 2, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 334173, 
                                                          root := ~, 
                                                          start := 334165, 
                                                          stop := 334172 ), 
                                                      rec( 
                                                          content := " describ\
es a proper colouring of a digraph\n      ", count := [ 7, 2, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 334236, 
                                                          root := ~, 
                                                          start := 334222, 
                                                          stop := 334235 ), 
                                                      rec( content := ", if ",
                                                          count := 
                                                            [ 7, 2, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
mageListOfTransformation(", count := [ 7, 2, 21, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "t\
", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      21, 7 ],
                                                                  mathmode := \
"Text", name := "A", next := 334278, root := ~, start := 334270, stop := 33427\
7 ), rec( content := ",\n      DigraphNrVertices(", count := [ 7, 2, 21, 7 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "A", 
                                                                  next := 3343\
18, root := ~, start := 334304, stop := 334317 ), rec( content := "))", 
                                                                  count := 
                                                                    [ 7, 2, 
                                                                      21, 7 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 2, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 334324, 
                                                          root := ~, 
                                                          start := 334241, 
                                                          stop := 334323 ), 
                                                      rec( 
                                                          content := " is a pr\
oper colouring of \n      ", count := [ 7, 2, 21, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 2, 21, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 2, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 334371, 
                                                          root := ~, 
                                                          start := 334357, 
                                                          stop := 334370 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 2, 21, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 2, 21, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 334377, 
                                                          root := ~, 
                                                          start := 334373, 
                                                          stop := 334376 ), 
                                                      rec( 
                                                          content := "\n\n    \
  See also ", count := [ 7, 2, 21, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsDigra\
phHomomorphism" ), content := 0, count := [ 7, 2, 21, 8 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 334429, 
                                                          root := ~, 
                                                          start := 334394, 
                                                          stop := 334428 ), 
                                                      rec( 
                                                          content := ".\n     \
 \n      ", count := [ 7, 2, 21, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := JohnsonDigraph(5, 3);\n<immutable symmetric digraph with 10 vertice\
s, 60 edges>\ngap> IsDigraphColouring(D, [1, 2, 3, 3, 2, 1, 4, 5, 6, 7]);\ntru\
e\ngap> IsDigraphColouring(D, [1, 2, 3, 3, 2, 1, 2, 5, 6, 7]);\nfalse\ngap> Is\
DigraphColouring(D, [1, 2, 3, 3, 2, 1, 2, 5, 6, -1]);\nfalse\ngap> IsDigraphCo\
louring(D, [1, 2, 3]);\nfalse\ngap> IsDigraphColouring(D, IdentityTransformati\
on);\ntrue\n", count := [ 7, 2, 21, 9 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 7, 2, 21, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 334865, 
                                                          root := ~, 
                                                          start := 334444, 
                                                          stop := 334864 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 7, 2, 21, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 2, 21, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 334884, root := ~, 
                                                  start := 333562, 
                                                  stop := 334883 ) ], 
                                          count := [ 7, 2, 21, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 334900, root := ~, 
                                          start := 333342, stop := 334899 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 7, 2, 21, 10 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 7, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 334914, 
                                  root := ~, start := 290992, stop := 334913 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 7, 2, 21, 10 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Homomorphisms of \
digraphs", count := [ 7, 3, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 7, 3, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 334971, 
                                          root := ~, start := 334927, 
                                          stop := 334970 ), 
                                      rec( 
                                          content := "\n\n    The following me\
thods exist to find homomorphisms between digraphs.\n    If an argument to one\
 of these methods is a digraph with multiple edges,\n    then the multiplicity\
 of edges will be ignored in order to perform the\n    calculation; the digrap\
h will be treated as if it has no multiple edges.\n\n    ", 
                                          count := [ 7, 3, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "D1, D2, hook, us\
er_param, max_results, hint, injective, image, partial_map, colors1, colors2[,\
 order, aut_grp]", Name := "HomomorphismDigraphsFinder" ), content := 0, 
                                                  count := [ 7, 3, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 335452, root := ~, 
                                                  start := 335294, 
                                                  stop := 335451 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "The argum\
ent ", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
ser_param", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 335494, 
                                                          root := ~, 
                                                          start := 335477, 
                                                          stop := 335493 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 335505, root := ~, 
                                                  start := 335455, 
                                                  stop := 335504 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function finds homomorphisms from the digraph ", count := [ 7, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 335586, 
                                                          root := ~, 
                                                          start := 335577, 
                                                          stop := 335585 ), 
                                                      rec( 
                                                          content := " to the \
digraph\n    ", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
2", count := [ 7, 3, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 335615, 
                                                          root := ~, 
                                                          start := 335606, 
                                                          stop := 335614 ), 
                                                      rec( 
                                                          content := " subject\
 to the conditions imposed by the other arguments as\n    described below.", 
                                                          count := 
                                                            [ 7, 3, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 335700, 
                                                          root := ~, 
                                                          start := 335696, 
                                                          stop := 335699 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 335717, 
                                                          root := ~, 
                                                          start := 335709, 
                                                          stop := 335716 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 335730, 
                                                          root := ~, 
                                                          start := 335722, 
                                                          stop := 335729 ), 
                                                      rec( 
                                                          content := " are hom\
omorphisms found by\n    ", count := [ 7, 3, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
omomorphismDigraphsFinder", count := [ 7, 3, 1, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 1, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 335795, 
                                                          root := ~, 
                                                          start := 335762, 
                                                          stop := 335794 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 335810, 
                                                          root := ~, 
                                                          start := 335802, 
                                                          stop := 335809 ), 
                                                      rec( 
                                                          content := " cannot \
be obtained from\n    ", count := [ 7, 3, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 335847, 
                                                          root := ~, 
                                                          start := 335839, 
                                                          stop := 335846 ), 
                                                      rec( 
                                                          content := " by righ\
t multiplying by an automorphism of ", count := [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
2", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 335900, 
                                                          root := ~, 
                                                          start := 335891, 
                                                          stop := 335899 ), 
                                                      rec( 
                                                          content := " in\n   \
 ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
ut_grp", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 335922, 
                                                          root := ~, 
                                                          start := 335908, 
                                                          stop := 335921 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 3, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content :\
= "hook", count := [ 7, 3, 1, 5 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 3, 1, 5 ], mathmode := "Text", name := "A", next := 33\
5959, root := ~, start := 335948, stop := 335958 ) ], count := [ 7, 3, 1, 5 ],
                                                                  name := "Mar\
k", next := 335966, root := ~, start := 335942, stop := 335965 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        This argument should be a f\
unction or ", count := [ 7, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "fail", coun\
t := [ 7, 3, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 7, 3, 1, 6 ], mathmode := "Text", name := "K", next := 336037, root := \
~, start := 336026, stop := 336036 ), rec( content := ".", count := [ 7, 3, 1,\
 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\
c(  ), content := 0, count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "P",
                                                                          next\
 := 336042, root := ~, start := 336038, stop := 336041 ), rec( content := "\n\
\n        If ", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "hook", coun\
t := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 7, 3, 1, 7 ], mathmode := "Text", name := "A", next := 336066, root := \
~, start := 336055, stop := 336065 ), rec( content := " is a function, then it\
 must have two arguments\n        ", count := [ 7, 3, 1, 7 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ re\
c( content := "user_param", count := [ 7, 3, 1, 7 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name \
:= "A", next := 336139, root := ~, start := 336122, stop := 336138 ), rec( 
                                                                          cont\
ent := " (see below) and a transformation ", count := [ 7, 3, 1, 7 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content\
 := [ rec( content := "t", count := [ 7, 3, 1, 7 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name :\
= "C", next := 336181, root := ~, start := 336173, stop := 336180 ), rec( cont\
ent := ". The\n        function ", count := [ 7, 3, 1, 7 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( attri\
butes := rec(  ), content := [ rec( content := "hook", count := [ 7, 3, 1, 7 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ]\
, mathmode := "Text", name := "A", next := 336218, root := ~, start := 336207,\
 stop := 336217 ), rec( content := "(", count := [ 7, 3, 1, 7 ], mathmode := "\
Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [\
 rec( content := "user_param", count := [ 7, 3, 1, 7 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", na\
me := "A", next := 336236, root := ~, start := 336219, stop := 336235 ), rec( \
content := ", t)", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 336244, root := ~, start := 336204, stop := 336243 ), rec( content := " is\
 called every time\n        a new homomorphism ", count := [ 7, 3, 1, 7 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "t", count := [ 7, 3, 1, 7 ], mathmode := "Text", nam\
e := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 336301, root := ~, start := 336293, stop := 336300 ), 
                                                                      rec( 
                                                                          cont\
ent := " is found by\n        ", count := [ 7, 3, 1, 7 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "HomomorphismDigraphsFinder", count := [ 7, 3, 1, 7 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text\
", name := "C", next := 336355, root := ~, start := 336322, stop := 336354 ), 
                                                                      rec( 
                                                                          cont\
ent := ". If the function returns ", count := [ 7, 3, 1, 7 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ re\
c( content := "true", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "K"
                                                                            , 
                                                                          next\
 := 336392, root := ~, start := 336381, stop := 336391 ), rec( content := ",\n\
        then ", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "Homomorphis\
mDigraphsFinder", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 336440, root := ~, start := 336407, stop := 336439 ), rec( content := " st\
ops and does not find any\n        further homomorphisms. This feature might b\
e useful if you are\n        searching for a homomorphism that satisfies some \
condition that you\n        cannot specify via the other arguments to\n       \
 ", count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "HomomorphismDigraphsFinder", \
count := [ 7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 7, 3, 1, 7 ], mathmode := "Text", name := "C", next := 336707, root := \
~, start := 336674, stop := 336706 ), rec( content := ".\n        ", count := 
                                                                            [ \
7, 3, 1, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := 0, count := [ 7, 3, 1, 8 ], mathmode := "Text", name\
 := "P", next := 336721, root := ~, start := 336717, stop := 336720 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n\n        If ", count := [ 7, 3, 1, 8 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "hook", count := [ 7, 3, 1, 8 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 3, 1, 8 ], mathmode := "Text", name := "A", next := 3\
36745, root := ~, start := 336734, stop := 336744 ), rec( content := " is ", 
                                                                          coun\
t := [ 7, 3, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "fail", count := [ 7, 3, 1, 8 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 8 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "K", next := 336760, root := ~, start := 336749, stop \
:= 336759 ), rec( content := ", then a default function is used which\n       \
 simply adds every new homomorphism found by\n        ", count := [ 7, 3, 1, 8\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
  ), content := [ rec( content := "HomomorphismDigraphsFinder", count := [ 7, \
3, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, \
3, 1, 8 ], mathmode := "Text", name := "C", next := 336893, root := ~, start :\
= 336860, stop := 336892 ), rec( content := " to ", count := [ 7, 3, 1, 8 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "user_param", count := [ 7, 3, 1, 8 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 8 ], mathmode := "T\
ext", name := "A", next := 336914, root := ~, start := 336897, stop := 336913 
                                                                         ), 
                                                                      rec( 
                                                                          cont\
ent := ", which must be a\n        mutable list in this case.\n      ", count \
:= [ 7, 3, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      1, 6 ], 
                                                                  name := "Ite\
m", next := 336980, root := ~, start := 335973, stop := 336979 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "user_param", count := [ 7, 3, 1, 9 ], mathmode := "Text", name := "PCDATA"\
, root := ~ ) ], count := [ 7, 3, 1, 9 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 337011, root := ~, start := 336994, stop := 337010 ) ], count := 
                                                                    [ 7, 3, 
                                                                      1, 9 ], 
                                                                  name := "Mar\
k", next := 337018, root := ~, start := 336988, stop := 337017 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        If ", count := [ 7, 3, 1, 1\
0 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\
(  ), content := [ rec( content := "hook", count := [ 7, 3, 1, 10 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode\
 := "Text", name := "A", next := 337054, root := ~, start := 337043, stop := 3\
37053 ), rec( content := " is a function, then ", count := [ 7, 3, 1, 10 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "user_param", count := [ 7, 3, 1, 10 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := \
"Text", name := "A", next := 337092, root := ~, start := 337075, stop := 33709\
1 ), rec( content := " can be any ", count := [ 7, 3, 1, 10 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ r\
ec( content := "GAP", count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "\
Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := "\n\
        object. The object ", count := [ 7, 3, 1, 10 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "user_param", count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "A"
                                                                            , 
                                                                          next\
 := 337154, root := ~, start := 337137, stop := 337153 ), rec( content := " is\
 used as the first argument of\n        the function ", count := [ 7, 3, 1, 10\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
  ), content := [ rec( content := "hook", count := [ 7, 3, 1, 10 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode \
:= "Text", name := "A", next := 337220, root := ~, start := 337209, stop := 33\
7219 ), rec( content := ". For example, ", count := [ 7, 3, 1, 10 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content \
:= [ rec( content := "user_param", count := [ 7, 3, 1, 10 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := "Tex\
t", name := "A", next := 337252, root := ~, start := 337235, stop := 337251 ),
                                                                      rec( 
                                                                          cont\
ent := " might be a\n        transformation semigroup, and ", count := [ 7, 3,\
 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "hook", count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := "Text", name := "A", next :=\
 337316, root := ~, start := 337305, stop := 337315 ), rec( content := "(", co\
unt := [ 7, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec\
( attributes := rec(  ), content := [ rec( content := "user_param", count := [\
 7, 3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := \
[ 7, 3, 1, 10 ], mathmode := "Text", name := "A", next := 337334, root := ~, s\
tart := 337317, stop := 337333 ), rec( content := ", t)", count := [ 7, 3, 1, \
10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1,\
 10 ], mathmode := "Text", name := "C", next := 337342, root := ~, start := 33\
7302, stop := 337341 ), rec( content := "\n        might set ", count := [ 7, \
3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\
 := rec(  ), content := [ rec( content := "user_param", count := [ 7, 3, 1, 10\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 1\
0 ], mathmode := "Text", name := "A", next := 337378, root := ~, start := 3373\
61, stop := 337377 ), rec( content := " to be the closure of ", count := [ 7, \
3, 1, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\
 := rec(  ), content := [ rec( content := "user_param", count := [ 7, 3, 1, 10\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 1\
0 ], mathmode := "Text", name := "A", next := 337417, root := ~, start := 3374\
00, stop := 337416 ), rec( content := " and\n        ", count := [ 7, 3, 1, 10\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
  ), content := [ rec( content := "t", count := [ 7, 3, 1, 10 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], mathmode := \
"Text", name := "C", next := 337438, root := ~, start := 337430, stop := 33743\
7 ), rec( content := ". ", count := [ 7, 3, 1, 10 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 0, count := 
                                                                            [ \
7, 3, 1, 11 ], mathmode := "Text", name := "P", next := 337444, root := ~, 
                                                                          star\
t := 337440, stop := 337443 ), rec( content := "\n\n        If the value of ",
                                                                          coun\
t := [ 7, 3, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "hook", count := [ 7, 3, 1, 11\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 1\
1 ], mathmode := "Text", name := "A", next := 337481, root := ~, start := 3374\
70, stop := 337480 ), rec( content := " is ", count := [ 7, 3, 1, 11 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conte\
nt := [ rec( content := "fail", count := [ 7, 3, 1, 11 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 11 ], mathmode := "Text",
                                                                          name\
 := "K", next := 337496, root := ~, start := 337485, stop := 337495 ), 
                                                                      rec( 
                                                                          cont\
ent := ", then the value of\n        ", count := [ 7, 3, 1, 11 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                            [ \
rec( content := "user_param", count := [ 7, 3, 1, 11 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 11 ], mathmode := "Text", 
                                                                          name\
 := "A", next := 337541, root := ~, start := 337524, stop := 337540 ), 
                                                                      rec( 
                                                                          cont\
ent := " must be a mutable list.\n      ", count := [ 7, 3, 1, 11 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 10 ], 
                                                                  name := "Ite\
m", next := 337579, root := ~, start := 337025, stop := 337578 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "max_results", count := [ 7, 3, 1, 12 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 3, 1, 12 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 337611, root := ~, start := 337593, stop := 337610 ) ], count := 
                                                                    [ 7, 3, 
                                                                      1, 12 ],
                                                                  name := "Mar\
k", next := 337618, root := ~, start := 337587, stop := 337617 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        This argument should be a p\
ositive integer or ", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "P\
CDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := \
"infinity", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "PCDATA", ro\
ot := ~ ) ], count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "K", next :\
= 337701, root := ~, start := 337686, stop := 337700 ), rec( content := ".\n  \
      ", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ), rec( attributes := rec(  ), content := [ rec( content := "Homomorphism\
DigraphsFinder", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 337744, root := ~, start := 337711, stop := 337743 ), rec( content := " wi\
ll return after it has found\n        ", count := [ 7, 3, 1, 13 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :=\
 [ rec( content := "max_results", count := [ 7, 3, 1, 13 ], mathmode := "Text"\
, name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 13 ], mathmode := "Text\
", name := "A", next := 337802, root := ~, start := 337784, stop := 337801 ), 
                                                                      rec( 
                                                                          cont\
ent := " homomorphisms or the search is complete, whichever\n        happens f\
irst.\n      ", count := [ 7, 3, 1, 13 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 7, 3, 1, 13 ], name := "Item", next := 337890, 
                                                                  root := ~, 
                                                                  start := 337\
625, stop := 337889 ), rec( attributes := rec(  ), content := [ rec( attribute\
s := rec(  ), content := [ rec( content := "hint", count := [ 7, 3, 1, 14 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 14 ], 
                                                                          math\
mode := "Text", name := "A", next := 337915, root := ~, start := 337904, stop \
:= 337914 ) ], count := [ 7, 3, 1, 14 ], name := "Mark", next := 337922, 
                                                                  root := ~, 
                                                                  start := 337\
898, stop := 337921 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        This argument should be a positive integer or ", count := [ 7, 3,\
 1, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( content := "fail", count := [ 7, 3, 1, 15 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 15 ], 
                                                                          math\
mode := "Text", name := "K", next := 338001, root := ~, start := 337990, stop \
:= 338000 ), rec( content := ". ", count := [ 7, 3, 1, 15 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 0, 
                                                                          coun\
t := [ 7, 3, 1, 16 ], mathmode := "Text", name := "P", next := 338007, root :=\
 ~, start := 338003, stop := 338006 ), rec( content := "\n\n        If ", coun\
t := [ 7, 3, 1, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "hint", count := [ 7, 3, 1, 16\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 1\
6 ], mathmode := "Text", name := "A", next := 338031, root := ~, start := 3380\
20, stop := 338030 ), rec( content := " is a positive integer, then only homor\
phisms of rank\n        ", count := [ 7, 3, 1, 16 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conten\
t := "hint", count := [ 7, 3, 1, 16 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 7, 3, 1, 16 ], mathmode := "Text", name := "A", next \
:= 338104, root := ~, start := 338093, stop := 338103 ), rec( content := " are\
 found.", count := [ 7, 3, 1, 16 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ), rec( attributes := rec(  ), content := 0, count := [ 7, 3, 1, 17 ], 
                                                                          math\
mode := "Text", name := "P", next := 338119, root := ~, start := 338115, stop \
:= 338118 ), rec( content := "\n\n        If ", count := [ 7, 3, 1, 17 ], math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "hint", count := [ 7, 3, 1, 17 ], mathmode := "Text",\
 name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 17 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "A", next := 338143, root := ~, start := 338132, stop := 338142 ), 
                                                                      rec( 
                                                                          cont\
ent := " is ", count := [ 7, 3, 1, 17 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "fail", coun\
t := [ 7, 3, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 7, 3, 1, 17 ], mathmode := "Text", name := "K", next := 338158, root :=\
 ~, start := 338147, stop := 338157 ), rec( content := ", then no restriction \
is put on the rank\n        of homomorphisms found.\n      ", count := [ 7, 3,\
 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 7, 3, 
                                                                      1, 15 ],
                                                                  name := "Ite\
m", next := 338244, root := ~, start := 337929, stop := 338243 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "injective", count := [ 7, 3, 1, 18 ], mathmode := "Text", name := "PCDATA"\
, root := ~ ) ], count := [ 7, 3, 1, 18 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 338274, root := ~, start := 338258, stop := 338273 ) ], count := 
                                                                    [ 7, 3, 
                                                                      1, 18 ],
                                                                  name := "Mar\
k", next := 338281, root := ~, start := 338252, stop := 338280 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        This argument should be ", 
                                                                          coun\
t := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "0", count := [ 7, 3, 1, 19 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 19 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 338335, root := ~, start := 338327, stop \
:= 338334 ), rec( content := ", ", count := [ 7, 3, 1, 19 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec\
( content := "1", count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 338345, root := ~, start := 338337, stop := 338344 ), rec( content := ", o\
r ", count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~\
 ), rec( attributes := rec(  ), content := [ rec( content := "2", count := [ 7\
, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \
7, 3, 1, 19 ], mathmode := "Text", name := "C", next := 338358, root := ~, 
                                                                          star\
t := 338350, stop := 338357 ), rec( content := ".  If it is\n        ", count \
:= [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "2", count := [ 7, 3, 1, 19 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 19 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 338386, root := ~, start := 338378, stop \
:= 338385 ), rec( content := ", then only embeddings are found, if it is ", 
                                                                          coun\
t := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "1", count := [ 7, 3, 1, 19 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 19 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 338437, root := ~, start := 338429, stop \
:= 338436 ), rec( content := ", then only\n        injective homomorphisms are\
 found, and if it is ", count := [ 7, 3, 1, 19 ], mathmode := "Text", name := \
"PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :\
= "0", count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "PCDATA", root :=\
 ~ ) ], count := [ 7, 3, 1, 19 ], mathmode := "Text", name := "C", next := 338\
513, root := ~, start := 338505, stop := 338512 ), rec( content := " there are\
 no\n        restrictions imposed by this argument.\n        ", count := [ 7, \
3, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\
 := rec(  ), content := 0, count := [ 7, 3, 1, 20 ], mathmode := "Text", name \
:= "P", next := 338586, root := ~, start := 338582, stop := 338585 ), rec( 
                                                                          cont\
ent := "\n\n        For backwards compatibility, ", count := [ 7, 3, 1, 20 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "injective", count := [ 7, 3, 1, 20 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 20 ], mathmode := "\
Text", name := "A", next := 338641, root := ~, start := 338625, stop := 338640\
 ), rec( content := " can also be ", count := [ 7, 3, 1, 20 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ r\
ec( content := "false", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ 7, 3, 1, 20 ], mathmode := "Text", name :=\
 "K", next := 338666, root := ~, start := 338654, stop := 338665 ), rec( conte\
nt := "\n        or ", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :=\
 "true", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "K", next := 3\
38689, root := ~, start := 338678, stop := 338688 ), rec( content := " which c\
orrespond to the values ", count := [ 7, 3, 1, 20 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conten\
t := "0", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 7, 3, 1, 20 ], mathmode := "Text", name := "C", next := \
338729, root := ~, start := 338721, stop := 338728 ), rec( content := " and ",
                                                                          coun\
t := [ 7, 3, 1, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "1", count := [ 7, 3, 1, 20 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 20 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 338742, root := ~, start := 338734, stop \
:= 338741 ), rec( content := "\n        described in the previous paragraph, r\
espectively. \n      ", count := [ 7, 3, 1, 20 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ 7, 3, 1, 19 ], name := "Item", 
                                                                  next := 3388\
16, root := ~, start := 338288, stop := 338815 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "image", count := [ 7, 3, 1, 2\
1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, \
21 ], mathmode := "Text", name := "A", next := 338842, root := ~, start := 338\
830, stop := 338841 ) ], count := [ 7, 3, 1, 21 ], name := "Mark", 
                                                                  next := 3388\
49, root := ~, start := 338824, stop := 338848 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n        This argument should be a subset of the vertices of the grap\
h ", count := [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~\
 ), rec( attributes := rec(  ), content := [ rec( content := "D2", count := [ \
7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                            [ \
7, 3, 1, 22 ], mathmode := "Text", name := "A", next := 338942, root := ~, 
                                                                          star\
t := 338933, stop := 338941 ), rec( content := ".\n        ", count := [ 7, 3,\
 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( content := "HomomorphismDigraphsFinder", count :=\
 [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\
= [ 7, 3, 1, 22 ], mathmode := "Text", name := "C", next := 338985, root := ~,
                                                                          star\
t := 338952, stop := 338984 ), rec( content := " only finds homomorphisms from\
\n        ", count := [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "D1", count \
:= [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\
 := [ 7, 3, 1, 22 ], mathmode := "Text", name := "A", next := 339033, root := \
~, start := 339024, stop := 339032 ), rec( content := " to the subgraph of ", 
                                                                          coun\
t := [ 7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "D2", count := [ 7, 3, 1, 22 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 22 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 339062, root := ~, start := 339053, stop \
:= 339061 ), rec( content := " induced by the vertices\n        ", count := [ \
7, 3, 1, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "image", count := [ 7, 3, 1, 22 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 22 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 339107, root := ~, start := 339095, stop \
:= 339106 ), rec( content := ".\n      ", count := [ 7, 3, 1, 22 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 22 ], 
                                                                  name := "Ite\
m", next := 339122, root := ~, start := 338856, stop := 339121 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "partial_map", count := [ 7, 3, 1, 23 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 3, 1, 23 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 339154, root := ~, start := 339136, stop := 339153 ) ], count := 
                                                                    [ 7, 3, 
                                                                      1, 23 ],
                                                                  name := "Mar\
k", next := 339161, root := ~, start := 339130, stop := 339160 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        This argument should be a p\
artial map from ", count := [ 7, 3, 1, 24 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "D1\
", count := [ 7, 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ )\
 ], count := [ 7, 3, 1, 24 ], mathmode := "Text", name := "A", next := 339235,
                                                                          root\
 := ~, start := 339226, stop := 339234 ), rec( content := " to ", count := [ 7\
, 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := [ rec( content := "D2", count := [ 7, 3, 1, 24 ], ma\
thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 24 ], 
                                                                          math\
mode := "Text", name := "A", next := 339248, root := ~, start := 339239, stop \
:= 339247 ), rec( content := ",\n        that is, a (not necessarily dense) li\
st of vertices of the digraph\n        ", count := [ 7, 3, 1, 24 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :\
= [ rec( content := "D2", count := [ 7, 3, 1, 24 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 24 ], mathmode := "Text", name \
:= "A", next := 339342, root := ~, start := 339333, stop := 339341 ), rec( 
                                                                          cont\
ent := " of length no greater than the number vertices in the digraph\n       \
 ", count := [ 7, 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "D1", count := [ 7, 3, 1, 24 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 24 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 339421, root := ~, start := 339412, stop \
:= 339420 ), rec( content := ". ", count := [ 7, 3, 1, 24 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec\
( content := "HomomorphismDigraphsFinder", count := [ 7, 3, 1, 24 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 24 ], mathmode\
 := "Text", name := "C", next := 339456, root := ~, start := 339423, stop := 3\
39455 ), rec( content := " only finds homomorphisms\n        extending ", coun\
t := [ 7, 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "partial_map", count := [ 7, 3\
, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, \
3, 1, 24 ], mathmode := "Text", name := "A", next := 339518, root := ~, start \
:= 339500, stop := 339517 ), rec( content := " (if any).\n      ", count := [ \
7, 3, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      1, 24 ],
                                                                  name := "Ite\
m", next := 339542, root := ~, start := 339168, stop := 339541 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "colors1", count := [ 7, 3, 1, 25 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 7, 3, 1, 25 ], mathmode := "Text", name := "A", next\
 := 339576, root := ~, start := 339562, stop := 339575 ) ], count := 
                                                                    [ 7, 3, 
                                                                      1, 25 ],
                                                                  name := "Mar\
k", next := 339583, root := ~, start := 339556, stop := 339582 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        This should be a list repre\
senting possible colours of vertices in the\n        digraph ", count := [ 7, \
3, 1, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\
 := rec(  ), content := [ rec( content := "D1", count := [ 7, 3, 1, 26 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 26 ], 
                                                                          math\
mode := "Text", name := "A", next := 339701, root := ~, start := 339692, stop \
:= 339700 ), rec( content := "; see \n        ", count := [ 7, 3, 1, 26 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label :\
= "for a digraph and a homogeneous list", Oper := "AutomorphismGroup" ), conte\
nt := 0, count := [ 7, 3, 1, 26 ], mathmode := "Text", name := "Ref", next := \
339803, root := ~, start := 339716, stop := 339802 ), rec( content := " \n    \
    for details of the permissible values for this argument.\n      ", count :\
= [ 7, 3, 1, 26 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      1, 26 ],
                                                                  name := "Ite\
m", next := 339883, root := ~, start := 339590, stop := 339882 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "colors2", count := [ 7, 3, 1, 27 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 7, 3, 1, 27 ], mathmode := "Text", name := "A", next\
 := 339917, root := ~, start := 339903, stop := 339916 ) ], count := 
                                                                    [ 7, 3, 
                                                                      1, 27 ],
                                                                  name := "Mar\
k", next := 339924, root := ~, start := 339897, stop := 339923 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        This should be a list repre\
senting possible colours of vertices in the\n        digraph ", count := [ 7, \
3, 1, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\
 := rec(  ), content := [ rec( content := "D2", count := [ 7, 3, 1, 28 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 28 ], 
                                                                          math\
mode := "Text", name := "A", next := 340042, root := ~, start := 340033, stop \
:= 340041 ), rec( content := "; see \n        ", count := [ 7, 3, 1, 28 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label :\
= "for a digraph and a homogeneous list", Oper := "AutomorphismGroup" ), conte\
nt := 0, count := [ 7, 3, 1, 28 ], mathmode := "Text", name := "Ref", next := \
340144, root := ~, start := 340057, stop := 340143 ), rec( content := " \n    \
    for details of the permissible values for this argument.\n      ", count :\
= [ 7, 3, 1, 28 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      1, 28 ],
                                                                  name := "Ite\
m", next := 340224, root := ~, start := 339931, stop := 340223 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "order", count := [ 7, 3, 1, 29 ], mathmode := "Text", name := "PCDATA", ro\
ot := ~ ) ], count := [ 7, 3, 1, 29 ], mathmode := "Text", name := "A", next :\
= 340249, root := ~, start := 340237, stop := 340248 ) ], count := [ 7, 3, 1, 
                                                                      29 ], 
                                                                  name := "Mar\
k", next := 340256, root := ~, start := 340231, stop := 340255 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        The optional argument ", 
                                                                          coun\
t := [ 7, 3, 1, 30 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "order", count := [ 7, 3, 1, 3\
0 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, \
30 ], mathmode := "Text", name := "A", next := 340312, root := ~, start := 340\
300, stop := 340311 ), rec( content := " specifies the order the\n        vert\
ices in ", count := [ 7, 3, 1, 30 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "D1", count \
:= [ 7, 3, 1, 30 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\
 := [ 7, 3, 1, 30 ], mathmode := "Text", name := "A", next := 340366, root := \
~, start := 340357, stop := 340365 ), rec( content := " appear in the search f\
or homomorphisms. \n        The value of this parameter can have a large impac\
t\n        on the runtime of the function. It seems in many cases to be a good\
\n        idea for this to be the ", count := [ 7, 3, 1, 30 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "DigraphWe\
lshPowellOrder" ), content := 0, count := [ 7, 3, 1, 30 ], mathmode := "Text",
                                                                          name\
 := "Ref", next := 340613, root := ~, start := 340576, stop := 340612 ), 
                                                                      rec( 
                                                                          cont\
ent := ", i.e.\n        vertices ordered from highest to lowest degree.\n     \
 ", count := [ 7, 3, 1, 30 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ) ], 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      1, 30 ],
                                                                  name := "Ite\
m", next := 340689, root := ~, start := 340263, stop := 340688 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        The optional argument ", 
                                                                          coun\
t := [ 7, 3, 1, 32 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "aut_grp", count := [ 7, 3, 1,\
 32 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1\
, 32 ], mathmode := "Text", name := "A", next := 340747, root := ~, start := 3\
40733, stop := 340746 ), rec( content := " should be a subgroup of the\n      \
  automorphism group of ", count := [ 7, 3, 1, 32 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conten\
t := "D2", count := [ 7, 3, 1, 32 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 7, 3, 1, 32 ], mathmode := "Text", name := "A", next :=\
 340815, root := ~, start := 340806, stop := 340814 ), rec( content := ". This\
 function returns unique\n        representatives of the homomorphisms found u\
p to right multiplication\n        by ", count := [ 7, 3, 1, 32 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :=\
 [ rec( content := "aut_grp", count := [ 7, 3, 1, 32 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 32 ], mathmode := "Text", 
                                                                          name\
 := "A", next := 340949, root := ~, start := 340935, stop := 340948 ), 
                                                                      rec( 
                                                                          cont\
ent := ". If this argument is not specific, it defaults to the\n        full a\
utomorphism group of ", count := [ 7, 3, 1, 32 ], mathmode := "Text", name := \
"PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :\
= "D2", count := [ 7, 3, 1, 32 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ) ], count := [ 7, 3, 1, 32 ], mathmode := "Text", name := "A", next := 34\
1048, root := ~, start := 341039, stop := 341047 ), rec( content := ", which m\
ay be costly to calculate.\n      ", count := [ 7, 3, 1, 32 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 1, 32 ], name := "Item"
                                                                    , 
                                                                  next := 3410\
97, root := ~, start := 340696, stop := 341096 ) ], count := [ 7, 3, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 341109, 
                                                          root := ~, 
                                                          start := 335929, 
                                                          stop := 341108 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 1, 34 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := ChainDigraph(10);\n<immutable chain digraph with 10 vertices>\ngap>\
 D := DigraphSymmetricClosure(D);\n<immutable symmetric digraph with 10 vertic\
es, 18 edges>\ngap> HomomorphismDigraphsFinder(D, D, fail, [], infinity, 2, 0,\
\n> [3, 4], [], fail, fail);\n[ Transformation( [ 3, 4, 3, 4, 3, 4, 3, 4, 3, 4\
 ] ), \n  Transformation( [ 4, 3, 4, 3, 4, 3, 4, 3, 4, 3 ] ) ]\ngap> D2 := Com\
pleteDigraph(6);;\ngap> HomomorphismDigraphsFinder(D, D2, fail, [], 1, fail, 0\
,\n> [1 .. 6], [1, 2, 1], fail, fail);\n[ Transformation( [ 1, 2, 1, 3, 4, 5, \
6, 1, 2, 1 ] ) ]\ngap> func := function(user_param, t)\n> Add(user_param, t * \
user_param[1]);\n> end;;\ngap> HomomorphismDigraphsFinder(D, D2, func, [Transf\
ormation([2, 2])],\n> 3, fail, 0, [1 .. 6], [1, 2, 1], fail, fail);\n[ Transfo\
rmation( [ 2, 2 ] ), \n  Transformation( [ 2, 2, 2, 3, 4, 5, 6, 2, 2, 2 ] ), \
\n  Transformation( [ 2, 2, 2, 3, 4, 5, 6, 2, 2, 3 ] ), \n  Transformation( [ \
2, 2, 2, 3, 4, 5, 6, 2, 2, 4 ] ) ]\ngap> HomomorphismDigraphsFinder(NullDigrap\
h(2), NullDigraph(3), fail,\n> [], infinity, fail, 1, [1, 2, 3], fail, fail, f\
ail, fail,\n> Group(()));\n[ IdentityTransformation, Transformation( [ 1, 3, 3\
 ] ), \n  Transformation( [ 2, 1 ] ), Transformation( [ 2, 3, 3 ] ), \n  Trans\
formation( [ 3, 1, 3 ] ), Transformation( [ 3, 2, 3 ] ) ]\ngap> HomomorphismDi\
graphsFinder(NullDigraph(2), NullDigraph(3), fail,\n> [], infinity, fail, 1, [\
1, 2, 3], fail, fail, fail, fail,\n> Group((1, 2)));\n[ IdentityTransformation\
, Transformation( [ 1, 3, 3 ] ), \n  Transformation( [ 3, 1, 3 ] ) ]", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      1, 35 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 1, 35 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 342664, 
                                                          root := ~, 
                                                          start := 341115, 
                                                          stop := 342663 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 1, 36 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 342681, root := ~, 
                                                  start := 335508, 
                                                  stop := 342680 ) ], 
                                          count := [ 7, 3, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 342695, root := ~, 
                                          start := 335279, stop := 342694 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 1, 36 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "DigraphHomomorphism" ), content := 0, count := [ 7, 3, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 342775, root := ~, 
                                                  start := 342716, 
                                                  stop := 342774 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A transf\
ormation, or ", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 342820, 
                                                          root := ~, 
                                                          start := 342809, 
                                                          stop := 342819 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 342831, root := ~, 
                                                  start := 342778, 
                                                  stop := 342830 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A h\
omomorphism from ", count := [ 7, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 342887, 
                                                          root := ~, 
                                                          start := 342872, 
                                                          stop := 342886 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 342906, 
                                                          root := ~, 
                                                          start := 342891, 
                                                          stop := 342905 ), 
                                                      rec( 
                                                          content := " is a ma\
pping from\n    the vertex set of ", count := [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 342962, 
                                                          root := ~, 
                                                          start := 342947, 
                                                          stop := 342961 ), 
                                                      rec( 
                                                          content := " to a su\
bset of the vertices of\n    ", count := [ 7, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 343013, 
                                                          root := ~, 
                                                          start := 342998, 
                                                          stop := 343012 ), 
                                                      rec( 
                                                          content := ", such t\
hat every pair of vertices ", count := [ 7, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i,j]", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 343060, 
                                                          root := ~, 
                                                          start := 343048, 
                                                          stop := 343059 ), 
                                                      rec( 
                                                          content := " which h\
as\n    an edge ", count := [ 7, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
->j", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 343094, 
                                                          root := ~, 
                                                          start := 343083, 
                                                          stop := 343093 ), 
                                                      rec( 
                                                          content := " is mapp\
ed to a pair of vertices ", count := [ 7, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
a,b]", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 343139, 
                                                          root := ~, 
                                                          start := 343127, 
                                                          stop := 343138 ), 
                                                      rec( 
                                                          content := " which\n\
    has an edge ", count := [ 7, 3, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
->b", count := [ 7, 3, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 343173, 
                                                          root := ~, 
                                                          start := 343162, 
                                                          stop := 343172 ), 
                                                      rec( 
                                                          content := ".  Note \
that non-adjacent vertices can still be\n    mapped to adjacent vertices. ", 
                                                          count := 
                                                            [ 7, 3, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 343258, 
                                                          root := ~, 
                                                          start := 343254, 
                                                          stop := 343257 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphHomomorphism", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 2, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 343290, 
                                                          root := ~, 
                                                          start := 343264, 
                                                          stop := 343289 ), 
                                                      rec( 
                                                          content := " returns\
 a single homomorphism between\n    ", count := [ 7, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 343348, 
                                                          root := ~, 
                                                          start := 343333, 
                                                          stop := 343347 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 343368, 
                                                          root := ~, 
                                                          start := 343353, 
                                                          stop := 343367 ), 
                                                      rec( 
                                                          content := " if it e\
xists, otherwise it returns\n    ", count := [ 7, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 343419, 
                                                          root := ~, 
                                                          start := 343408, 
                                                          stop := 343418 ), 
                                                      rec( content := ".\n", 
                                                          count := 
                                                            [ 7, 3, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph([[3, 5], [2], [3, 1], [], \
[4]]);\n<immutable digraph with 5 vertices, 6 edges>\ngap> DigraphHomomorphism\
(gr1, gr1);\nIdentityTransformation\ngap> map := DigraphHomomorphism(gr1, gr2)\
;\nTransformation( [ 3, 1, 5, 4, 5 ] )\ngap> IsDigraphHomomorphism(gr1, gr2, m\
ap);\ntrue\n", count := [ 7, 3, 2, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 7, 3, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 343767, 
                                                          root := ~, 
                                                          start := 343421, 
                                                          stop := 343766 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 343784, root := ~, 
                                                  start := 342834, 
                                                  stop := 343783 ) ], 
                                          count := [ 7, 3, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 343798, root := ~, 
                                          start := 342701, stop := 343797 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 2, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "HomomorphismsDigraphs" ), content := 0, count := [ 7, 3, 3, 2 ],
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 343880, root := ~, 
                                                  start := 343819, 
                                                  stop := 343879 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "HomomorphismsDigraphsRepresentatives" ), content := 0, 
                                                  count := [ 7, 3, 3, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 343959, root := ~, 
                                                  start := 343883, 
                                                  stop := 343958 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A list o\
f transformations.", count := [ 7, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 3, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 344008, root := ~, 
                                                  start := 343962, 
                                                  stop := 344007 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
omomorphismsDigraphsRepresentatives", count := [ 7, 3, 3, 5 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 344072, 
                                                          root := ~, 
                                                          start := 344029, 
                                                          stop := 344071 ), 
                                                      rec( 
                                                          content := " finds e\
very\n    ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Homomorphism" ), content := 0, count := [ 7, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 344122, 
                                                          root := ~, 
                                                          start := 344089, 
                                                          stop := 344121 ), 
                                                      rec( 
                                                          content := " between\
 ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 344146, 
                                                          root := ~, 
                                                          start := 344131, 
                                                          stop := 344145 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 344170, 
                                                          root := ~, 
                                                          start := 344155, 
                                                          stop := 344169 ), 
                                                      rec( 
                                                          content := ", up to \
right multiplication by an element of the\n    ", count := [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := [ 7, 3, 3, 5 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 344277, 
                                                          root := ~, 
                                                          start := 344224, 
                                                          stop := 344276 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 344296, 
                                                          root := ~, 
                                                          start := 344281, 
                                                          stop := 344295 ), 
                                                      rec( 
                                                          content := ".\n    I\
n other words, every homomorphism ", count := [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 344345, 
                                                          root := ~, 
                                                          start := 344337, 
                                                          stop := 344344 ), 
                                                      rec( 
                                                          content := " between\
 ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 344369, 
                                                          root := ~, 
                                                          start := 344354, 
                                                          stop := 344368 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 344393, 
                                                          root := ~, 
                                                          start := 344378, 
                                                          stop := 344392 ), 
                                                      rec( 
                                                          content := " can be \
written as the composition ", count := [ 7, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
 = g * x", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 344444, 
                                                          root := ~, 
                                                          start := 344428, 
                                                          stop := 344443 ), 
                                                      rec( 
                                                          content := ",\n    w\
here ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "g\
", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 344464, 
                                                          root := ~, 
                                                          start := 344456, 
                                                          stop := 344463 ), 
                                                      rec( 
                                                          content := " is one \
of the ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
omomorphismsDigraphsRepresentatives", count := [ 7, 3, 3, 5 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 344522, 
                                                          root := ~, 
                                                          start := 344479, 
                                                          stop := 344521 ), 
                                                      rec( 
                                                          content := "\n    an\
d ", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 344539, 
                                                          root := ~, 
                                                          start := 344531, 
                                                          stop := 344538 ), 
                                                      rec( 
                                                          content := " is an a\
utomorphism of ", count := [ 7, 3, 3, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 344577, 
                                                          root := ~, 
                                                          start := 344562, 
                                                          stop := 344576 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 344587, 
                                                          root := ~, 
                                                          start := 344583, 
                                                          stop := 344586 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "H\
omomorphismsDigraphs", count := [ 7, 3, 3, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 3, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 344621, 
                                                          root := ~, 
                                                          start := 344593, 
                                                          stop := 344620 ), 
                                                      rec( 
                                                          content := " returns\
 all homomorphisms between\n    ", count := [ 7, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 344675, 
                                                          root := ~, 
                                                          start := 344660, 
                                                          stop := 344674 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 344695, 
                                                          root := ~, 
                                                          start := 344680, 
                                                          stop := 344694 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph([[3, 5], [2], [3, 1], [], \
[4]]);\n<immutable digraph with 5 vertices, 6 edges>\ngap> HomomorphismsDigrap\
hs(gr1, gr2);\n[ Transformation( [ 1, 3, 1 ] ), Transformation( [ 1, 3, 3 ] ),\
 \n  Transformation( [ 1, 5, 4, 4, 5 ] ), Transformation( [ 2, 2, 2 ] ), \n  T\
ransformation( [ 3, 1, 3 ] ), Transformation( [ 3, 1, 5, 4, 5 ] ), \n  Transfo\
rmation( [ 3, 3, 1 ] ), Transformation( [ 3, 3, 3 ] ) ]\ngap> HomomorphismsDig\
raphsRepresentatives(gr1, CompleteDigraph(3));\n[ Transformation( [ 2, 1 ] ), \
Transformation( [ 2, 1, 2 ] ) ]\n", count := [ 7, 3, 3, 7 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 345301, 
                                                          root := ~, 
                                                          start := 344701, 
                                                          stop := 345300 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 3, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 3, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 345318, root := ~, 
                                                  start := 344011, 
                                                  stop := 345317 ) ], 
                                          count := [ 7, 3, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 345332, root := ~, 
                                          start := 343804, stop := 345331 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 3, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "DigraphMonomorphism" ), content := 0, count := [ 7, 3, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 345412, root := ~, 
                                                  start := 345353, 
                                                  stop := 345411 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A transfo\
rmation, or ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 345456, 
                                                          root := ~, 
                                                          start := 345445, 
                                                          stop := 345455 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 345467, root := ~, 
                                                  start := 345415, 
                                                  stop := 345466 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphMonomorphism", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 345514, 
                                                          root := ~, 
                                                          start := 345488, 
                                                          stop := 345513 ), 
                                                      rec( 
                                                          content := " returns\
 a single ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
njective", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 345548, 
                                                          root := ~, 
                                                          start := 345532, 
                                                          stop := 345547 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Homomorphism" ), content := 0, count := [ 7, 3, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 345588, 
                                                          root := ~, 
                                                          start := 345549, 
                                                          stop := 345587 ), 
                                                      rec( 
                                                          content := " between\
 ", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 345612, 
                                                          root := ~, 
                                                          start := 345597, 
                                                          stop := 345611 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 345632, 
                                                          root := ~, 
                                                          start := 345617, 
                                                          stop := 345631 ), 
                                                      rec( 
                                                          content := "\n    if\
 one exists, otherwise it returns ", count := [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 345684, 
                                                          root := ~, 
                                                          start := 345673, 
                                                          stop := 345683 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph([[3, 5], [2], [3, 1], [], \
[4]]);\n<immutable digraph with 5 vertices, 6 edges>\ngap> DigraphMonomorphism\
(gr1, gr1);\nIdentityTransformation\ngap> DigraphMonomorphism(gr1, gr2);\nTran\
sformation( [ 3, 1, 5, 4, 5 ] )\n", count := [ 7, 3, 4, 4 ], name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 345981, 
                                                          root := ~, 
                                                          start := 345690, 
                                                          stop := 345980 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 345998, root := ~, 
                                                  start := 345470, 
                                                  stop := 345997 ) ], 
                                          count := [ 7, 3, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 346012, root := ~, 
                                          start := 345338, stop := 346011 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 4, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "MonomorphismsDigraphs" ), content := 0, count := [ 7, 3, 5, 2 ],
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 346094, root := ~, 
                                                  start := 346033, 
                                                  stop := 346093 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "MonomorphismsDigraphsRepresentatives" ), content := 0, 
                                                  count := [ 7, 3, 5, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 346173, root := ~, 
                                                  start := 346097, 
                                                  stop := 346172 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 transformations.", count := [ 7, 3, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 346221, root := ~, 
                                                  start := 346176, 
                                                  stop := 346220 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
se operations behave the same as ", count := [ 7, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Homomor\
phismsDigraphs" ), content := 0, count := [ 7, 3, 5, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 346313, 
                                                          root := ~, 
                                                          start := 346278, 
                                                          stop := 346312 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Homomor\
phismsDigraphsRepresentatives" ), content := 0, count := [ 7, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 346372, 
                                                          root := ~, 
                                                          start := 346322, 
                                                          stop := 346371 ), 
                                                      rec( 
                                                          content := ", except\
 they only return\n    ", count := [ 7, 3, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
njective", count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 346418, 
                                                          root := ~, 
                                                          start := 346402, 
                                                          stop := 346417 ), 
                                                      rec( 
                                                          content := " homomor\
phisms.\n    ", count := [ 7, 3, 5, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph([[3, 5], [2], [3, 1], [], \
[4]]);\n<immutable digraph with 5 vertices, 6 edges>\ngap> MonomorphismsDigrap\
hs(gr1, gr2);\n[ Transformation( [ 1, 5, 4, 4, 5 ] ), \n  Transformation( [ 3,\
 1, 5, 4, 5 ] ) ]\ngap> MonomorphismsDigraphsRepresentatives(gr1, CompleteDigr\
aph(3));\n[ Transformation( [ 2, 1 ] ) ]\n", count := [ 7, 3, 5, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 5, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 346815, 
                                                          root := ~, 
                                                          start := 346438, 
                                                          stop := 346814 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 346832, root := ~, 
                                                  start := 346224, 
                                                  stop := 346831 ) ], 
                                          count := [ 7, 3, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 346846, root := ~, 
                                          start := 346018, stop := 346845 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 5, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "DigraphEpimorphism" ), content := 0, count := [ 7, 3, 6, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 346925, root := ~, 
                                                  start := 346867, 
                                                  stop := 346924 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A transfo\
rmation, or ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 346969, 
                                                          root := ~, 
                                                          start := 346958, 
                                                          stop := 346968 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 346980, root := ~, 
                                                  start := 346928, 
                                                  stop := 346979 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEpimorphism", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "C", 
                                                          next := 347026, 
                                                          root := ~, 
                                                          start := 347001, 
                                                          stop := 347025 ), 
                                                      rec( 
                                                          content := " returns\
 a single ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
urjective", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 347061, 
                                                          root := ~, 
                                                          start := 347044, 
                                                          stop := 347060 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Homomorphism" ), content := 0, count := [ 7, 3, 6, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 347101, 
                                                          root := ~, 
                                                          start := 347062, 
                                                          stop := 347100 ), 
                                                      rec( 
                                                          content := " between\
 ", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 347125, 
                                                          root := ~, 
                                                          start := 347110, 
                                                          stop := 347124 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 347145, 
                                                          root := ~, 
                                                          start := 347130, 
                                                          stop := 347144 ), 
                                                      rec( 
                                                          content := "\n    if\
 one exists, otherwise it returns ", count := [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 347197, 
                                                          root := ~, 
                                                          start := 347186, 
                                                          stop := 347196 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := DigraphReverse(ChainDigraph(4));\n<immutable digraph with 4 verti\
ces, 3 edges>\ngap> gr2 := DigraphRemoveEdge(CompleteDigraph(3), [1, 2]);\n<im\
mutable digraph with 3 vertices, 5 edges>\ngap> DigraphEpimorphism(gr2, gr1);\
\nfail\ngap> DigraphEpimorphism(gr1, gr2);\nTransformation( [ 3, 1, 2, 3 ] )\n\
", count := [ 7, 3, 6, 4 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 7, 3, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 347537, 
                                                          root := ~, 
                                                          start := 347203, 
                                                          stop := 347536 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 347554, root := ~, 
                                                  start := 346983, 
                                                  stop := 347553 ) ], 
                                          count := [ 7, 3, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 347568, root := ~, 
                                          start := 346852, stop := 347567 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 6, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "EpimorphismsDigraphs" ), content := 0, count := [ 7, 3, 7, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 347649, root := ~, 
                                                  start := 347589, 
                                                  stop := 347648 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "EpimorphismsDigraphsRepresentatives" ), content := 0, 
                                                  count := [ 7, 3, 7, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 347727, root := ~, 
                                                  start := 347652, 
                                                  stop := 347726 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 transformations.", count := [ 7, 3, 7, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 7, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 347775, root := ~, 
                                                  start := 347730, 
                                                  stop := 347774 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
se operations behave the same as ", count := [ 7, 3, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Homomor\
phismsDigraphs" ), content := 0, count := [ 7, 3, 7, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 347867, 
                                                          root := ~, 
                                                          start := 347832, 
                                                          stop := 347866 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Homomor\
phismsDigraphsRepresentatives" ), content := 0, count := [ 7, 3, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 347926, 
                                                          root := ~, 
                                                          start := 347876, 
                                                          stop := 347925 ), 
                                                      rec( 
                                                          content := ", except\
 they only return\n    ", count := [ 7, 3, 7, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
urjective", count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 347973, 
                                                          root := ~, 
                                                          start := 347956, 
                                                          stop := 347972 ), 
                                                      rec( 
                                                          content := " homomor\
phisms.\n    ", count := [ 7, 3, 7, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr1 := DigraphReverse(ChainDigraph(4));\n<immutable digraph with 4 verti\
ces, 3 edges>\ngap> gr2 := DigraphSymmetricClosure(CycleDigraph(3));\n<immutab\
le symmetric digraph with 3 vertices, 6 edges>\ngap> EpimorphismsDigraphsRepre\
sentatives(gr1, gr2);\n[ Transformation( [ 3, 1, 2, 1 ] ), Transformation( [ 3\
, 1, 2, 3 ] ), \n  Transformation( [ 2, 1, 2, 3 ] ) ]\ngap> EpimorphismsDigrap\
hs(gr1, gr2);\n[ Transformation( [ 1, 2, 1, 3 ] ), Transformation( [ 1, 2, 3, \
1 ] ), \n  Transformation( [ 1, 2, 3, 2 ] ), Transformation( [ 1, 3, 1, 2 ] ),\
 \n  Transformation( [ 1, 3, 2, 1 ] ), Transformation( [ 1, 3, 2, 3 ] ), \n  T\
ransformation( [ 2, 1, 2, 3 ] ), Transformation( [ 2, 1, 3, 1 ] ), \n  Transfo\
rmation( [ 2, 1, 3, 2 ] ), Transformation( [ 2, 3, 1, 2 ] ), \n  Transformatio\
n( [ 2, 3, 1, 3 ] ), Transformation( [ 2, 3, 2, 1 ] ), \n  Transformation( [ 3\
, 1, 2, 1 ] ), Transformation( [ 3, 1, 2, 3 ] ), \n  Transformation( [ 3, 1, 3\
, 2 ] ), Transformation( [ 3, 2, 1, 2 ] ), \n  Transformation( [ 3, 2, 1, 3 ] \
), Transformation( [ 3, 2, 3, 1 ] ) ]\n", count := [ 7, 3, 7, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 7, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 349060, 
                                                          root := ~, 
                                                          start := 347993, 
                                                          stop := 349059 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 7, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 349077, root := ~, 
                                                  start := 347778, 
                                                  stop := 349076 ) ], 
                                          count := [ 7, 3, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 349091, root := ~, 
                                          start := 347574, stop := 349090 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 7, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph1, digrap\
h2", Name := "DigraphEmbedding" ), content := 0, count := [ 7, 3, 8, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 349168, root := ~, 
                                                  start := 349112, 
                                                  stop := 349167 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A transf\
ormation, or ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 349213, 
                                                          root := ~, 
                                                          start := 349202, 
                                                          stop := 349212 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 349224, root := ~, 
                                                  start := 349171, 
                                                  stop := 349223 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    An \
embedding of a digraph ", count := [ 7, 3, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 349286, 
                                                          root := ~, 
                                                          start := 349271, 
                                                          stop := 349285 ), 
                                                      rec( 
                                                          content := " into an\
other digraph\n    ", count := [ 7, 3, 8, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 349327, 
                                                          root := ~, 
                                                          start := 349312, 
                                                          stop := 349326 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Monomorphism" ), content := 0, count := [ 7, 3, 8, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 349366, 
                                                          root := ~, 
                                                          start := 349333, 
                                                          stop := 349365 ), 
                                                      rec( 
                                                          content := " from ",
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 349387, 
                                                          root := ~, 
                                                          start := 349372, 
                                                          stop := 349386 ), 
                                                      rec( 
                                                          content := "\n    to\
 ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 349410, 
                                                          root := ~, 
                                                          start := 349395, 
                                                          stop := 349409 ), 
                                                      rec( 
                                                          content := " which h\
as the additional property that a pair of\n    vertices ", 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i, j]", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 349486, 
                                                          root := ~, 
                                                          start := 349473, 
                                                          stop := 349485 ), 
                                                      rec( 
                                                          content := " which h\
ave no edge ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 -> j", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 349519, 
                                                          root := ~, 
                                                          start := 349506, 
                                                          stop := 349518 ), 
                                                      rec( content := " in ", 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 349538, 
                                                          root := ~, 
                                                          start := 349523, 
                                                          stop := 349537 ), 
                                                      rec( 
                                                          content := " are\n\n\
    mapped to a pair of vertices ", count := [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
a, b]", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 349590, 
                                                          root := ~, 
                                                          start := 349577, 
                                                          stop := 349589 ), 
                                                      rec( 
                                                          content := " which h\
ave no edge ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "a\
->b", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 349621, 
                                                          root := ~, 
                                                          start := 349610, 
                                                          stop := 349620 ), 
                                                      rec( 
                                                          content := " in\n   \
 ", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 8, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 349644, 
                                                          root := ~, 
                                                          start := 349629, 
                                                          stop := 349643 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 8, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 349649, 
                                                          root := ~, 
                                                          start := 349645, 
                                                          stop := 349648 ), 
                                                      rec( 
                                                          content := "\n\n    \
In other words, an embedding ", count := [ 7, 3, 8, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 349692, 
                                                          root := ~, 
                                                          start := 349684, 
                                                          stop := 349691 ), 
                                                      rec( 
                                                          content := " is an i\
somorphism from\n    ", count := [ 7, 3, 8, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph1", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 349735, 
                                                          root := ~, 
                                                          start := 349720, 
                                                          stop := 349734 ), 
                                                      rec( 
                                                          content := " to the \
", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Induced\
Subdigraph" ), content := 0, count := [ 7, 3, 8, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 349774, 
                                                          root := ~, 
                                                          start := 349743, 
                                                          stop := 349773 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph2", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 349793, 
                                                          root := ~, 
                                                          start := 349778, 
                                                          stop := 349792 ), 
                                                      rec( 
                                                          content := "\n    on\
 the image of ", count := [ 7, 3, 8, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
", count := [ 7, 3, 8, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 349822, 
                                                          root := ~, 
                                                          start := 349814, 
                                                          stop := 349821 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 3, 8, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 349828, 
                                                          root := ~, 
                                                          start := 349824, 
                                                          stop := 349827 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphEmbedding", count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "C", 
                                                          next := 349857, 
                                                          root := ~, 
                                                          start := 349834, 
                                                          stop := 349856 ), 
                                                      rec( 
                                                          content := " returns\
 a single embedding if one exists, otherwise\n    it returns ", 
                                                          count := 
                                                            [ 7, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 8, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 349936, 
                                                          root := ~, 
                                                          start := 349925, 
                                                          stop := 349935 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 8, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := ChainDigraph(3);\n<immutable chain digraph with 3 vertices>\ngap> \
DigraphEmbedding(gr, CompleteDigraph(4));\nfail\ngap> DigraphEmbedding(gr, Dig\
raph([[3], [1, 4], [1], [3]]));\nTransformation( [ 2, 4, 3, 4 ] )\n", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      8, 6 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 8, 6 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 350190, 
                                                          root := ~, 
                                                          start := 349942, 
                                                          stop := 350189 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 8, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 350207, root := ~, 
                                                  start := 349227, 
                                                  stop := 350206 ) ], 
                                          count := [ 7, 3, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 350221, root := ~, 
                                          start := 349097, stop := 350220 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 8, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D1, D2", 
                                                      Name := "EmbeddingsDigra\
phs" ), content := 0, count := [ 7, 3, 9, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 350288, root := ~, 
                                                  start := 350242, 
                                                  stop := 350287 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D1, D2", 
                                                      Name := "EmbeddingsDigra\
phsRepresentatives" ), content := 0, count := [ 7, 3, 9, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 350352, root := ~, 
                                                  start := 350291, 
                                                  stop := 350351 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 transformations.", count := [ 7, 3, 9, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 350400, root := ~, 
                                                  start := 350355, 
                                                  stop := 350399 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
se operations behave the same as ", count := [ 7, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Homomor\
phismsDigraphs" ), content := 0, count := [ 7, 3, 9, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 350492, 
                                                          root := ~, 
                                                          start := 350457, 
                                                          stop := 350491 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Homomor\
phismsDigraphsRepresentatives" ), content := 0, count := [ 7, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 350551, 
                                                          root := ~, 
                                                          start := 350501, 
                                                          stop := 350550 ), 
                                                      rec( 
                                                          content := ", except\
 they only return\n    embeddings of ", count := [ 7, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
1", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 350604, 
                                                          root := ~, 
                                                          start := 350595, 
                                                          stop := 350603 ), 
                                                      rec( 
                                                          content := " into ",
                                                          count := 
                                                            [ 7, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
2", count := [ 7, 3, 9, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 350619, 
                                                          root := ~, 
                                                          start := 350610, 
                                                          stop := 350618 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 350624, 
                                                          root := ~, 
                                                          start := 350620, 
                                                          stop := 350623 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 7, 3, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsDigra\
phEmbedding" ), content := 0, count := [ 7, 3, 9, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 350671, 
                                                          root := ~, 
                                                          start := 350639, 
                                                          stop := 350670 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D1 := NullDigraph(2);\n<immutable empty digraph with 2 vertices>\ngap> D\
2 := CycleDigraph(5);\n<immutable cycle digraph with 5 vertices>\ngap> Embeddi\
ngsDigraphsRepresentatives(D1, D2);\n[ Transformation( [ 1, 3, 3 ] ), Transfor\
mation( [ 1, 4, 3, 4 ] ) ]\ngap> EmbeddingsDigraphs(D1, D2);\n[ Transformation\
( [ 1, 3, 3 ] ), Transformation( [ 1, 4, 3, 4 ] ), \n  Transformation( [ 2, 4,\
 4, 5, 1 ] ), \n  Transformation( [ 2, 5, 4, 5, 1 ] ), \n  Transformation( [ 3\
, 1, 5, 1, 2 ] ), \n  Transformation( [ 3, 5, 5, 1, 2 ] ), \n  Transformation(\
 [ 4, 1, 1, 2, 3 ] ), \n  Transformation( [ 4, 2, 1, 2, 3 ] ), \n  Transformat\
ion( [ 5, 2, 2, 3, 4 ] ), \n  Transformation( [ 5, 3, 2, 3, 4 ] ) ]\n", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      9, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 9, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 351385, 
                                                          root := ~, 
                                                          start := 350677, 
                                                          stop := 351384 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 9, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 351402, root := ~, 
                                                  start := 350403, 
                                                  stop := 351401 ) ], 
                                          count := [ 7, 3, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 351416, root := ~, 
                                          start := 350227, stop := 351415 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 9, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "src, ran, x",
                                                      Label := "for digraphs a\
nd a permutation or transformation", Name := "IsDigraphHomomorphism" ), 
                                                  content := 0, 
                                                  count := [ 7, 3, 10, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 351557, root := ~, 
                                                  start := 351437, 
                                                  stop := 351556 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "src, ran, x, col\
1, col2", Name := "IsDigraphHomomorphism" ), content := 0, 
                                                  count := [ 7, 3, 10, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 351626, root := ~, 
                                                  start := 351560, 
                                                  stop := 351625 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "src, ran, x",
                                                      Label := "for digraphs a\
nd a permutation or transformation", Name := "IsDigraphEpimorphism" ), 
                                                  content := 0, 
                                                  count := [ 7, 3, 10, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 351747, root := ~, 
                                                  start := 351629, 
                                                  stop := 351746 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "src, ran, x, col\
1, col2", Name := "IsDigraphEpimorphism" ), content := 0, 
                                                  count := [ 7, 3, 10, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 351815, root := ~, 
                                                  start := 351750, 
                                                  stop := 351814 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "src, ran, x",
                                                      Label := "for digraphs a\
nd a permutation or transformation", Name := "IsDigraphMonomorphism" ), 
                                                  content := 0, 
                                                  count := [ 7, 3, 10, 10 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 351937, root := ~, 
                                                  start := 351818, 
                                                  stop := 351936 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "src, ran, x, col\
1, col2", Name := "IsDigraphMonomorphism" ), content := 0, 
                                                  count := [ 7, 3, 10, 12 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 352006, root := ~, 
                                                  start := 351940, 
                                                  stop := 352005 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, x", 
                                                      Label := "for digraphs a\
nd a permutation or transformation", Name := "IsDigraphEndomorphism" ), 
                                                  content := 0, 
                                                  count := [ 7, 3, 10, 14 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 352127, root := ~, 
                                                  start := 352009, 
                                                  stop := 352126 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, x, col"
                                                        , 
                                                      Name := "IsDigraphEndomo\
rphism" ), content := 0, count := [ 7, 3, 10, 16 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 352188, root := ~, 
                                                  start := 352130, 
                                                  stop := 352187 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 352211, 
                                                          root := ~, 
                                                          start := 352200, 
                                                          stop := 352210 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 352227, 
                                                          root := ~, 
                                                          start := 352215, 
                                                          stop := 352226 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 10, 17 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 352238, root := ~, 
                                                  start := 352191, 
                                                  stop := 352237 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphHomomorphism", count := [ 7, 3, 10, 17 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 10, 17 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 352287, 
                                                          root := ~, 
                                                          start := 352259, 
                                                          stop := 352286 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 352307, 
                                                          root := ~, 
                                                          start := 352296, 
                                                          stop := 352306 ), 
                                                      rec( 
                                                          content := " if the \
permutation\n    or transformation ", count := [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352357, 
                                                          root := ~, 
                                                          start := 352349, 
                                                          stop := 352356 ), 
                                                      rec( 
                                                          content := " is a ho\
momorphism from the digraph\n    ", count := [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352407, 
                                                          root := ~, 
                                                          start := 352397, 
                                                          stop := 352406 ), 
                                                      rec( 
                                                          content := " to the \
digraph ", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 3, 10, 17 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352433, 
                                                          root := ~, 
                                                          start := 352423, 
                                                          stop := 352432 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 10, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 10, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 352443, 
                                                          root := ~, 
                                                          start := 352439, 
                                                          stop := 352442 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphEpimorphism", count := [ 7, 3, 10, 18 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 10, 18 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 352476, 
                                                          root := ~, 
                                                          start := 352449, 
                                                          stop := 352475 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 352496, 
                                                          root := ~, 
                                                          start := 352485, 
                                                          stop := 352495 ), 
                                                      rec( 
                                                          content := " if the \
permutation\n    or transformation ", count := [ 7, 3, 10, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 10, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352546, 
                                                          root := ~, 
                                                          start := 352538, 
                                                          stop := 352545 ), 
                                                      rec( 
                                                          content := " is a su\
rjective homomorphism from the digraph\n    ", count := [ 7, 3, 10, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352607, 
                                                          root := ~, 
                                                          start := 352597, 
                                                          stop := 352606 ), 
                                                      rec( 
                                                          content := " to the \
digraph ", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 3, 10, 18 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352633, 
                                                          root := ~, 
                                                          start := 352623, 
                                                          stop := 352632 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 10, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 10, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 352643, 
                                                          root := ~, 
                                                          start := 352639, 
                                                          stop := 352642 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphMonomorphism", count := [ 7, 3, 10, 19 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 10, 19 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 352677, 
                                                          root := ~, 
                                                          start := 352649, 
                                                          stop := 352676 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 352697, 
                                                          root := ~, 
                                                          start := 352686, 
                                                          stop := 352696 ), 
                                                      rec( 
                                                          content := " if the \
permutation\n    or transformation ", count := [ 7, 3, 10, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 10, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352747, 
                                                          root := ~, 
                                                          start := 352739, 
                                                          stop := 352746 ), 
                                                      rec( 
                                                          content := " is an i\
njective homomorphism from the digraph\n    ", count := [ 7, 3, 10, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352808, 
                                                          root := ~, 
                                                          start := 352798, 
                                                          stop := 352807 ), 
                                                      rec( 
                                                          content := " to the \
digraph ", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 3, 10, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352834, 
                                                          root := ~, 
                                                          start := 352824, 
                                                          stop := 352833 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 10, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 10, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 352844, 
                                                          root := ~, 
                                                          start := 352840, 
                                                          stop := 352843 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphEndomorphism", count := [ 7, 3, 10, 20 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 10, 20 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 352878, 
                                                          root := ~, 
                                                          start := 352850, 
                                                          stop := 352877 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 352898, 
                                                          root := ~, 
                                                          start := 352887, 
                                                          stop := 352897 ), 
                                                      rec( 
                                                          content := " if the \
permutation\n    or transformation ", count := [ 7, 3, 10, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 10, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 352948, 
                                                          root := ~, 
                                                          start := 352940, 
                                                          stop := 352947 ), 
                                                      rec( 
                                                          content := " is an e\
ndomorphism of the digraph\n    ", count := [ 7, 3, 10, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 10, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 353001, 
                                                          root := ~, 
                                                          start := 352987, 
                                                          stop := 353000 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 10, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 10, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 353011, 
                                                          root := ~, 
                                                          start := 353007, 
                                                          stop := 353010 ), 
                                                      rec( 
                                                          content := "\n\n    \
A permutation or transformation ", count := [ 7, 3, 10, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 10, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 353057, 
                                                          root := ~, 
                                                          start := 353049, 
                                                          stop := 353056 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 7, 3, 10, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
omomorphism", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 353082, 
                                                          root := ~, 
                                                          start := 353063, 
                                                          stop := 353081 ), 
                                                      rec( 
                                                          content := " from a\\
n    digraph ", count := [ 7, 3, 10, 21 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 353112, 
                                                          root := ~, 
                                                          start := 353102, 
                                                          stop := 353111 ), 
                                                      rec( 
                                                          content := " to a di\
graph ", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 3, 10, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 353136, 
                                                          root := ~, 
                                                          start := 353126, 
                                                          stop := 353135 ), 
                                                      rec( 
                                                          content := " if the \
following hold:\n    ", count := [ 7, 3, 10, 21 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 7, 3, 10, 23 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "[u ^ ", count := [ 7, 3, 10, 23 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec\
( content := "x", count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "A"\
, next := 353208, root := ~, start := 353200, stop := 353207 ), rec( content :\
= ", v ^ ", count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ), rec( attributes := rec(  ), content := [ rec( content := "x", coun\
t := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], co\
unt := [ 7, 3, 10, 23 ], mathmode := "Text", name := "A", next := 353222, root\
 := ~, start := 353214, stop := 353221 ), rec( content := "]", count := [ 7, 3\
, 10, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7,\
 3, 10, 23 ], mathmode := "Text", name := "C", next := 353227, root := ~, star\
t := 353192, stop := 353226 ), rec( content := " is an edge of\n        ", 
                                                                          coun\
t := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "ran", count := [ 7, 3, 10, 23\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, \
23 ], mathmode := "Text", name := "A", next := 353260, root := ~, start := 353\
250, stop := 353259 ), rec( content := " whenever ", count := [ 7, 3, 10, 23 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "[u, v]", count := [ 7, 3, 10, 23 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 23 ], mathmode := "T\
ext", name := "C", next := 353283, root := ~, start := 353270, stop := 353282 
                                                                         ), 
                                                                      rec( 
                                                                          cont\
ent := " is an\n        edge of ", count := [ 7, 3, 10, 23 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ re\
c( content := "src", count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 7, 3, 10, 23 ], mathmode := "Text", name := \
"A", next := 353316, root := ~, start := 353306, stop := 353315 ), rec( conten\
t := "; and ", count := [ 7, 3, 10, 23 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 7, 3, 10, 23 ], name := "Item", next := 353329, 
                                                                  root := ~, 
                                                                  start := 353\
177, stop := 353328 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        ", count := [ 7, 3, 10, 25 ], mathmode := "Text", name := "PCDATA\
", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "x", \
count := [ 7, 3, 10, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ]
                                                                            , 
                                                                          coun\
t := [ 7, 3, 10, 25 ], mathmode := "Text", name := "A", next := 353359, root :\
= ~, start := 353351, stop := 353358 ), rec( content := " fixes every ", count\
 := [ 7, 3, 10, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "i", count := [ 7, 3, 10, 25 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 25\
 ], mathmode := "Text", name := "C", next := 353380, root := ~, start := 35337\
2, stop := 353379 ), rec( content := " which is not a vertex of ", count := [ \
7, 3, 10, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\
utes := rec(  ), content := [ rec( content := "src", count := [ 7, 3, 10, 25 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 25\
 ], mathmode := "Text", name := "A", next := 353416, root := ~, start := 35340\
6, stop := 353415 ), rec( content := ".\n      ", count := [ 7, 3, 10, 25 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 25 ], 
                                                                  name := "Ite\
m", next := 353431, root := ~, start := 353336, stop := 353430 ) ], 
                                                          count := 
                                                            [ 7, 3, 10, 22 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 353443, 
                                                          root := ~, 
                                                          start := 353164, 
                                                          stop := 353442 ), 
                                                      rec( 
                                                          content := "\n    Se\
e also ", count := [ 7, 3, 10, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Generat\
orsOfEndomorphismMonoid" ), content := 0, count := [ 7, 3, 10, 27 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 353501, 
                                                          root := ~, 
                                                          start := 353457, 
                                                          stop := 353500 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 10, 27 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 10, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 353506, 
                                                          root := ~, 
                                                          start := 353502, 
                                                          stop := 353505 ), 
                                                      rec( 
                                                          content := "\n\n\n  \
  If ", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol1", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 353527, 
                                                          root := ~, 
                                                          start := 353516, 
                                                          stop := 353526 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 3, 10, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol2", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 353543, 
                                                          root := ~, 
                                                          start := 353532, 
                                                          stop := 353542 ), 
                                                      rec( content := ", or ",
                                                          count := 
                                                            [ 7, 3, 10, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol", count := [ 7, 3, 10, 28 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 353558, 
                                                          root := ~, 
                                                          start := 353548, 
                                                          stop := 353557 ), 
                                                      rec( 
                                                          content := ", are gi\
ven, then they must\n    represent vertex colourings; see \n    ", 
                                                          count := 
                                                            [ 7, 3, 10, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and a homogeneous list", Oper := "AutomorphismGroup" ), content := 0, 
                                                          count := 
                                                            [ 7, 3, 10, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 353704, 
                                                          root := ~, 
                                                          start := 353628, 
                                                          stop := 353703 ), 
                                                      rec( 
                                                          content := " \n    f\
or details of the permissible values for these argument. The\n    homomorphism\
 must then also have the property:\n  \n    ", count := [ 7, 3, 10, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        ", count := [ 7, 3, 10, 30 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "col[i] = col[i ^ x]", count := [ 7, 3, 10, 30 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 30 ], 
                                                                          math\
mode := "Text", name := "C", next := 353884, root := ~, start := 353858, stop \
:= 353883 ), rec( content := " for all vertices ", count := [ 7, 3, 10, 30 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "i", count := [ 7, 3, 10, 30 ], mathmode := "Text", n\
ame := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 30 ], mathmode := "Text",
                                                                          name\
 := "C", next := 353910, root := ~, start := 353902, stop := 353909 ), 
                                                                      rec( 
                                                                          cont\
ent := " of ", count := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "digraph", c\
ount := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA", root := ~ ) ],
                                                                          coun\
t := [ 7, 3, 10, 30 ], mathmode := "Text", name := "A", next := 353928, root :\
= ~, start := 353914, stop := 353927 ), rec( content := ",\n        in the cas\
e of ", count := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ), rec( attributes := rec(  ), content := [ rec( content := "IsDigraphEnd\
omorphism", count := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 7, 3, 10, 30 ], mathmode := "Text", name := "C", next\
 := 353981, root := ~, start := 353953, stop := 353980 ), rec( content := ".",
                                                                          coun\
t := [ 7, 3, 10, 30 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      10, 30 ]
                                                                    , 
                                                                  name := "Ite\
m", next := 353989, root := ~, start := 353843, stop := 353988 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        ", count := [ 7, 3, 10, 32 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "col1[i] = col2[i ^ x]", count := [ 7, 3, 10, 32 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 32 ],
                                                                          math\
mode := "Text", name := "C", next := 354039, root := ~, start := 354011, stop \
:= 354038 ), rec( content := " for all vertices ", count := [ 7, 3, 10, 32 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "i", count := [ 7, 3, 10, 32 ], mathmode := "Text", n\
ame := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 32 ], mathmode := "Text",
                                                                          name\
 := "C", next := 354065, root := ~, start := 354057, stop := 354064 ), 
                                                                      rec( 
                                                                          cont\
ent := " of ", count := [ 7, 3, 10, 32 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "src", count\
 := [ 7, 3, 10, 32 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 7, 3, 10, 32 ], mathmode := "Text", name := "A", next := 354079, root :\
= ~, start := 354069, stop := 354078 ), rec( content := ",\n        in the cas\
es of the other operations.", count := [ 7, 3, 10, 32 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 7, 3, 10, 32 ], name := "Item", 
                                                                  next := 3541\
33, root := ~, start := 353996, stop := 354132 ) ], count := [ 7, 3, 10, 29 ],
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 354145, 
                                                          root := ~, 
                                                          start := 353830, 
                                                          stop := 354144 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 7, 3, 10, 34 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
sRespectsColouring" ), content := 0, count := [ 7, 3, 10, 34 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 354199, 
                                                          root := ~, 
                                                          start := 354160, 
                                                          stop := 354198 ), 
                                                      rec( 
                                                          content := ".\n    \\
n    ", count := [ 7, 3, 10, 34 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> src := Digraph([[1], [1, 2], [1, 3]]);\n<immutable digraph with 3 vertic\
es, 5 edges>\ngap> ran := Digraph([[1], [1, 2]]);\n<immutable digraph with 2 v\
ertices, 3 edges>\ngap> IsDigraphHomomorphism(src, ran, Transformation([1, 2, \
2]));\ntrue\ngap> IsDigraphHomomorphism(src, ran, Transformation([2, 1, 2]));\
\nfalse\ngap> IsDigraphHomomorphism(src, ran, Transformation([3, 3, 3]));\nfal\
se\ngap> IsDigraphHomomorphism(src, src, Transformation([3, 3, 3]));\ntrue\nga\
p> IsDigraphHomomorphism(src, ran, Transformation([1, 2, 2]),\n>              \
            [1, 2, 2], [1, 2]);\ntrue\ngap> IsDigraphHomomorphism(src, ran, Tr\
ansformation([1, 2, 2]),\n>                          [2, 1, 1], [1, 2]);\nfals\
e\ngap> IsDigraphEndomorphism(src, Transformation([3, 3, 3]));\ntrue\ngap> IsD\
igraphEndomorphism(src, Transformation([3, 3, 3]), [1, 1, 1]);\ntrue\ngap> IsD\
igraphEndomorphism(src, Transformation([3, 3, 3]), [1, 1, 2]);\nfalse\ngap> Is\
DigraphEpimorphism(src, ran, Transformation([3, 3, 3]));\nfalse\ngap> IsDigrap\
hMonomorphism(src, ran, Transformation([1, 2, 2]));\nfalse\ngap> IsDigraphEpim\
orphism(src, ran, Transformation([1, 2, 2]));\ntrue\ngap> IsDigraphMonomorphis\
m(ran, src, ());\ntrue", count := [ 7, 3, 10, 35 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 10, 35 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 355401, 
                                                          root := ~, 
                                                          start := 354210, 
                                                          stop := 355400 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 10, 36 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 10, 17 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 355418, root := ~, 
                                                  start := 352241, 
                                                  stop := 355417 ) ], 
                                          count := [ 7, 3, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 355432, root := ~, 
                                          start := 351422, stop := 355431 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 10, 36 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "src, ran, x",
                                                      Label := "for digraphs a\
nd a permutation or transformation", Name := "IsDigraphEmbedding" ), 
                                                  content := 0, 
                                                  count := [ 7, 3, 11, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 355569, root := ~, 
                                                  start := 355453, 
                                                  stop := 355568 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "src, ran, x, col\
1, col2", Name := "IsDigraphEmbedding" ), content := 0, 
                                                  count := [ 7, 3, 11, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 355635, root := ~, 
                                                  start := 355572, 
                                                  stop := 355634 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 355658, 
                                                          root := ~, 
                                                          start := 355647, 
                                                          stop := 355657 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 355674, 
                                                          root := ~, 
                                                          start := 355662, 
                                                          stop := 355673 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 355685, root := ~, 
                                                  start := 355638, 
                                                  stop := 355684 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDigraphEmbedding", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 11, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 355731, 
                                                          root := ~, 
                                                          start := 355706, 
                                                          stop := 355730 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 355751, 
                                                          root := ~, 
                                                          start := 355740, 
                                                          stop := 355750 ), 
                                                      rec( 
                                                          content := " if the \
permutation\n    or transformation ", count := [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 355801, 
                                                          root := ~, 
                                                          start := 355793, 
                                                          stop := 355800 ), 
                                                      rec( 
                                                          content := " is a em\
bedding of the digraph\n    ", count := [ 7, 3, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 355846, 
                                                          root := ~, 
                                                          start := 355836, 
                                                          stop := 355845 ), 
                                                      rec( 
                                                          content := " into th\
e digraph ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 355874, 
                                                          root := ~, 
                                                          start := 355864, 
                                                          stop := 355873 ), 
                                                      rec( 
                                                          content := ", while \
respecting the colourings\n    ", count := [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol1", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 355923, 
                                                          root := ~, 
                                                          start := 355912, 
                                                          stop := 355922 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol2", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 355939, 
                                                          root := ~, 
                                                          start := 355928, 
                                                          stop := 355938 ), 
                                                      rec( 
                                                          content := " if give\
n.\n    ", count := [ 7, 3, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 355958, 
                                                          root := ~, 
                                                          start := 355954, 
                                                          stop := 355957 ), 
                                                      rec( 
                                                          content := "\n\n    \
A permutation or transformation ", count := [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356004, 
                                                          root := ~, 
                                                          start := 355996, 
                                                          stop := 356003 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
mbedding", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 356026, 
                                                          root := ~, 
                                                          start := 356010, 
                                                          stop := 356025 ), 
                                                      rec( 
                                                          content := " of a di\
graph\n    ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356054, 
                                                          root := ~, 
                                                          start := 356044, 
                                                          stop := 356053 ), 
                                                      rec( 
                                                          content := " into a \
digraph ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356080, 
                                                          root := ~, 
                                                          start := 356070, 
                                                          stop := 356079 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356092, 
                                                          root := ~, 
                                                          start := 356084, 
                                                          stop := 356091 ), 
                                                      rec( 
                                                          content := " is a mo\
nomorphism from\n    ", count := [ 7, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356130, 
                                                          root := ~, 
                                                          start := 356120, 
                                                          stop := 356129 ), 
                                                      rec( content := " to ", 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356144, 
                                                          root := ~, 
                                                          start := 356134, 
                                                          stop := 356143 ), 
                                                      rec( 
                                                          content := " and the\
 inverse of ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356172, 
                                                          root := ~, 
                                                          start := 356164, 
                                                          stop := 356171 ), 
                                                      rec( 
                                                          content := " is a mo\
nomorphism from\n    the subdigraph of ", count := [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
an", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356228, 
                                                          root := ~, 
                                                          start := 356218, 
                                                          stop := 356227 ), 
                                                      rec( 
                                                          content := " induced\
 by the image of ", count := [ 7, 3, 11, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356261, 
                                                          root := ~, 
                                                          start := 356253, 
                                                          stop := 356260 ), 
                                                      rec( 
                                                          content := " to\n   \
 ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 356279, 
                                                          root := ~, 
                                                          start := 356269, 
                                                          stop := 356278 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 See also ", count := [ 7, 3, 11, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsDigra\
phHomomorphism" ), content := 0, count := [ 7, 3, 11, 6 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 356330, 
                                                          root := ~, 
                                                          start := 356295, 
                                                          stop := 356329 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 356335, 
                                                          root := ~, 
                                                          start := 356331, 
                                                          stop := 356334 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 11, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> src := Digraph([[1], [1, 2]]);\n<immutable digraph with 2 vertices, 3 ed\
ges>\ngap> ran := Digraph([[1], [1, 2], [1, 3]]);\n<immutable digraph with 3 v\
ertices, 5 edges>\ngap> IsDigraphMonomorphism(src, ran, ());\ntrue\ngap> IsDig\
raphEmbedding(src, ran, ());\ntrue\ngap> IsDigraphEmbedding(src, ran, (), [2, \
1], [2, 1, 1]);\ntrue\ngap> IsDigraphEmbedding(src, ran, (), [2, 1], [1, 2, 1]\
);\nfalse\ngap> ran := Digraph([[1, 2], [1, 2], [1, 3]]);\n<immutable digraph \
with 3 vertices, 6 edges>\ngap> IsDigraphMonomorphism(src, ran, IdentityTransf\
ormation);\ntrue\ngap> IsDigraphEmbedding(src, ran, IdentityTransformation);\n\
false", count := [ 7, 3, 11, 8 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 7, 3, 11, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 356984, 
                                                          root := ~, 
                                                          start := 356341, 
                                                          stop := 356983 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 11, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 11, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 357001, root := ~, 
                                                  start := 355688, 
                                                  stop := 357000 ) ], 
                                          count := [ 7, 3, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 357015, root := ~, 
                                          start := 355438, stop := 357014 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 7, 3, 11, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "src, ran, x, col\
1, col2", Name := "DigraphsRespectsColouring" ), content := 0, 
                                                  count := [ 7, 3, 12, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 357110, root := ~, 
                                                  start := 357040, 
                                                  stop := 357109 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 357136, 
                                                          root := ~, 
                                                          start := 357125, 
                                                          stop := 357135 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 357152, 
                                                          root := ~, 
                                                          start := 357140, 
                                                          stop := 357151 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 357164, root := ~, 
                                                  start := 357115, 
                                                  stop := 357163 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      T\
he operation ", count := [ 7, 3, 12, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphsRespectsColouring", count := [ 7, 3, 12, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 357235, 
                                                          root := ~, 
                                                          start := 357203, 
                                                          stop := 357234 ), 
                                                      rec( 
                                                          content := " verifie\
s whether or not \n      the permutation or transformation ", 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "x\
", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 357309, 
                                                          root := ~, 
                                                          start := 357301, 
                                                          stop := 357308 ), 
                                                      rec( 
                                                          content := " respect\
s the vertex colourings\n      ", count := [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol1", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 357358, 
                                                          root := ~, 
                                                          start := 357347, 
                                                          stop := 357357 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol2", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 357374, 
                                                          root := ~, 
                                                          start := 357363, 
                                                          stop := 357373 ), 
                                                      rec( 
                                                          content := " of the \
digraphs ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 357401, 
                                                          root := ~, 
                                                          start := 357391, 
                                                          stop := 357400 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "r\
ange", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 357418, 
                                                          root := ~, 
                                                          start := 357406, 
                                                          stop := 357417 ), 
                                                      rec( 
                                                          content := ".\n     \
 That is, ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphsRespectsColouring", count := [ 7, 3, 12, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 357467, 
                                                          root := ~, 
                                                          start := 357435, 
                                                          stop := 357466 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 357487, 
                                                          root := ~, 
                                                          start := 357476, 
                                                          stop := 357486 ), 
                                                      rec( 
                                                          content := " if and \
only if for\n      all vertices ", count := [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 357534, 
                                                          root := ~, 
                                                          start := 357526, 
                                                          stop := 357533 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
rc", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 357548, 
                                                          root := ~, 
                                                          start := 357538, 
                                                          stop := 357547 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 7, 3, 12, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ol1[i] = col2[i ^ x]", count := [ 7, 3, 12, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 12, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 357578, 
                                                          root := ~, 
                                                          start := 357550, 
                                                          stop := 357577 ), 
                                                      rec( 
                                                          content := ".\n     \
 ", count := [ 7, 3, 12, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 12, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 357590, 
                                                          root := ~, 
                                                          start := 357586, 
                                                          stop := 357589 ), 
                                                      rec( 
                                                          content := "\n\n    \
  ", count := [ 7, 3, 12, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> src := Digraph([[1], [1, 2]]);\n<immutable digraph with 2 vertices, 3 ed\
ges>\ngap> ran := Digraph([[1], [1, 2], [1, 3]]);\n<immutable digraph with 3 v\
ertices, 5 edges>\ngap> DigraphsRespectsColouring(src, ran, (1, 2), [2, 1], [1\
, 2, 1]);\ntrue\ngap> DigraphsRespectsColouring(src, ran, (1, 2), [2, 1], [2, \
1, 1]);\nfalse\n", count := [ 7, 3, 12, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 7, 3, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 357949, 
                                                          root := ~, 
                                                          start := 357598, 
                                                          stop := 357948 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 7, 3, 12, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 12, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 357968, root := ~, 
                                                  start := 357169, 
                                                  stop := 357967 ) ], 
                                          count := [ 7, 3, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 357984, root := ~, 
                                          start := 357023, stop := 357983 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 12, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, colors\
][, limit]", Name := "GeneratorsOfEndomorphismMonoid" ), content := 0, 
                                                  count := [ 7, 3, 13, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 358083, root := ~, 
                                                  start := 358005, 
                                                  stop := 358082 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "GeneratorsOfEnd\
omorphismMonoidAttr" ), content := 0, count := [ 7, 3, 13, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 358149, root := ~, 
                                                  start := 358086, 
                                                  stop := 358148 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A list o\
f transformations.", count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 13, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 358198, root := ~, 
                                                  start := 358152, 
                                                  stop := 358197 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    An \
endomorphism of ", count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 358252, 
                                                          root := ~, 
                                                          start := 358238, 
                                                          stop := 358251 ), 
                                                      rec( 
                                                          content := " is a ho\
momorphism\n    ", count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Homomorphism" ), content := 0, count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 358308, 
                                                          root := ~, 
                                                          start := 358275, 
                                                          stop := 358307 ), 
                                                      rec( 
                                                          content := " from ",
                                                          count := 
                                                            [ 7, 3, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 358328, 
                                                          root := ~, 
                                                          start := 358314, 
                                                          stop := 358327 ), 
                                                      rec( 
                                                          content := " back to\
 itself.\n\n    ", count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
eneratorsOfEndomorphismMonoid", count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 358387, 
                                                          root := ~, 
                                                          start := 358350, 
                                                          stop := 358386 ), 
                                                      rec( 
                                                          content := ", called\
 with a single argument,\n    returns a generating set for the monoid of all e\
ndomorphisms of\n    ", count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 358506, 
                                                          root := ~, 
                                                          start := 358492, 
                                                          stop := 358505 ), 
                                                      rec( content := ". If ",
                                                          count := 
                                                            [ 7, 3, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 358525, 
                                                          root := ~, 
                                                          start := 358511, 
                                                          stop := 358524 ), 
                                                      rec( 
                                                          content := "  belong\
s to ", count := [ 7, 3, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 358576, 
                                                          root := ~, 
                                                          start := 358538, 
                                                          stop := 358575 ), 
                                                      rec( 
                                                          content := ", then t\
he value of\n    ", count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
eneratorsOfEndomorphismMonoid", count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 13, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 358637, 
                                                          root := ~, 
                                                          start := 358600, 
                                                          stop := 358636 ), 
                                                      rec( 
                                                          content := " will no\
t be recomputed on future\n    calls.", count := [ 7, 3, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 358685, 
                                                          root := ~, 
                                                          start := 358681, 
                                                          stop := 358684 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the ", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olors", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 358711, 
                                                          root := ~, 
                                                          start := 358698, 
                                                          stop := 358710 ), 
                                                      rec( 
                                                          content := " argumen\
t is specified, then\n    ", count := [ 7, 3, 13, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
eneratorsOfEndomorphismMonoid", count := [ 7, 3, 13, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 13, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 358781, 
                                                          root := ~, 
                                                          start := 358744, 
                                                          stop := 358780 ), 
                                                      rec( 
                                                          content := " will re\
turn a generating\n    set for the monoid of endomorphisms which respect the g\
iven colouring.\n    The colouring ", count := [ 7, 3, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olors", count := [ 7, 3, 13, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 358913, 
                                                          root := ~, 
                                                          start := 358900, 
                                                          stop := 358912 ), 
                                                      rec( 
                                                          content := " can be \
in one of two forms: ", count := [ 7, 3, 13, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 13, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 358946, 
                                                          root := ~, 
                                                          start := 358942, 
                                                          stop := 358945 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        A list of positive integers \
of size the number of vertices of\n        ", count := [ 7, 3, 13, 9 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conte\
nt := [ rec( content := "digraph", count := [ 7, 3, 13, 9 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 9 ], mathmode := "Tex\
t", name := "A", next := 359064, root := ~, start := 359050, stop := 359063 ),
                                                                      rec( 
                                                                          cont\
ent := ", where ", count := [ 7, 3, 13, 9 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "co\
lors", count := [ 7, 3, 13, 9 ], mathmode := "Text", name := "PCDATA", root :=\
 ~ ) ], count := [ 7, 3, 13, 9 ], mathmode := "Text", name := "A", next := 359\
085, root := ~, start := 359072, stop := 359084 ), rec( attributes := rec(  ),
                                                                          cont\
ent := [ rec( content := "[i]", count := [ 7, 3, 13, 9 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 9 ], mathmode := "Text",
                                                                          name\
 := "C", next := 359095, root := ~, start := 359085, stop := 359094 ), 
                                                                      rec( 
                                                                          cont\
ent := " is the colour of vertex\n        ", count := [ 7, 3, 13, 9 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conten\
t := [ rec( content := "i", count := [ 7, 3, 13, 9 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 9 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 359136, root := ~, start := 359128, stop := 359135 ), 
                                                                      rec( 
                                                                          cont\
ent := ".\n      ", count := [ 7, 3, 13, 9 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 13, 9 ], name := "Item", next := 359151,
                                                                  root := ~, 
                                                                  start := 358\
965, stop := 359150 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        A list of lists, such that ", count := [ 7, 3, 13, 11 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content\
 := [ rec( content := "colors", count := [ 7, 3, 13, 11 ], mathmode := "Text",\
 name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, 11 ], mathmode := "Text\
", name := "A", next := 359213, root := ~, start := 359200, stop := 359212 ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "[i]", count := [ 7, 3, 13, 11\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 13, \
11 ], mathmode := "Text", name := "C", next := 359223, root := ~, start := 359\
213, stop := 359222 ), rec( content := " is a list of all\n        vertices wi\
th colour ", count := [ 7, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "i", count :\
= [ 7, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\
 := [ 7, 3, 13, 11 ], mathmode := "Text", name := "C", next := 359278, root :=\
 ~, start := 359270, stop := 359277 ), rec( content := ".\n      ", count := 
                                                                            [ \
7, 3, 13, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      13, 11 ]
                                                                    , 
                                                                  name := "Ite\
m", next := 359293, root := ~, start := 359158, stop := 359292 ) ], 
                                                          count := 
                                                            [ 7, 3, 13, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 359305, 
                                                          root := ~, 
                                                          start := 358952, 
                                                          stop := 359304 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the ", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
imit", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 359330, 
                                                          root := ~, 
                                                          start := 359318, 
                                                          stop := 359329 ), 
                                                      rec( 
                                                          content := " argumen\
t is specified, then it will return only the\n    first ", 
                                                          count := 
                                                            [ 7, 3, 13, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
imit", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 359405, 
                                                          root := ~, 
                                                          start := 359393, 
                                                          stop := 359404 ), 
                                                      rec( 
                                                          content := " homomor\
phisms, where ", count := [ 7, 3, 13, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
imit", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 359439, 
                                                          root := ~, 
                                                          start := 359427, 
                                                          stop := 359438 ), 
                                                      rec( 
                                                          content := " must be\
 a positive\n    integer or ", count := [ 7, 3, 13, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 7, 3, 13, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 13, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 359489, 
                                                          root := ~, 
                                                          start := 359474, 
                                                          stop := 359488 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 3, 13, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 13, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 359495, 
                                                          root := ~, 
                                                          start := 359491, 
                                                          stop := 359494 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 13, 14 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph(List([1 .. 3], x -> [1 .. 3]));;\ngap> GeneratorsOfEndomor\
phismMonoid(gr);\n[ Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 1 ] ),\
 \n  IdentityTransformation, Transformation( [ 1, 2, 1 ] ), \n  Transformation\
( [ 1, 2, 2 ] ), Transformation( [ 1, 1, 2 ] ), \n  Transformation( [ 1, 1, 1 \
] ) ]\ngap> GeneratorsOfEndomorphismMonoid(gr, 3);\n[ Transformation( [ 1, 3, \
2 ] ), Transformation( [ 2, 1 ] ), \n  IdentityTransformation ]\ngap> gr := Co\
mpleteDigraph(3);;\ngap> GeneratorsOfEndomorphismMonoid(gr);\n[ Transformation\
( [ 2, 3, 1 ] ), Transformation( [ 2, 1 ] ), \n  IdentityTransformation ]\ngap\
> GeneratorsOfEndomorphismMonoid(gr, [1, 2, 2]);\n[ Transformation( [ 1, 3, 2 \
] ), IdentityTransformation ]\ngap> GeneratorsOfEndomorphismMonoid(gr, [[1], [\
2, 3]]);\n[ Transformation( [ 1, 3, 2 ] ), IdentityTransformation ]\n", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      13, 15 ]
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 13, 15 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 360364, 
                                                          root := ~, 
                                                          start := 359501, 
                                                          stop := 360363 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 13, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 13, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 360381, root := ~, 
                                                  start := 358201, 
                                                  stop := 360380 ) ], 
                                          count := [ 7, 3, 13, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 360395, root := ~, 
                                          start := 357990, stop := 360394 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 13, 16 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, n", 
                                                      Label := "for a digraph \
and a number of colours", Name := "DigraphColouring" ), content := 0, 
                                                  count := [ 7, 3, 14, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 360514, root := ~, 
                                                  start := 360416, 
                                                  stop := 360513 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A transf\
ormation, or ", count := [ 7, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 360559, 
                                                          root := ~, 
                                                          start := 360548, 
                                                          stop := 360558 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 360570, root := ~, 
                                                  start := 360517, 
                                                  stop := 360569 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roper colouring", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "E", 
                                                          next := 360616, 
                                                          root := ~, 
                                                          start := 360593, 
                                                          stop := 360615 ), 
                                                      rec( 
                                                          content := " of a di\
graph is a labelling of its vertices in\n    such a way that adjacent vertices\
 have different labels. A ", count := [ 7, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roper\n      ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "n", count := [ 7, 3, 14, 3 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], 
                                                                  mathmode := \
"Text", name := "C", next := 360751, root := ~, start := 360743, stop := 36075\
0 ), rec( content := "-colouring", count := [ 7, 3, 14, 3 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 360765, 
                                                          root := ~, 
                                                          start := 360727, 
                                                          stop := 360764 ), 
                                                      rec( 
                                                          content := " is a pr\
oper colouring that uses exactly ", count := [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 360814, 
                                                          root := ~, 
                                                          start := 360806, 
                                                          stop := 360813 ), 
                                                      rec( 
                                                          content := "\n    co\
lours.  Equivalently, a proper (", count := [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 360861, 
                                                          root := ~, 
                                                          start := 360853, 
                                                          stop := 360860 ), 
                                                      rec( 
                                                          content := "-)colour\
ing of a digraph can be\n    defined to be a ", count := [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Epimorphism" ), content := 0, count := [ 7, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 360945, 
                                                          root := ~, 
                                                          start := 360913, 
                                                          stop := 360944 ), 
                                                      rec( 
                                                          content := " from a \
digraph onto the\n    complete digraph (with ", count := [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 361005, 
                                                          root := ~, 
                                                          start := 360997, 
                                                          stop := 361004 ), 
                                                      rec( 
                                                          content := " vertice\
s); see ", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Complet\
eDigraph" ), content := 0, count := [ 7, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 361056, 
                                                          root := ~, 
                                                          start := 361021, 
                                                          stop := 361055 ), 
                                                      rec( 
                                                          content := ".  Note \
that a digraph with loops (", count := [ 7, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ 7, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 361126, 
                                                          root := ~, 
                                                          start := 361091, 
                                                          stop := 361125 ), 
                                                      rec( 
                                                          content := ") does n\
ot have a proper ", count := [ 7, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 361159, 
                                                          root := ~, 
                                                          start := 361151, 
                                                          stop := 361158 ), 
                                                      rec( 
                                                          content := "-colouri\
ng for\n    any value ", count := [ 7, 3, 14, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 14, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 361196, 
                                                          root := ~, 
                                                          start := 361188, 
                                                          stop := 361195 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 14, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 361206, 
                                                          root := ~, 
                                                          start := 361202, 
                                                          stop := 361205 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 361229, 
                                                          root := ~, 
                                                          start := 361215, 
                                                          stop := 361228 ), 
                                                      rec( 
                                                          content := " is a di\
graph and ", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 361255, 
                                                          root := ~, 
                                                          start := 361247, 
                                                          stop := 361254 ), 
                                                      rec( 
                                                          content := " is a no\
n-negative integer, then\n    ", count := [ 7, 3, 14, 4 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphColouring(", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "di\
graph", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "A", 
                                                                  next := 3613\
26, root := ~, start := 361312, stop := 361325 ), rec( content := ", ", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      14, 4 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "n", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "A", 
                                                                  next := 3613\
36, root := ~, start := 361328, stop := 361335 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      14, 4 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 361341, 
                                                          root := ~, 
                                                          start := 361292, 
                                                          stop := 361340 ), 
                                                      rec( 
                                                          content := " returns\
 an epimorphism\n    from ", count := [ 7, 3, 14, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 361388, 
                                                          root := ~, 
                                                          start := 361374, 
                                                          stop := 361387 ), 
                                                      rec( 
                                                          content := " onto th\
e complete digraph with ", count := [ 7, 3, 14, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 361428, 
                                                          root := ~, 
                                                          start := 361420, 
                                                          stop := 361427 ), 
                                                      rec( 
                                                          content := " vertice\
s if one\n    exists, else it returns ", count := [ 7, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 14, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 361484, 
                                                          root := ~, 
                                                          start := 361473, 
                                                          stop := 361483 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 7, 3, 14, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 361490, 
                                                          root := ~, 
                                                          start := 361486, 
                                                          stop := 361489 ), 
                                                      rec( 
                                                          content := "\n\n    \
See also ", count := [ 7, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
GreedyColouring", Label := "for a digraph" ), content := 0, 
                                                          count := 
                                                            [ 7, 3, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 361563, 
                                                          root := ~, 
                                                          start := 361505, 
                                                          stop := 361562 ), 
                                                      rec( 
                                                          content := " and \n \
   ", count := [ 7, 3, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 361577, 
                                                          root := ~, 
                                                          start := 361573, 
                                                          stop := 361576 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that a digraph with at least two vertices has a 2-colouring if and only\n\
    if it is bipartite, see ", count := [ 7, 3, 14, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBipar\
titeDigraph" ), content := 0, count := [ 7, 3, 14, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 361720, 
                                                          root := ~, 
                                                          start := 361688, 
                                                          stop := 361719 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 3, 14, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> DigraphColouring(CompleteDigraph(5), 4);\nfail\ngap> DigraphColouring(Ch\
ainDigraph(10), 1);\nfail\ngap> D := ChainDigraph(10);;\ngap> t := DigraphColo\
uring(D, 2);\nTransformation( [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ] )\ngap> IsDigra\
phColouring(D, t); \ntrue\ngap> DigraphGreedyColouring(D);\nTransformation( [ \
2, 1, 2, 1, 2, 1, 2, 1, 2, 1 ] )\n", count := [ 7, 3, 14, 7 ], name := "PCDATA\
", root := ~ ) ], count := [ 7, 3, 14, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 362093, 
                                                          root := ~, 
                                                          start := 361727, 
                                                          stop := 362092 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 14, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 14, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 362110, root := ~, 
                                                  start := 360573, 
                                                  stop := 362109 ) ], 
                                          count := [ 7, 3, 14, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 362124, root := ~, 
                                          start := 360401, stop := 362123 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 14, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, order",
                                                      Label := "for a digraph \
and vertex order", Name := "DigraphGreedyColouring" ), content := 0, 
                                                  count := [ 7, 3, 15, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 362260, root := ~, 
                                                  start := 362145, 
                                                  stop := 362259 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, func", 
                                                      Label := "for a digraph \
and vertex order function", Name := "DigraphGreedyColouring" ), content := 0, 
                                                  count := [ 7, 3, 15, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 362386, root := ~, 
                                                  start := 362263, 
                                                  stop := 362385 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Label := "for a digraph"
                                                        , 
                                                      Name := "DigraphGreedyCo\
louring" ), content := 0, count := [ 7, 3, 15, 6 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 362480, root := ~, 
                                                  start := 362389, 
                                                  stop := 362479 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A transf\
ormation, or ", count := [ 7, 3, 15, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 362525, 
                                                          root := ~, 
                                                          start := 362514, 
                                                          stop := 362524 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 15, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 362536, root := ~, 
                                                  start := 362483, 
                                                  stop := 362535 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roper colouring", count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 3, 15, 7 ], mathmode := "Text", name := "E", 
                                                          next := 362582, 
                                                          root := ~, 
                                                          start := 362559, 
                                                          stop := 362581 ), 
                                                      rec( 
                                                          content := " of a di\
graph is a labelling of its vertices in\n    such a way that adjacent vertices\
 have different labels. Note that a digraph \n    with loops (", 
                                                          count := 
                                                            [ 7, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ 7, 3, 15, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 362757, 
                                                          root := ~, 
                                                          start := 362728, 
                                                          stop := 362756 ), 
                                                      rec( 
                                                          content := ") does n\
ot have any proper \n    colouring.\n    ", count := [ 7, 3, 15, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 362808, 
                                                          root := ~, 
                                                          start := 362804, 
                                                          stop := 362807 ), 
                                                      rec( 
                                                          content := "\n    \n\
    If ", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 362835, 
                                                          root := ~, 
                                                          start := 362821, 
                                                          stop := 362834 ), 
                                                      rec( 
                                                          content := " is a di\
graph and ", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
rder", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 362865, 
                                                          root := ~, 
                                                          start := 362853, 
                                                          stop := 362864 ), 
                                                      rec( 
                                                          content := " is a de\
nse list consisting \n    of all of the vertices of ", count := 
                                                            [ 7, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 362938, 
                                                          root := ~, 
                                                          start := 362924, 
                                                          stop := 362937 ), 
                                                      rec( 
                                                          content := " (in any\
 order), then  \n    ", count := [ 7, 3, 15, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphGreedyColouring", count := [ 7, 3, 15, 8 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 15, 8 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 362995, 
                                                          root := ~, 
                                                          start := 362966, 
                                                          stop := 362994 ), 
                                                      rec( 
                                                          content := "\n    us\
es a greedy algorithm with the specified order to obtain some proper\n    colo\
uring of ", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 15, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 363102, 
                                                          root := ~, 
                                                          start := 363088, 
                                                          stop := 363101 ), 
                                                      rec( 
                                                          content := ", which \
may not use the minimal number of\n    colours. ", count := [ 7, 3, 15, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 15, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 363161, 
                                                          root := ~, 
                                                          start := 363157, 
                                                          stop := 363160 ), 
                                                      rec( 
                                                          content := "\n    \n\
    If ", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 15, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 363188, 
                                                          root := ~, 
                                                          start := 363174, 
                                                          stop := 363187 ), 
                                                      rec( 
                                                          content := " is a di\
graph and ", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
unc", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 15, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 363217, 
                                                          root := ~, 
                                                          start := 363206, 
                                                          stop := 363216 ), 
                                                      rec( 
                                                          content := " is a fu\
nction whose argument \n    is a digraph, and that returns a dense list ", 
                                                          count := 
                                                            [ 7, 3, 15, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
rder", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 15, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 363308, 
                                                          root := ~, 
                                                          start := 363296, 
                                                          stop := 363307 ), 
                                                      rec( 
                                                          content := ", then \\
n    ", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphGreedyColouring(", count := [ 7, 3, 15, 9 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "d\
igraph", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", 
                                                                  next := 3633\
60, root := ~, start := 363346, stop := 363359 ), rec( content := ", ", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      15, 9 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "func", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", 
                                                                  next := 3633\
73, root := ~, start := 363362, stop := 363372 ), rec( content := ")", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      15, 9 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 363378, 
                                                          root := ~, 
                                                          start := 363320, 
                                                          stop := 363377 ), 
                                                      rec( 
                                                          content := " returns\
\n    ", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphGreedyColouring(", count := [ 7, 3, 15, 9 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "d\
igraph", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", 
                                                                  next := 3634\
31, root := ~, start := 363417, stop := 363430 ), rec( content := ", ", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      15, 9 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "func", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", 
                                                                  next := 3634\
44, root := ~, start := 363433, stop := 363443 ), rec( content := "(", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      15, 9 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph", count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 3, 15, 9 ], mathmode := "Text", name := "A", 
                                                                  next := 3634\
59, root := ~, start := 363445, stop := 363458 ), rec( content := "))", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      15, 9 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 15, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 363465, 
                                                          root := ~, 
                                                          start := 363391, 
                                                          stop := 363464 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 15, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 15, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 363475, 
                                                          root := ~, 
                                                          start := 363471, 
                                                          stop := 363474 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional second argument (either a list or a function), is not \n    sp\
ecified, then ", count := [ 7, 3, 15, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
WelshPowellOrder" ), content := 0, count := [ 7, 3, 15, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 363609, 
                                                          root := ~, 
                                                          start := 363572, 
                                                          stop := 363608 ), 
                                                      rec( 
                                                          content := " is used\
 by default. \n    ", count := [ 7, 3, 15, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 15, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 363639, 
                                                          root := ~, 
                                                          start := 363635, 
                                                          stop := 363638 ), 
                                                      rec( 
                                                          content := "\n    \n\
    See also\n    ", count := [ 7, 3, 15, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and a number of colours", Oper := "DigraphColouring" ), content := 0, 
                                                          count := 
                                                            [ 7, 3, 15, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 363748, 
                                                          root := ~, 
                                                          start := 363662, 
                                                          stop := 363747 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 15, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 15, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 363758, 
                                                          root := ~, 
                                                          start := 363754, 
                                                          stop := 363757 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 15, 12 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> DigraphGreedyColouring(ChainDigraph(10));\nTransformation( [ 2, 1, 2, 1,\
 2, 1, 2, 1, 2, 1 ] )\ngap> DigraphGreedyColouring(ChainDigraph(10), [1 .. 10]\
);\nTransformation( [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ] )\n", count := [ 7, 3, 
                                                                      15, 13 ]
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 15, 13 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 364003, 
                                                          root := ~, 
                                                          start := 363764, 
                                                          stop := 364002 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 15, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 15, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 364020, root := ~, 
                                                  start := 362539, 
                                                  stop := 364019 ) ], 
                                          count := [ 7, 3, 15, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 364034, root := ~, 
                                          start := 362130, stop := 364033 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 15, 14 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphWelshPow\
ellOrder" ), content := 0, count := [ 7, 3, 16, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 364107, root := ~, 
                                                  start := 364055, 
                                                  stop := 364106 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A list o\
f the vertices.", count := [ 7, 3, 16, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 16, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 364153, root := ~, 
                                                  start := 364110, 
                                                  stop := 364152 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 7, 3, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphWelshPowellOrder", count := [ 7, 3, 16, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 16, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 364204, 
                                                          root := ~, 
                                                          start := 364174, 
                                                          stop := 364203 ), 
                                                      rec( 
                                                          content := " returns\
 a list of all of the vertices of \n    the digraph ", count := 
                                                            [ 7, 3, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 16, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 16, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 364277, 
                                                          root := ~, 
                                                          start := 364263, 
                                                          stop := 364276 ), 
                                                      rec( 
                                                          content := " ordered\
 according to the sum of the number of \n    out- and in-neighbours, from high\
est to lowest. \n    ", count := [ 7, 3, 16, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 16, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 364386, 
                                                          root := ~, 
                                                          start := 364382, 
                                                          stop := 364385 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 7, 3, 16, 4 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> DigraphWelshPowellOrder(Digraph([[4], [9], [9], [], \n>                 \
                    [4, 6, 9], [1], [], [], \n>                               \
      [4, 5], [4, 5]]));\n[ 5, 9, 4, 1, 6, 10, 2, 3, 7, 8 ]\n", count := 
                                                                    [ 7, 3, 
                                                                      16, 5 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 16, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 364636, 
                                                          root := ~, 
                                                          start := 364392, 
                                                          stop := 364635 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 16, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 16, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 364653, root := ~, 
                                                  start := 364156, 
                                                  stop := 364652 ) ], 
                                          count := [ 7, 3, 16, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 364667, root := ~, 
                                          start := 364040, stop := 364666 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 7, 3, 16, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "ChromaticNumber\
" ), content := 0, count := [ 7, 3, 17, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 364732, root := ~, 
                                                  start := 364688, 
                                                  stop := 364731 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " A non-ne\
gative integer.", count := [ 7, 3, 17, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 364778, root := ~, 
                                                  start := 364735, 
                                                  stop := 364777 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    A "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
roper colouring", count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 7, 3, 17, 3 ], mathmode := "Text", name := "E", 
                                                          next := 364824, 
                                                          root := ~, 
                                                          start := 364801, 
                                                          stop := 364823 ), 
                                                      rec( 
                                                          content := " of a di\
graph is a labelling of its\n    vertices in such a way that adjacent vertices\
 have different labels.\n    Equivalently, a proper digraph colouring can be d\
efined to be a ", count := [ 7, 3, 17, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Epimorphism" ), content := 0, count := [ 7, 3, 17, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 365039, 
                                                          root := ~, 
                                                          start := 365001, 
                                                          stop := 365038 ), 
                                                      rec( 
                                                          content := " from a \
digraph onto a complete digraph. ", count := [ 7, 3, 17, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 365084, 
                                                          root := ~, 
                                                          start := 365080, 
                                                          stop := 365083 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 365107, 
                                                          root := ~, 
                                                          start := 365093, 
                                                          stop := 365106 ), 
                                                      rec( 
                                                          content := " is a di\
graph without loops (see ", count := [ 7, 3, 17, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ 7, 3, 17, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 365175, 
                                                          root := ~, 
                                                          start := 365140, 
                                                          stop := 365174 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
hromaticNumber", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "C", 
                                                          next := 365204, 
                                                          root := ~, 
                                                          start := 365182, 
                                                          stop := 365203 ), 
                                                      rec( 
                                                          content := " returns\
 the least\n    non-negative integer ", count := [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 365256, 
                                                          root := ~, 
                                                          start := 365248, 
                                                          stop := 365255 ), 
                                                      rec( 
                                                          content := " such th\
at there is a proper colouring of\n    ", count := [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 365316, 
                                                          root := ~, 
                                                          start := 365302, 
                                                          stop := 365315 ), 
                                                      rec( 
                                                          content := " with ",
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 365330, 
                                                          root := ~, 
                                                          start := 365322, 
                                                          stop := 365329 ), 
                                                      rec( 
                                                          content := " colours\
.  In other words, for a digraph with at\n    least one vertex, ", 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
hromaticNumber", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "C", 
                                                          next := 365423, 
                                                          root := ~, 
                                                          start := 365401, 
                                                          stop := 365422 ), 
                                                      rec( 
                                                          content := " returns\
 the least number ", count := [ 7, 3, 17, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 365457, 
                                                          root := ~, 
                                                          start := 365449, 
                                                          stop := 365456 ), 
                                                      rec( 
                                                          content := "\n    su\
ch that ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphColouring(", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "di\
graph", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ) ], count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "A", 
                                                                  next := 3655\
06, root := ~, start := 365492, stop := 365505 ), rec( content := ", n)", 
                                                                  count := 
                                                                    [ 7, 3, 
                                                                      17, 4 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 365514, 
                                                          root := ~, 
                                                          start := 365472, 
                                                          stop := 365513 ), 
                                                      rec( 
                                                          content := " does no\
t return\n    ", count := [ 7, 3, 17, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 365546, 
                                                          root := ~, 
                                                          start := 365535, 
                                                          stop := 365545 ), 
                                                      rec( 
                                                          content := ". See ",
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and a number of colours", Oper := "DigraphColouring" ), content := 0, 
                                                          count := 
                                                            [ 7, 3, 17, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 365634, 
                                                          root := ~, 
                                                          start := 365552, 
                                                          stop := 365633 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 7, 3, 17, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> ChromaticNumber(NullDigraph(10));\n1\ngap> ChromaticNumber(CompleteDigra\
ph(10));\n10\ngap> ChromaticNumber(CompleteBipartiteDigraph(5, 5));\n2\ngap> C\
hromaticNumber(Digraph([[], [3], [5], [2, 3], [4]]));\n3\ngap> ChromaticNumber\
(NullDigraph(0));\n0\ngap> D := PetersenGraph(IsMutableDigraph);\n<mutable dig\
raph with 10 vertices, 30 edges>\ngap> ChromaticNumber(D);\n3\n", count := 
                                                                    [ 7, 3, 
                                                                      17, 5 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 7, 3, 17, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 366033, 
                                                          root := ~, 
                                                          start := 365641, 
                                                          stop := 366032 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 7, 3, 17, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 17, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 366050, root := ~, 
                                                  start := 364781, 
                                                  stop := 366049 ) ], 
                                          count := [ 7, 3, 17, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 366064, root := ~, 
                                          start := 364673, stop := 366063 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 7, 3, 17, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "D", 
                                                      Name := "DigraphCore" ),
                                                  content := 0, 
                                                  count := [ 7, 3, 18, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 366127, root := ~, 
                                                  start := 366089, 
                                                  stop := 366126 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A list of\
 positive integers.", count := [ 7, 3, 18, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 366179, root := ~, 
                                                  start := 366132, 
                                                  stop := 366178 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      I\
f ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 366215, 
                                                          root := ~, 
                                                          start := 366207, 
                                                          stop := 366214 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphCore", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 366253, 
                                                          root := ~, 
                                                          start := 366235, 
                                                          stop := 366252 ), 
                                                      rec( 
                                                          content := " returns\
 a list of vertices\n      corresponding to the ", count := [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ore", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 366319, 
                                                          root := ~, 
                                                          start := 366308, 
                                                          stop := 366318 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 366331, 
                                                          root := ~, 
                                                          start := 366323, 
                                                          stop := 366330 ), 
                                                      rec( 
                                                          content := ". In par\
ticular, the subdigraph\n      of ", count := [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 366380, 
                                                          root := ~, 
                                                          start := 366372, 
                                                          stop := 366379 ), 
                                                      rec( 
                                                          content := " induced\
 by this list is isomorphic to the core of ", count := [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 7, 3, 18, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 366439, 
                                                          root := ~, 
                                                          start := 366431, 
                                                          stop := 366438 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 7, 3, 18, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 7, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 366444, 
                                                          root := ~, 
                                                          start := 366440, 
                                                          stop := 366443 ), 
                                                      rec( 
                                                          content := "\n\n    \
The ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
ore", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 7, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 366465, 
                                                          root := ~, 
                                                          start := 366454, 
                                                          stop := 366464 ), 
                                                      rec( 
                                                          content := " of a di\
graph ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 366487, 
                                                          root := ~, 
                                                          start := 366479, 
                                                          stop := 366486 ), 
                                                      rec( 
                                                          content := " is the \
minimal subdigraph ", count := [ 7, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 366522, 
                                                          root := ~, 
                                                          start := 366514, 
                                                          stop := 366521 ), 
                                                      rec( 
                                                          content := " of\n   \
 ", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 366538, 
                                                          root := ~, 
                                                          start := 366530, 
                                                          stop := 366537 ), 
                                                      rec( 
                                                          content := " which i\
s a homomorphic image of ", count := [ 7, 3, 18, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
", count := [ 7, 3, 18, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 7, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 366579, 
                                                          root := ~, 
                                                          start := 366571, 
                                                          stop := 366578 ), 
                                                      rec( 
                                                          content := ". The co\
re of a digraph \n    is unique up to isomorphism.\n      ", 
                                                          count := 
                                                            [ 7, 3, 18, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := DigraphSymmetricClosure(CycleDigraph(8));\n<immutable symmetric dig\
raph with 8 vertices, 16 edges>\ngap> DigraphCore(D);\n[ 1, 2 ]\ngap> D := Pet\
ersenGraph();\n<immutable digraph with 10 vertices, 30 edges>\ngap> DigraphCor\
e(D);\n[ 1 .. 10 ]\ngap> D := Digraph(IsMutableDigraph, [[3], [3], [4], [5], [\
2]]);\n<mutable digraph with 5 vertices, 5 edges>\ngap> DigraphCore(D);\n[ 2, \
3, 4, 5 ]\n", count := [ 7, 3, 18, 5 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 7, 3, 18, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 367063, 
                                                          root := ~, 
                                                          start := 366643, 
                                                          stop := 367062 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 7, 3, 18, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 7, 3, 18, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 367082, root := ~, 
                                                  start := 366184, 
                                                  stop := 367081 ) ], 
                                          count := [ 7, 3, 18, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 367098, root := ~, 
                                          start := 366072, stop := 367097 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 7, 3, 18, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 7, 3, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 367112, 
                                  root := ~, start := 334918, stop := 367111 )
                                , 
                              rec( content := "\n\n", 
                                  count := [ 7, 3, 18, 6 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 7, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 367124, root := ~, start := 286090, 
                          stop := 367123 ), 
                      rec( content := "\n ", count := [ 7, 3, 18, 6 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " homomorphisms ", 
                          count := [ 7, 3, 18, 6 ], mathmode := "Text", 
                          name := "XMLCOMMENT", root := ~ ), 
                      rec( content := "\n  ", count := [ 7, 3, 18, 6 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( 
                          attributes := 
                            rec( 
                              Label := "Finding cliques and independent sets" 
                             ), 
                          content := 
                            [ 
                              rec( content := "\n  ", count := [ 8, 0, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "Finding cliques and indep\
endent sets", count := [ 8, 0, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ) ], 
                                  count := [ 8, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 367263, 
                                  root := ~, start := 367208, stop := 367262 )
                                , 
                              rec( content := "\n\n    In ", 
                                  count := [ 8, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 8, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 3 ], mathmode := "Text",
                                  name := "Package", next := 28, root := ~, 
                                  start := 1, stop := 27 ), 
                              rec( content := ", a ", count := [ 8, 0, 0, 3 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "clique", 
                                          count := [ 8, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 3 ], mathmode := "Text",
                                  name := "E", next := 367299, root := ~, 
                                  start := 367286, stop := 367298 ), 
                              rec( 
                                  content := " of a digraph is a set of mutual\
ly adjacent\n    vertices of the digraph, and an ", count := [ 8, 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "independent set", 
                                          count := [ 8, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 3 ], mathmode := "Text",
                                  name := "E", next := 367401, root := ~, 
                                  start := 367379, stop := 367400 ), 
                              rec( 
                                  content := " is a set of mutually\n    non-a\
djacent vertices of the digraph. A ", count := [ 8, 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "maximal clique", 
                                          count := [ 8, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 3 ], mathmode := "Text",
                                  name := "E", next := 367488, root := ~, 
                                  start := 367467, stop := 367487 ), 
                              rec( 
                                  content := " is a clique\n    which is not p\
roperly contained in another clique, and a ", count := [ 8, 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "maximal\n      independen\
t set", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                          root := ~ ) ], 
                                  count := [ 8, 0, 0, 3 ], mathmode := "Text",
                                  name := "E", next := 367598, root := ~, 
                                  start := 367562, stop := 367597 ), 
                              rec( 
                                  content := " is an independent set which is \
not properly contained\n    in another independent set.  Using this definition\
 in ", count := [ 8, 0, 0, 3 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 8, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 3 ], mathmode := "Text",
                                  name := "Package", next := 28, root := ~, 
                                  start := 1, stop := 27 ), 
                              rec( 
                                  content := ", cliques\n    and independent s\
ets are both permitted, but not required, to contain vertices\n    at which th\
ere is a loop.  Another name for a clique is a ", count := [ 8, 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "complete\n      subgraph"
                                            , count := [ 8, 0, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 3 ], mathmode := "Text",
                                  name := "E", next := 367906, root := ~, 
                                  start := 367876, stop := 367905 ), 
                              rec( content := ".\n    ", 
                                  count := [ 8, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 8, 0, 0, 4 ], mathmode := "Text",
                                  name := "P", next := 367916, root := ~, 
                                  start := 367912, stop := 367915 ), 
                              rec( content := "\n\n    ", 
                                  count := [ 8, 0, 0, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 8, 0, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 4 ], mathmode := "Text",
                                  name := "Package", next := 28, root := ~, 
                                  start := 1, stop := 27 ), 
                              rec( 
                                  content := " provides extensive functionalit\
y for computing cliques and\n    independent sets of a digraph, whether maxima\
l or not.  The fundamental\n    algorithm used in most of the methods in ", 
                                  count := [ 8, 0, 0, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 8, 0, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 4 ], mathmode := "Text",
                                  name := "Package", next := 28, root := ~, 
                                  start := 1, stop := 27 ), 
                              rec( 
                                  content := " to calculate cliques\n    and i\
ndependent sets is a version of the Bron-Kerbosch algorithm.\n    Calculating \
the cliques and independent sets of a digraph is a well-known\n    and hard pr\
oblem, and searching for cliques or independent sets in a\n    digraph can be \
very lengthy, even for a digraph with a small number of\n    vertices.  ", 
                                  count := [ 8, 0, 0, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 8, 0, 0, 4 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 4 ], mathmode := "Text",
                                  name := "Package", next := 28, root := ~, 
                                  start := 1, stop := 27 ), 
                              rec( 
                                  content := " uses several strategies to incr\
ease the performance\n    of these calculations.\n    ", 
                                  count := [ 8, 0, 0, 4 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 8, 0, 0, 5 ], mathmode := "Text",
                                  name := "P", next := 368554, root := ~, 
                                  start := 368550, stop := 368553 ), 
                              rec( 
                                  content := "\n\n    From the definition of c\
liques and independent sets, it follows that the\n    presence of loops and mu\
ltiple edges in a digraph is irrelevant to the\n    existence of cliques and i\
ndependent sets in the digraph.  See ", count := [ 8, 0, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( Prop := "DigraphHasLoops" ), 
                                  content := 0, count := [ 8, 0, 0, 5 ], 
                                  mathmode := "Text", name := "Ref", 
                                  next := 368810, root := ~, start := 368775, 
                                  stop := 368809 ), 
                              rec( content := " and ", 
                                  count := [ 8, 0, 0, 5 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  attributes := rec( Prop := "IsMultiDigraph" 
                                     ), content := 0, count := [ 8, 0, 0, 5 ],
                                  mathmode := "Text", name := "Ref", 
                                  next := 368843, root := ~, start := 368815, 
                                  stop := 368842 ), 
                              rec( 
                                  content := " for more\n    information about\
 these properties.  Therefore given a digraph\n    ", count := [ 8, 0, 0, 5 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "digraph", 
                                          count := [ 8, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 5 ], mathmode := "Text",
                                  name := "A", next := 368938, root := ~, 
                                  start := 368924, stop := 368937 ), 
                              rec( 
                                  content := ", the cliques and independent se\
ts of ", count := [ 8, 0, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "digraph", 
                                          count := [ 8, 0, 0, 5 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 5 ], mathmode := "Text",
                                  name := "A", next := 368990, root := ~, 
                                  start := 368976, stop := 368989 ), 
                              rec( 
                                  content := " are\n    equal to the cliques a\
nd independent sets of the digraph:\n\n    ", count := [ 8, 0, 0, 5 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "\n        ", 
                                                  count := [ 8, 0, 0, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "DigraphRe\
moveLoops(DigraphRemoveAllMultipleEdges(", count := [ 8, 0, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 0, 0, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "C", 
                                                  next := 369146, root := ~, 
                                                  start := 369090, 
                                                  stop := 369145 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "digraph",
                                                          count := 
                                                            [ 8, 0, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 0, 0, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "A", 
                                                  next := 369160, root := ~, 
                                                  start := 369146, 
                                                  stop := 369159 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "))", 
                                                          count := 
                                                            [ 8, 0, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 0, 0, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "C", 
                                                  next := 369169, root := ~, 
                                                  start := 369160, 
                                                  stop := 369168 ), 
                                              rec( content := ".\n      ", 
                                                  count := [ 8, 0, 0, 7 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 8, 0, 0, 7 ],
                                          name := "Item", next := 369184, 
                                          root := ~, start := 369075, 
                                          stop := 369183 ) ], 
                                  count := [ 8, 0, 0, 6 ], mathmode := "Text",
                                  name := "List", next := 369196, root := ~, 
                                  start := 369062, stop := 369195 ), 
                              rec( content := "\n\n    See ", 
                                  count := [ 8, 0, 0, 9 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( Oper := "DigraphRemoveLoops" ), 
                                  content := 0, count := [ 8, 0, 0, 9 ], 
                                  mathmode := "Text", name := "Ref", 
                                  next := 369238, root := ~, start := 369206, 
                                  stop := 369237 ), 
                              rec( content := " and ", 
                                  count := [ 8, 0, 0, 9 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( 
                                      Oper := "DigraphRemoveAllMultipleEdges" 
                                     ), content := 0, count := [ 8, 0, 0, 9 ],
                                  mathmode := "Text", name := "Ref", 
                                  next := 369292, root := ~, start := 369243, 
                                  stop := 369291 ), 
                              rec( 
                                  content := " for more information about thes\
e\n    attributes.  Furthermore, the cliques of this digraph are equal to the\
\n    cliques of the digraph formed by removing any edge ", 
                                  count := [ 8, 0, 0, 9 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "[u,v]", 
                                          count := [ 8, 0, 0, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 9 ], mathmode := "Text",
                                  name := "C", next := 369468, root := ~, 
                                  start := 369456, stop := 369467 ), 
                              rec( 
                                  content := " for which\n    the correspondin\
g reverse edge ", count := [ 8, 0, 0, 9 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "[v,u]", 
                                          count := [ 8, 0, 0, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 9 ], mathmode := "Text",
                                  name := "C", next := 369526, root := ~, 
                                  start := 369514, stop := 369525 ), 
                              rec( 
                                  content := " is not present.  Therefore,\n  \
  overall, the cliques of ", count := [ 8, 0, 0, 9 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "digraph", 
                                          count := [ 8, 0, 0, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 9 ], mathmode := "Text",
                                  name := "A", next := 369597, root := ~, 
                                  start := 369583, stop := 369596 ), 
                              rec( 
                                  content := " are equal to the cliques of the\
\n    symmetric digraph:\n\n    ", count := [ 8, 0, 0, 9 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "\n        ", 
                                                  count := [ 8, 0, 0, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "MaximalSy\
mmetricSubdigraphWithoutLoops(", count := [ 8, 0, 0, 11 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 0, 0, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "C", 
                                                  next := 369732, root := ~, 
                                                  start := 369686, 
                                                  stop := 369731 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "digraph",
                                                          count := 
                                                            [ 8, 0, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 0, 0, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "A", 
                                                  next := 369746, root := ~, 
                                                  start := 369732, 
                                                  stop := 369745 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := ")", 
                                                          count := 
                                                            [ 8, 0, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 0, 0, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "C", 
                                                  next := 369754, root := ~, 
                                                  start := 369746, 
                                                  stop := 369753 ), 
                                              rec( content := ".\n      ", 
                                                  count := [ 8, 0, 0, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ 8, 0, 0, 11 ], 
                                          name := "Item", next := 369769, 
                                          root := ~, start := 369671, 
                                          stop := 369768 ) ], 
                                  count := [ 8, 0, 0, 10 ], 
                                  mathmode := "Text", name := "List", 
                                  next := 369781, root := ~, start := 369658, 
                                  stop := 369780 ), 
                              rec( content := "\n\n    See ", 
                                  count := [ 8, 0, 0, 13 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( 
                                      Oper := "MaximalSymmetricSubdigraphWitho\
utLoops" ), content := 0, count := [ 8, 0, 0, 13 ], mathmode := "Text", 
                                  name := "Ref", next := 369843, root := ~, 
                                  start := 369791, stop := 369842 ), 
                              rec( 
                                  content := " for more\n    information about\
 this. The ", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( Attr := "AutomorphismGroup", 
                                      Label := "for a digraph" ), 
                                  content := 0, count := [ 8, 0, 0, 13 ], 
                                  mathmode := "Text", name := "Ref", 
                                  next := 369945, root := ~, start := 369885, 
                                  stop := 369944 ), 
                              rec( 
                                  content := " of this symmetric digraph conta\
ins the\n    automorphism group of ", count := [ 8, 0, 0, 13 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "digraph", 
                                          count := [ 8, 0, 0, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 13 ], 
                                  mathmode := "Text", name := "A", 
                                  next := 370025, root := ~, start := 370011, 
                                  stop := 370024 ), 
                              rec( 
                                  content := " as a subgroup.  By performing t\
he\n    search for maximal cliques with the help of this larger automorphism g\
roup\n    to reduce the search space, the computation time may be reduced.  Th\
e\n    functions and attributes which return representatives of cliques of\n  \
  ", count := [ 8, 0, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "digraph", 
                                          count := [ 8, 0, 0, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 13 ], 
                                  mathmode := "Text", name := "A", 
                                  next := 370303, root := ~, start := 370289, 
                                  stop := 370302 ), 
                              rec( 
                                  content := " will return orbit representativ\
es of cliques under the\n    action of the automorphism group of the ", 
                                  count := [ 8, 0, 0, 13 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "maximal symmetric subdigr\
aph\n      without loops", count := [ 8, 0, 0, 13 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 13 ], 
                                  mathmode := "Text", name := "E", 
                                  next := 370458, root := ~, start := 370403, 
                                  stop := 370457 ), 
                              rec( content := " on sets of vertices.", 
                                  count := [ 8, 0, 0, 13 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 8, 0, 0, 14 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 370483, root := ~, start := 370479, 
                                  stop := 370482 ), 
                              rec( 
                                  content := "\n\n    The independent sets of \
a digraph are equal to the independent sets of the\n    ", 
                                  count := [ 8, 0, 0, 14 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( 
                                  attributes := 
                                    rec( Oper := "DigraphSymmetricClosure" ), 
                                  content := 0, count := [ 8, 0, 0, 14 ], 
                                  mathmode := "Text", name := "Ref", 
                                  next := 370605, root := ~, start := 370568, 
                                  stop := 370604 ), 
                              rec( 
                                  content := ".  Therefore, overall, the indep\
endent\n    sets of ", count := [ 8, 0, 0, 14 ], mathmode := "Text", 
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "digraph", 
                                          count := [ 8, 0, 0, 14 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 14 ], 
                                  mathmode := "Text", name := "A", 
                                  next := 370670, root := ~, start := 370656, 
                                  stop := 370669 ), 
                              rec( 
                                  content := " are equal to the independent se\
ts of the symmetric\n    digraph:\n\n    ", count := [ 8, 0, 0, 14 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "\n        ", 
                                                  count := [ 8, 0, 0, 16 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "DigraphSy\
mmetricClosure(DigraphRemoveLoops(DigraphRemoveAllMultipleEdges(\n        ", 
                                                          count := 
                                                            [ 8, 0, 0, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 0, 0, 16 ], 
                                                  mathmode := "Text", 
                                                  name := "C", 
                                                  next := 370857, root := ~, 
                                                  start := 370768, 
                                                  stop := 370856 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "digraph",
                                                          count := 
                                                            [ 8, 0, 0, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 0, 0, 16 ], 
                                                  mathmode := "Text", 
                                                  name := "A", 
                                                  next := 370871, root := ~, 
                                                  start := 370857, 
                                                  stop := 370870 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := ")))", 
                                                          count := 
                                                            [ 8, 0, 0, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 0, 0, 16 ], 
                                                  mathmode := "Text", 
                                                  name := "C", 
                                                  next := 370881, root := ~, 
                                                  start := 370871, 
                                                  stop := 370880 ), 
                                              rec( content := ".\n      ", 
                                                  count := [ 8, 0, 0, 16 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], 
                                          count := [ 8, 0, 0, 16 ], 
                                          name := "Item", next := 370896, 
                                          root := ~, start := 370753, 
                                          stop := 370895 ) ], 
                                  count := [ 8, 0, 0, 15 ], 
                                  mathmode := "Text", name := "List", 
                                  next := 370908, root := ~, start := 370740, 
                                  stop := 370907 ), 
                              rec( 
                                  content := "\n\n    Again, the automorphism \
group of this symmetric digraph contains the\n    automorphism group of ", 
                                  count := [ 8, 0, 0, 18 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "digraph", 
                                          count := [ 8, 0, 0, 18 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 18 ], 
                                  mathmode := "Text", name := "A", 
                                  next := 371023, root := ~, start := 371009, 
                                  stop := 371022 ), 
                              rec( 
                                  content := ". Since a search for independent\
 sets\n    is equal to a search for cliques in the ", 
                                  count := [ 8, 0, 0, 18 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Oper := "DigraphDual" ),
                                  content := 0, count := [ 8, 0, 0, 18 ], 
                                  mathmode := "Text", name := "Ref", 
                                  next := 371130, root := ~, start := 371105, 
                                  stop := 371129 ), 
                              rec( content := ", the\n    methods used in ", 
                                  count := [ 8, 0, 0, 18 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 8, 0, 0, 18 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 18 ], 
                                  mathmode := "Text", name := "Package", 
                                  next := 28, root := ~, start := 1, 
                                  stop := 27 ), 
                              rec( 
                                  content := " usually transform a search for \
independent sets\n    into a search for cliques, as described above.  The func\
tions and\n    attributes which return representatives of independent sets of\
\n    ", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "digraph", 
                                          count := [ 8, 0, 0, 18 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 18 ], 
                                  mathmode := "Text", name := "A", 
                                  next := 371370, root := ~, start := 371356, 
                                  stop := 371369 ), 
                              rec( 
                                  content := " will return orbit representativ\
es of independent sets under\n    the action of the automorphism group of the \
", count := [ 8, 0, 0, 18 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                , 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "symmetric closure", 
                                          count := [ 8, 0, 0, 18 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 18 ], 
                                  mathmode := "Text", name := "E", 
                                  next := 371503, root := ~, start := 371479, 
                                  stop := 371502 ), 
                              rec( 
                                  content := " of the\n    digraph formed by r\
emoving loops and multiple edges.", count := [ 8, 0, 0, 18 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 8, 0, 0, 19 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 371571, root := ~, start := 371567, 
                                  stop := 371570 ), 
                              rec( content := "\n\n    Please note that in ", 
                                  count := [ 8, 0, 0, 19 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 8, 0, 0, 19 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 19 ], 
                                  mathmode := "Text", name := "Package", 
                                  next := 28, root := ~, start := 1, 
                                  stop := 27 ), 
                              rec( 
                                  content := ", cliques and independent sets a\
re not\n    required to be maximal. Some authors use the word clique to mean\n\
    ", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "maximal", 
                                          count := [ 8, 0, 0, 19 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 19 ], 
                                  mathmode := "Text", name := "E", 
                                  next := 371733, root := ~, start := 371719, 
                                  stop := 371732 ), 
                              rec( 
                                  content := " clique, and some authors use th\
e phrase independent set to\n    mean ", count := [ 8, 0, 0, 19 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "maximal", 
                                          count := [ 8, 0, 0, 19 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 19 ], 
                                  mathmode := "Text", name := "E", 
                                  next := 371816, root := ~, start := 371802, 
                                  stop := 371815 ), 
                              rec( 
                                  content := " independent set, but please not\
e that ", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Digraphs", 
                                          count := [ 8, 0, 0, 19 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 0, 0, 19 ], 
                                  mathmode := "Text", name := "Package", 
                                  next := 28, root := ~, start := 1, 
                                  stop := 27 ), 
                              rec( 
                                  content := " does\n    not use this definiti\
on.\n    ", count := [ 8, 0, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), content := 0, 
                                  count := [ 8, 0, 0, 20 ], 
                                  mathmode := "Text", name := "P", 
                                  next := 371908, root := ~, start := 371904, 
                                  stop := 371907 ), 
                              rec( content := "\n\n  ", 
                                  count := [ 8, 0, 0, 20 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Finding cliques",
                                                  count := [ 8, 1, 0, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 8, 1, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 371955, 
                                          root := ~, start := 371921, 
                                          stop := 371954 ), 
                                      rec( content := "\n    ", 
                                          count := [ 8, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, l", 
                                                      Name := "IsClique" ), 
                                                  content := 0, 
                                                  count := [ 8, 1, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 372013, root := ~, 
                                                  start := 371973, 
                                                  stop := 372012 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, l", 
                                                      Name := "IsMaximalClique\
" ), content := 0, count := [ 8, 1, 1, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 372061, root := ~, 
                                                  start := 372014, 
                                                  stop := 372060 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 372082, 
                                                          root := ~, 
                                                          start := 372071, 
                                                          stop := 372081 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 372098, 
                                                          root := ~, 
                                                          start := 372086, 
                                                          stop := 372097 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 372109, root := ~, 
                                                  start := 372062, 
                                                  stop := 372108 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n  If ",
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372143, 
                                                          root := ~, 
                                                          start := 372129, 
                                                          stop := 372142 ), 
                                                      rec( 
                                                          content := " is a di\
graph and ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372169, 
                                                          root := ~, 
                                                          start := 372161, 
                                                          stop := 372168 ), 
                                                      rec( 
                                                          content := " is a du\
plicate-free list of\n  vertices of ", count := [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372226, 
                                                          root := ~, 
                                                          start := 372212, 
                                                          stop := 372225 ), 
                                                      rec( 
                                                          content := ", then\n\
  ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sClique(", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 372251, 
                                                          root := ~, 
                                                          start := 372235, 
                                                          stop := 372250 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372265, 
                                                          root := ~, 
                                                          start := 372251, 
                                                          stop := 372264 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ",\
", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 372273, 
                                                          root := ~, 
                                                          start := 372265, 
                                                          stop := 372272 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372281, 
                                                          root := ~, 
                                                          start := 372273, 
                                                          stop := 372280 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 372289, 
                                                          root := ~, 
                                                          start := 372281, 
                                                          stop := 372288 ), 
                                                      rec( 
                                                          content := " returns\
 ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 372309, 
                                                          root := ~, 
                                                          start := 372298, 
                                                          stop := 372308 ), 
                                                      rec( 
                                                          content := "\n    if\
 ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372325, 
                                                          root := ~, 
                                                          start := 372317, 
                                                          stop := 372324 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
lique", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 372344, 
                                                          root := ~, 
                                                          start := 372331, 
                                                          stop := 372343 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372362, 
                                                          root := ~, 
                                                          start := 372348, 
                                                          stop := 372361 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 372379, 
                                                          root := ~, 
                                                          start := 372367, 
                                                          stop := 372378 ), 
                                                      rec( 
                                                          content := " if it i\
s\n    not.  Similarly,\n    ", count := [ 8, 1, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sMaximalClique(", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "C", 
                                                          next := 372437, 
                                                          root := ~, 
                                                          start := 372414, 
                                                          stop := 372436 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372451, 
                                                          root := ~, 
                                                          start := 372437, 
                                                          stop := 372450 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ",\
", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 372459, 
                                                          root := ~, 
                                                          start := 372451, 
                                                          stop := 372458 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372467, 
                                                          root := ~, 
                                                          start := 372459, 
                                                          stop := 372466 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 372475, 
                                                          root := ~, 
                                                          start := 372467, 
                                                          stop := 372474 ), 
                                                      rec( 
                                                          content := " returns\
\n    ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 372499, 
                                                          root := ~, 
                                                          start := 372488, 
                                                          stop := 372498 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372511, 
                                                          root := ~, 
                                                          start := 372503, 
                                                          stop := 372510 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
aximal clique", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 372538, 
                                                          root := ~, 
                                                          start := 372517, 
                                                          stop := 372537 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 372556, 
                                                          root := ~, 
                                                          start := 372542, 
                                                          stop := 372555 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 372577, 
                                                          root := ~, 
                                                          start := 372565, 
                                                          stop := 372576 ), 
                                                      rec( 
                                                          content := " if it i\
s not.  ", count := [ 8, 1, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 372597, 
                                                          root := ~, 
                                                          start := 372593, 
                                                          stop := 372596 ), 
                                                      rec( 
                                                          content := "\n\n    \
A ", count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
lique", count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 372618, 
                                                          root := ~, 
                                                          start := 372605, 
                                                          stop := 372617 ), 
                                                      rec( 
                                                          content := " of a di\
graph is a set of mutually adjacent vertices of the\n    digraph. A ", 
                                                          count := 
                                                            [ 8, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
aximal clique", count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 372714, 
                                                          root := ~, 
                                                          start := 372693, 
                                                          stop := 372713 ), 
                                                      rec( 
                                                          content := " is a cl\
ique that is not properly\n    contained in another clique. A clique is permit\
ted, but not required, to\n    contain vertices at which there is a loop.\n   \
 ", count := [ 8, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(4);;\ngap> IsClique(D, [1, 3, 2]);\ntrue\ngap> IsMa\
ximalClique(D, [1, 3, 2]);\nfalse\ngap> IsMaximalClique(D, DigraphVertices(D))\
;\ntrue\ngap> D := Digraph([[1, 2, 4, 4], [1, 3, 4], [2, 1], [1, 2]]);\n<immut\
able multidigraph with 4 vertices, 11 edges>\ngap> IsClique(D, [2, 3, 4]);\nfa\
lse\ngap> IsMaximalClique(D, [1, 2, 4]);\ntrue\ngap> D := CompleteDigraph(IsMu\
tableDigraph, 4);;\ngap> IsClique(D, [1, 3, 2]);\ntrue", count := [ 8, 1, 1, 
                                                                      7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 8, 1, 1, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 373336, 
                                                          root := ~, 
                                                          start := 372876, 
                                                          stop := 373335 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 8, 1, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 373353, root := ~, 
                                                  start := 372110, 
                                                  stop := 373352 ) ], 
                                          count := [ 8, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 373367, root := ~, 
                                          start := 371960, stop := 373366 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 8, 1, 1, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, hook, u\
ser_param, limit, include,\n    exclude, max, size, reps", 
                                                      Name := "CliquesFinder" 
                                                     ), content := 0, 
                                                  count := [ 8, 1, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 373494, root := ~, 
                                                  start := 373388, 
                                                  stop := 373493 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "The argum\
ent ", count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "u\
ser_param", count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 373536, 
                                                          root := ~, 
                                                          start := 373519, 
                                                          stop := 373535 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 8, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 373547, root := ~, 
                                                  start := 373497, 
                                                  stop := 373546 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function finds cliques of the digraph ", count := [ 8, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 2, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 2, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 373625, 
                                                          root := ~, 
                                                          start := 373611, 
                                                          stop := 373624 ), 
                                                      rec( 
                                                          content := " subject\
 to the\n    conditions imposed by the other arguments as described below. Not\
e\n    that a clique is represented by the immutable list of the vertices that\
\n    it contains.\n    ", count := [ 8, 1, 2, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 373813, 
                                                          root := ~, 
                                                          start := 373809, 
                                                          stop := 373812 ), 
                                                      rec( 
                                                          content := "\n\n    \
Let ", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 373831, 
                                                          root := ~, 
                                                          start := 373823, 
                                                          stop := 373830 ), 
                                                      rec( 
                                                          content := " denote \
the automorphism group of the maximal symmetric\n    subdigraph of ", 
                                                          count := 
                                                            [ 8, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 373919, 
                                                          root := ~, 
                                                          start := 373905, 
                                                          stop := 373918 ), 
                                                      rec( 
                                                          content := " without\
 loops (see ", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := [ 8, 1, 2, 4 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 373998, 
                                                          root := ~, 
                                                          start := 373939, 
                                                          stop := 373997 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Maximal\
SymmetricSubdigraphWithoutLoops" ), content := 0, count := [ 8, 1, 2, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 374061, 
                                                          root := ~, 
                                                          start := 374003, 
                                                          stop := 374060 ), 
                                                      rec( 
                                                          content := ").\n\n  \
  ", count := [ 8, 1, 2, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content :\
= "hook", count := [ 8, 1, 2, 5 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 8, 1, 2, 5 ], mathmode := "Text", name := "A", next := 37\
4099, root := ~, start := 374088, stop := 374098 ) ], count := [ 8, 1, 2, 5 ],
                                                                  name := "Mar\
k", next := 374106, root := ~, start := 374082, stop := 374105 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        This argument should be a f\
unction or ", count := [ 8, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "fail", coun\
t := [ 8, 1, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 8, 1, 2, 6 ], mathmode := "Text", name := "K", next := 374177, root := \
~, start := 374166, stop := 374176 ), rec( content := ".", count := [ 8, 1, 2,\
 6 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\
c(  ), content := 0, count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "P",
                                                                          next\
 := 374182, root := ~, start := 374178, stop := 374181 ), rec( content := "\n\
\n        If ", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "hook", coun\
t := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 8, 1, 2, 7 ], mathmode := "Text", name := "A", next := 374206, root := \
~, start := 374195, stop := 374205 ), rec( content := " is a function, then it\
 should have two arguments\n        ", count := [ 8, 1, 2, 7 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ \
rec( content := "user_param", count := [ 8, 1, 2, 7 ], mathmode := "Text", nam\
e := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", 
                                                                          name\
 := "A", next := 374281, root := ~, start := 374264, stop := 374280 ), 
                                                                      rec( 
                                                                          cont\
ent := " (see below) and a clique ", count := [ 8, 1, 2, 7 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ re\
c( content := "c", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 374315, root := ~, start := 374307, stop := 374314 ), rec( content := ". T\
he function\n        ", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( attributes\
 := rec(  ), content := [ rec( content := "hook", count := [ 8, 1, 2, 7 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 7 ], mat\
hmode := "Text", name := "A", next := 374352, root := ~, start := 374341, stop\
 := 374351 ), rec( content := "(", count := [ 8, 1, 2, 7 ], mathmode := "Text"\
, name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec(\
 content := "user_param", count := [ 8, 1, 2, 7 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name :=\
 "A", next := 374370, root := ~, start := 374353, stop := 374369 ), rec( conte\
nt := ", c)", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "C", next :\
= 374378, root := ~, start := 374338, stop := 374377 ), rec( content := " is c\
alled every time a new\n        clique ", count := [ 8, 1, 2, 7 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :=\
 [ rec( content := "c", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "\
C", next := 374429, root := ~, start := 374421, stop := 374428 ), rec( content\
 := " is found by ", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "C\
liquesFinder", count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 8, 1, 2, 7 ], mathmode := "Text", name := "C", next \
:= 374462, root := ~, start := 374442, stop := 374461 ), rec( content := ".", 
                                                                          coun\
t := [ 8, 1, 2, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 8, 1, 2, 8 ], mathmode := "Text", 
                                                                          name\
 := "P", next := 374467, root := ~, start := 374463, stop := 374466 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n\n        If ", count := [ 8, 1, 2, 8 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "hook", count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "A", next := 3\
74491, root := ~, start := 374480, stop := 374490 ), rec( content := " is ", 
                                                                          coun\
t := [ 8, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "fail", count := [ 8, 1, 2, 8 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 8 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "K", next := 374506, root := ~, start := 374495, stop \
:= 374505 ), rec( content := ", then a default function is used that\n        \
simply adds every new clique found by ", count := [ 8, 1, 2, 8 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                            [ \
rec( content := "CliquesFinder", count := [ 8, 1, 2, 8 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 8 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 374611, root := ~, start := 374591, stop := 374610 ), 
                                                                      rec( 
                                                                          cont\
ent := " to\n        ", count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :=\
 "user_param", count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 8, 1, 2, 8 ], mathmode := "Text", name := "A", next \
:= 374640, root := ~, start := 374623, stop := 374639 ), rec( content := ", wh\
ich must be a list in this case.\n      ", count := [ 8, 1, 2, 8 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 6 ], 
                                                                  name := "Ite\
m", next := 374690, root := ~, start := 374113, stop := 374689 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "user_param", count := [ 8, 1, 2, 9 ], mathmode := "Text", name := "PCDATA"\
, root := ~ ) ], count := [ 8, 1, 2, 9 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 374721, root := ~, start := 374704, stop := 374720 ) ], count := 
                                                                    [ 8, 1, 
                                                                      2, 9 ], 
                                                                  name := "Mar\
k", next := 374728, root := ~, start := 374698, stop := 374727 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        If ", count := [ 8, 1, 2, 1\
0 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\
(  ), content := [ rec( content := "hook", count := [ 8, 1, 2, 10 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode\
 := "Text", name := "A", next := 374764, root := ~, start := 374753, stop := 3\
74763 ), rec( content := " is a function, then ", count := [ 8, 1, 2, 10 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "user_param", count := [ 8, 1, 2, 10 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := \
"Text", name := "A", next := 374802, root := ~, start := 374785, stop := 37480\
1 ), rec( content := " can be any ", count := [ 8, 1, 2, 10 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ r\
ec( content := "GAP", count := [ 8, 1, 2, 10 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "Text", name := "\
Package", next := 23, root := ~, start := 1, stop := 22 ), rec( content := "\n\
        object. The object ", count := [ 8, 1, 2, 10 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "user_param", count := [ 8, 1, 2, 10 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "Text", name := "A"
                                                                            , 
                                                                          next\
 := 374864, root := ~, start := 374847, stop := 374863 ), rec( content := " is\
 used as the first argument for\n        the function ", count := [ 8, 1, 2, 1\
0 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\
(  ), content := [ rec( content := "hook", count := [ 8, 1, 2, 10 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode\
 := "Text", name := "A", next := 374931, root := ~, start := 374920, stop := 3\
74930 ), rec( content := ". For example, ", count := [ 8, 1, 2, 10 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content\
 := [ rec( content := "user_param", count := [ 8, 1, 2, 10 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "Te\
xt", name := "A", next := 374963, root := ~, start := 374946, stop := 374962 )
                                                                        , 
                                                                      rec( 
                                                                          cont\
ent := " might be a\n        list, and ", count := [ 8, 1, 2, 10 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :\
= [ rec( attributes := rec(  ), content := [ rec( content := "hook", count := \
[ 8, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :=\
 [ 8, 1, 2, 10 ], mathmode := "Text", name := "A", next := 375007, root := ~, \
start := 374996, stop := 375006 ), rec( content := "(", count := [ 8, 1, 2, 10\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
  ), content := [ rec( content := "user_param", count := [ 8, 1, 2, 10 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mat\
hmode := "Text", name := "A", next := 375025, root := ~, start := 375008, stop\
 := 375024 ), rec( content := ", c)", count := [ 8, 1, 2, 10 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "\
Text", name := "C", next := 375033, root := ~, start := 374993, stop := 375032\
 ), rec( content := " might add the size\n        of the clique ", count := [ \
8, 1, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "c", count := [ 8, 1, 2, 10 ], ma\
thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], 
                                                                          math\
mode := "Text", name := "C", next := 375083, root := ~, start := 375075, stop \
:= 375082 ), rec( content := " to the list ", count := [ 8, 1, 2, 10 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conte\
nt := [ rec( content := "user_param", count := [ 8, 1, 2, 10 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], mathmode := "\
Text", name := "A", next := 375113, root := ~, start := 375096, stop := 375112\
 ), rec( content := ". ", count := [ 8, 1, 2, 10 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 0, count := [ \
8, 1, 2, 11 ], mathmode := "Text", name := "P", next := 375119, root := ~, 
                                                                          star\
t := 375115, stop := 375118 ), rec( content := "\n\n        If the value of ",
                                                                          coun\
t := [ 8, 1, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "hook", count := [ 8, 1, 2, 11\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 1\
1 ], mathmode := "Text", name := "A", next := 375156, root := ~, start := 3751\
45, stop := 375155 ), rec( content := " is ", count := [ 8, 1, 2, 11 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conte\
nt := [ rec( content := "fail", count := [ 8, 1, 2, 11 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 11 ], mathmode := "Text",
                                                                          name\
 := "K", next := 375171, root := ~, start := 375160, stop := 375170 ), 
                                                                      rec( 
                                                                          cont\
ent := ", then the value of\n        ", count := [ 8, 1, 2, 11 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                            [ \
rec( content := "user_param", count := [ 8, 1, 2, 11 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 11 ], mathmode := "Text", 
                                                                          name\
 := "A", next := 375216, root := ~, start := 375199, stop := 375215 ), 
                                                                      rec( 
                                                                          cont\
ent := " must be a list.\n      ", count := [ 8, 1, 2, 11 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 10 ], name := "Item", 
                                                                  next := 3752\
46, root := ~, start := 374735, stop := 375245 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "limit", count := [ 8, 1, 2, 1\
2 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, \
12 ], mathmode := "Text", name := "A", next := 375272, root := ~, start := 375\
260, stop := 375271 ) ], count := [ 8, 1, 2, 12 ], name := "Mark", 
                                                                  next := 3752\
79, root := ~, start := 375254, stop := 375278 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n        This argument should be a positive integer or ", count := [ \
8, 1, 2, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "infinity", count := [ 8, 1, 2, 1\
3 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, \
13 ], mathmode := "Text", name := "K", next := 375362, root := ~, start := 375\
347, stop := 375361 ), rec( content := ".\n        ", count := [ 8, 1, 2, 13 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "CliquesFinder", count := [ 8, 1, 2, 13 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 13 ], mathmode \
:= "Text", name := "C", next := 375392, root := ~, start := 375372, stop := 37\
5391 ), rec( content := " will return after it has found\n        ", count := 
                                                                            [ \
8, 1, 2, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "limit", count := [ 8, 1, 2, 13 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 13 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 375444, root := ~, start := 375432, stop \
:= 375443 ), rec( content := " cliques or the search is complete.\n      ", 
                                                                          coun\
t := [ 8, 1, 2, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 8, 1, 
                                                                      2, 13 ],
                                                                  name := "Ite\
m", next := 375493, root := ~, start := 375286, stop := 375492 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "include", count := [ 8, 1, 2, 14 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 8, 1, 2, 14 ], mathmode := "Text", name := "A", next\
 := 375521, root := ~, start := 375507, stop := 375520 ), rec( content := " an\
d ", count := [ 8, 1, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~\
 ), rec( attributes := rec(  ), content := [ rec( content := "exclude", count \
:= [ 8, 1, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\
 := [ 8, 1, 2, 14 ], mathmode := "Text", name := "A", next := 375540, root := \
~, start := 375526, stop := 375539 ) ], count := [ 8, 1, 2, 14 ], name := "Mar\
k", next := 375547, root := ~, start := 375501, stop := 375546 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        These arguments should each\
 be a (possibly empty) duplicate-free list\n        of vertices of ", count :=\
 [ 8, 1, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\
ibutes := rec(  ), content := [ rec( content := "digraph", count := [ 8, 1, 2,\
 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2\
, 15 ], mathmode := "Text", name := "A", next := 375676, root := ~, start := 3\
75662, stop := 375675 ), rec( content := " (i.e. positive integers less than t\
he\n        number of vertices of ", count := [ 8, 1, 2, 15 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ r\
ec( content := "digraph", count := [ 8, 1, 2, 15 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 15 ], mathmode := "Text", name \
:= "A", next := 375759, root := ~, start := 375745, stop := 375758 ), rec( 
                                                                          cont\
ent := "). ", count := [ 8, 1, 2, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := 0, count := [ 8, 1, 2, 16 ], 
                                                                          math\
mode := "Text", name := "P", next := 375766, root := ~, start := 375762, stop \
:= 375765 ), rec( content := "\n\n        ", count := [ 8, 1, 2, 16 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conten\
t := [ rec( content := "CliquesFinder", count := [ 8, 1, 2, 16 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 16 ], mathmode :=\
 "Text", name := "C", next := 375796, root := ~, start := 375776, stop := 3757\
95 ), rec( content := " will only look for cliques containing all of the\n    \
    vertices in ", count := [ 8, 1, 2, 16 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "in\
clude", count := [ 8, 1, 2, 16 ], mathmode := "Text", name := "PCDATA", root :\
= ~ ) ], count := [ 8, 1, 2, 16 ], mathmode := "Text", name := "A", next := 37\
5880, root := ~, start := 375866, stop := 375879 ), rec( content := " and cont\
aining none of the vertices in\n        ", count := [ 8, 1, 2, 16 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content \
:= [ rec( content := "exclude", count := [ 8, 1, 2, 16 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 16 ], mathmode := "Text",
                                                                          name\
 := "A", next := 375942, root := ~, start := 375928, stop := 375941 ), 
                                                                      rec( 
                                                                          cont\
ent := ". ", count := [ 8, 1, 2, 16 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := 0, count := [ 8, 1, 2, 17 ], 
                                                                          math\
mode := "Text", name := "P", next := 375948, root := ~, start := 375944, stop \
:= 375947 ), rec( content := "\n\n        Note that the search may be much mor\
e efficient if each of these lists\n        is invariant under the action of "
                                                                            , 
                                                                          coun\
t := [ 8, 1, 2, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "G", count := [ 8, 1, 2, 17 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 17 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 376078, root := ~, start := 376070, stop \
:= 376077 ), rec( content := " on sets of vertices.\n      ", count := [ 8, 1,\
 2, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 8, 1, 
                                                                      2, 15 ],
                                                                  name := "Ite\
m", next := 376113, root := ~, start := 375554, stop := 376112 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "max", count := [ 8, 1, 2, 18 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 8, 1, 2, 18 ], mathmode := "Text", name := "A", next := \
376137, root := ~, start := 376127, stop := 376136 ) ], count := [ 8, 1, 2, 
                                                                      18 ], 
                                                                  name := "Mar\
k", next := 376144, root := ~, start := 376121, stop := 376143 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        This argument should be ", 
                                                                          coun\
t := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "true", count := [ 8, 1, 2, 19\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 1\
9 ], mathmode := "Text", name := "K", next := 376201, root := ~, start := 3761\
90, stop := 376200 ), rec( content := " or ", count := [ 8, 1, 2, 19 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conte\
nt := [ rec( content := "false", count := [ 8, 1, 2, 19 ], mathmode := "Text",\
 name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 19 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "K", next := 376217, root := ~, start := 376205, stop := 376216 ), 
                                                                      rec( 
                                                                          cont\
ent := ".  If ", count := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA\
", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "max"\
, count := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                                             ]
                                                                            , 
                                                                          coun\
t := [ 8, 1, 2, 19 ], mathmode := "Text", name := "A", next := 376233, root :=\
 ~, start := 376223, stop := 376232 ), rec( content := " is\n        true then\
 ", count := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "CliquesFinder", count := [ 8,\
 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8\
, 1, 2, 19 ], mathmode := "Text", name := "C", next := 376275, root := ~, star\
t := 376255, stop := 376274 ), rec( content := " will only search for ", count\
 := [ 8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "maximal", count := [ 8, 1, 2,\
 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2\
, 19 ], mathmode := "Text", name := "E", next := 376311, root := ~, start := 3\
76297, stop := 376310 ), rec( content := "\n        cliques. If ", count := [ \
8, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "max", count := [ 8, 1, 2, 19 ], \
mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 19 ],
                                                                          math\
mode := "Text", name := "K", next := 376342, root := ~, start := 376332, stop \
:= 376341 ), rec( content := " is ", count := [ 8, 1, 2, 19 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ r\
ec( content := "false", count := [ 8, 1, 2, 19 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ 8, 1, 2, 19 ], mathmode := "Text", name :=\
 "K", next := 376358, root := ~, start := 376346, stop := 376357 ), rec( conte\
nt := " then non-maximal cliques may be\n        found.\n      ", count := [ 8\
, 1, 2, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 8, 1, 
                                                                      2, 19 ],
                                                                  name := "Ite\
m", next := 376419, root := ~, start := 376151, stop := 376418 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( content \
:= "size", count := [ 8, 1, 2, 20 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 8, 1, 2, 20 ], mathmode := "Text", name := "A", next :=\
 376444, root := ~, start := 376433, stop := 376443 ) ], count := [ 8, 1, 2, 
                                                                      20 ], 
                                                                  name := "Mar\
k", next := 376451, root := ~, start := 376427, stop := 376450 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        This argument should be ", 
                                                                          coun\
t := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "fail", count := [ 8, 1, 2, 21\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 2\
1 ], mathmode := "Text", name := "K", next := 376508, root := ~, start := 3764\
97, stop := 376507 ), rec( content := " or a positive integer.\n        If ", 
                                                                          coun\
t := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "size", count := [ 8, 1, 2, 21\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 2\
1 ], mathmode := "Text", name := "A", next := 376554, root := ~, start := 3765\
43, stop := 376553 ), rec( content := " is a positive integer then ", count :=\
 [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\
ibutes := rec(  ), content := [ rec( content := "CliquesFinder", count := [ 8,\
 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8\
, 1, 2, 21 ], mathmode := "Text", name := "C", next := 376602, root := ~, star\
t := 376582, stop := 376601 ), rec( content := " will\n        only search for\
 cliques that contain precisely ", count := [ 8, 1, 2, 21 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec\
( content := "size", count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "A\
", next := 376674, root := ~, start := 376663, stop := 376673 ), rec( content \
:= " vertices.\n        If ", count := [ 8, 1, 2, 21 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "size", count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "A", next\
 := 376707, root := ~, start := 376696, stop := 376706 ), rec( content := " is\
 ", count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "fail", count := [ 8, 1, 2, 21\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 2\
1 ], mathmode := "Text", name := "K", next := 376722, root := ~, start := 3767\
11, stop := 376721 ), rec( content := " then cliques of any size may be found.\
\n      ", count := [ 8, 1, 2, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 8, 1, 2, 21 ], name := "Item", next := 376775, 
                                                                  root := ~, 
                                                                  start := 376\
458, stop := 376774 ), rec( attributes := rec(  ), content := [ rec( attribute\
s := rec(  ), content := [ rec( content := "reps", count := [ 8, 1, 2, 22 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 22 ], 
                                                                          math\
mode := "Text", name := "A", next := 376800, root := ~, start := 376789, stop \
:= 376799 ) ], count := [ 8, 1, 2, 22 ], name := "Mark", next := 376807, 
                                                                  root := ~, 
                                                                  start := 376\
783, stop := 376806 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        This argument should be ", count := [ 8, 1, 2, 23 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                            [ \
rec( content := "true", count := [ 8, 1, 2, 23 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ 8, 1, 2, 23 ], mathmode := "Text", name :=\
 "K", next := 376864, root := ~, start := 376853, stop := 376863 ), rec( conte\
nt := " or ", count := [ 8, 1, 2, 23 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "false", cou\
nt := [ 8, 1, 2, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 1, 2, 23 ], mathmode := "Text", name := "K", next := 376880, root :=\
 ~, start := 376868, stop := 376879 ), rec( content := ".", count := [ 8, 1, 2\
, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := 
                                                                            re\
c(  ), content := 0, count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "P"
                                                                            , 
                                                                          next\
 := 376885, root := ~, start := 376881, stop := 376884 ), rec( content := "\n\
\n        If ", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "reps", coun\
t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "A", next := 376909, root :=\
 ~, start := 376898, stop := 376908 ), rec( content := " is ", count := [ 8, 1\
, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \
:= rec(  ), content := [ rec( content := "true", count := [ 8, 1, 2, 24 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 24 ], 
                                                                          math\
mode := "Text", name := "K", next := 376924, root := ~, start := 376913, stop \
:= 376923 ), rec( content := " then the arguments ", count := [ 8, 1, 2, 24 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "include", count := [ 8, 1, 2, 24 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 24 ], mathmode := "Te\
xt", name := "A", next := 376958, root := ~, start := 376944, stop := 376957 )
                                                                        , 
                                                                      rec( 
                                                                          cont\
ent := " and\n        ", count := [ 8, 1, 2, 24 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "exclude", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "A", next\
 := 376985, root := ~, start := 376971, stop := 376984 ), rec( content := " ar\
e each required to be invariant under the action of\n        ", count := [ 8, \
1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\
 := rec(  ), content := [ rec( content := "G", count := [ 8, 1, 2, 24 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 24 ], math\
mode := "Text", name := "C", next := 377056, root := ~, start := 377048, stop \
:= 377055 ), rec( content := " on sets of vertices.  In this case, ", count :=\
 [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attr\
ibutes := rec(  ), content := [ rec( content := "CliquesFinder", count := [ 8,\
 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8\
, 1, 2, 24 ], mathmode := "Text", name := "C", next := 377113, root := ~, star\
t := 377093, stop := 377112 ), rec( content := " will\n        find representa\
tives of the orbits of the desired cliques under the\n        action of ", 
                                                                          coun\
t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "G", count := [ 8, 1, 2, 24 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 24 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 377221, root := ~, start := 377213, stop \
:= 377220 ), rec( content := ", ", count := [ 8, 1, 2, 24 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec\
( content := "although representatives may be returned that\n          are in \
the same orbit", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "E", 
                                                                          next\
 := 377307, root := ~, start := 377223, stop := 377306 ), rec( content := ".\n\
        If ", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "reps", coun\
t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "A", next := 377331, root :=\
 ~, start := 377320, stop := 377330 ), rec( content := " is false then ", coun\
t := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "CliquesFinder", count := [ 8,\
 1, 2, 24 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8\
, 1, 2, 24 ], mathmode := "Text", name := "C", next := 377366, root := ~, star\
t := 377346, stop := 377365 ), rec( content := " will not take this into\n    \
    consideration.", count := [ 8, 1, 2, 24 ], mathmode := "Text", name := "PC\
DATA", root := ~ ), rec( attributes := rec(  ), content := 0, count := [ 8, 1,\
 2, 25 ], mathmode := "Text", name := "P", next := 377417, root := ~, start :=\
 377413, stop := 377416 ), rec( content := "\n\n        For a digraph such tha\
t ", count := [ 8, 1, 2, 25 ], mathmode := "Text", name := "PCDATA", root := ~\
 ), rec( attributes := rec(  ), content := [ rec( content := "G", count := [ 8\
, 1, 2, 25 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \
8, 1, 2, 25 ], mathmode := "Text", name := "C", next := 377459, root := ~, 
                                                                          star\
t := 377451, stop := 377458 ), rec( content := " is non-trivial, the search fo\
r\n        clique representatives can be much more efficient than the search f\
or\n        all cliques.\n      ", count := [ 8, 1, 2, 25 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 2, 23 ], name := "Item", 
                                                                  next := 3776\
03, root := ~, start := 376814, stop := 377602 ) ], count := [ 8, 1, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 377615, 
                                                          root := ~, 
                                                          start := 374069, 
                                                          stop := 377614 ), 
                                                      rec( 
                                                          content := "\n\n    \
This function uses a version of the Bron-Kerbosch algorithm.\n    ", 
                                                          count := 
                                                            [ 8, 1, 2, 27 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(5);\n<immutable complete digraph with 5 vertices>\n\
gap> user_param := [];;\ngap> f := function(a, b)  # Calculate size of clique\
\n>   AddSet(user_param, Size(b));\n> end;;\ngap> CliquesFinder(D, f, user_par\
am, infinity, [], [], false, fail,\n>                  true);\n[ 1, 2, 3, 4, 5\
 ]\ngap> CliquesFinder(D, fail, [], 5, [2, 4], [3], false, fail, false);\n[ [ \
2, 4 ], [ 1, 2, 4 ], [ 2, 4, 5 ], [ 1, 2, 4, 5 ] ]\ngap> CliquesFinder(D, fail\
, [], 2, [2, 4], [3], false, fail, false);\n[ [ 2, 4 ], [ 1, 2, 4 ] ]\ngap> Cl\
iquesFinder(D, fail, [], infinity, [], [], true, 5, false);\n[ [ 1, 2, 3, 4, 5\
 ] ]\ngap> CliquesFinder(D, fail, [], infinity, [1, 3], [], false, 3, false);\
\n[ [ 1, 2, 3 ], [ 1, 3, 4 ], [ 1, 3, 5 ] ]\ngap> CliquesFinder(D, fail, [], i\
nfinity, [1, 3], [], true, 3, false);\n[  ]\ngap> D := CompleteDigraph(IsMutab\
leDigraph, 5);\n<mutable digraph with 5 vertices, 20 edges>\ngap> user_param :\
= [];;\ngap> f := function(a, b)  # Calculate size of clique\n>   AddSet(user_\
param, Size(b));\n> end;;\ngap> CliquesFinder(D, f, user_param, infinity, [], \
[], false, fail,\n>                  true);\n[ 1, 2, 3, 4, 5 ]\ngap> CliquesFi\
nder(D, fail, [], 5, [2, 4], [3], false, fail, false);\n[ [ 2, 4 ], [ 1, 2, 4 \
], [ 2, 4, 5 ], [ 1, 2, 4, 5 ] ]\ngap> CliquesFinder(D, fail, [], 2, [2, 4], [\
3], false, fail, false);\n[ [ 2, 4 ], [ 1, 2, 4 ] ]\ngap> CliquesFinder(D, fai\
l, [], infinity, [], [], true, 5, false);\n[ [ 1, 2, 3, 4, 5 ] ]\ngap> Cliques\
Finder(D, fail, [], infinity, [1, 3], [], false, 3, false);\n[ [ 1, 2, 3 ], [ \
1, 3, 4 ], [ 1, 3, 5 ] ]\ngap> CliquesFinder(D, fail, [], infinity, [1, 3], []\
, true, 3, false);\n[  ]", count := [ 8, 1, 2, 28 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 2, 28 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 379340, 
                                                          root := ~, 
                                                          start := 377686, 
                                                          stop := 379339 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 8, 1, 2, 29 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 2, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 379357, root := ~, 
                                                  start := 373550, 
                                                  stop := 379356 ) ], 
                                          count := [ 8, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 379371, root := ~, 
                                          start := 373373, stop := 379370 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 8, 1, 2, 29 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[, exclude[, size]]]", Name := "DigraphClique" ), content := 0, 
                                                  count := [ 8, 1, 3, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 379464, root := ~, 
                                                  start := 379392, 
                                                  stop := 379463 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[, exclude[,\n    size]]]", Name := "DigraphMaximalClique" ), content := 0, 
                                                  count := [ 8, 1, 3, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 379550, root := ~, 
                                                  start := 379467, 
                                                  stop := 379549 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An immuta\
ble list of positive integers, or ", count := [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 379616, 
                                                          root := ~, 
                                                          start := 379605, 
                                                          stop := 379615 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 3, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 379627, root := ~, 
                                                  start := 379553, 
                                                  stop := 379626 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 379665, 
                                                          root := ~, 
                                                          start := 379651, 
                                                          stop := 379664 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then these functions returns a clique\n    of ", count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 379739, 
                                                          root := ~, 
                                                          start := 379725, 
                                                          stop := 379738 ), 
                                                      rec( 
                                                          content := " if one \
exists that satisfies the arguments, else it\n    returns ", 
                                                          count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 8, 1, 3, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 379815, 
                                                          root := ~, 
                                                          start := 379804, 
                                                          stop := 379814 ), 
                                                      rec( 
                                                          content := ".  A cli\
que is defined by the set of vertices that it\n    contains; see ", 
                                                          count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsCliqu\
e" ), content := 0, count := [ 8, 1, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 379909, 
                                                          root := ~, 
                                                          start := 379887, 
                                                          stop := 379908 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsMaxim\
alClique" ), content := 0, count := [ 8, 1, 3, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 379943, 
                                                          root := ~, 
                                                          start := 379914, 
                                                          stop := 379942 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 8, 1, 3, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 379948, 
                                                          root := ~, 
                                                          start := 379944, 
                                                          stop := 379947 ), 
                                                      rec( 
                                                          content := "\n\n    \
The optional arguments ", count := [ 8, 1, 3, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 379991, 
                                                          root := ~, 
                                                          start := 379977, 
                                                          stop := 379990 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380010, 
                                                          root := ~, 
                                                          start := 379996, 
                                                          stop := 380009 ), 
                                                      rec( 
                                                          content := " must ea\
ch be a\n    (possibly empty) duplicate-free list of vertices of ", 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380096, 
                                                          root := ~, 
                                                          start := 380082, 
                                                          stop := 380095 ), 
                                                      rec( 
                                                          content := ", and\n \
   the optional argument ", count := [ 8, 1, 3, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380139, 
                                                          root := ~, 
                                                          start := 380128, 
                                                          stop := 380138 ), 
                                                      rec( 
                                                          content := " must be\
 a positive integer.  By default,\n    ", count := [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380199, 
                                                          root := ~, 
                                                          start := 380185, 
                                                          stop := 380198 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380218, 
                                                          root := ~, 
                                                          start := 380204, 
                                                          stop := 380217 ), 
                                                      rec( 
                                                          content := " are emp\
ty. These functions will search for\n    a clique of ", count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380292, 
                                                          root := ~, 
                                                          start := 380278, 
                                                          stop := 380291 ), 
                                                      rec( 
                                                          content := " that in\
cludes the vertices of ", count := [ 8, 1, 3, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380337, 
                                                          root := ~, 
                                                          start := 380323, 
                                                          stop := 380336 ), 
                                                      rec( 
                                                          content := "\n    bu\
t does not include any vertices in ", count := [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380393, 
                                                          root := ~, 
                                                          start := 380379, 
                                                          stop := 380392 ), 
                                                      rec( 
                                                          content := "; if the\
 argument\n    ", count := [ 8, 1, 3, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380426, 
                                                          root := ~, 
                                                          start := 380415, 
                                                          stop := 380425 ), 
                                                      rec( 
                                                          content := " is supp\
lied, then additionally the clique will be required to\n    contain precisely \
", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380522, 
                                                          root := ~, 
                                                          start := 380511, 
                                                          stop := 380521 ), 
                                                      rec( 
                                                          content := " vertice\
s.", count := [ 8, 1, 3, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 1, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 380536, 
                                                          root := ~, 
                                                          start := 380532, 
                                                          stop := 380535 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 380559, 
                                                          root := ~, 
                                                          start := 380545, 
                                                          stop := 380558 ), 
                                                      rec( 
                                                          content := " is not \
a clique, then these functions return ", count := [ 8, 1, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 8, 1, 3, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 3, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 380616, 
                                                          root := ~, 
                                                          start := 380605, 
                                                          stop := 380615 ), 
                                                      rec( 
                                                          content := ".\n    O\
therwise, the functions behave in the following way, depending on the\n    num\
ber of arguments:\n\n    ", count := [ 8, 1, 3, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "One or two arguments", count := [ 8, 1\
, 3, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 8, 1, 
                                                                      3, 8 ], 
                                                                  name := "Mar\
k", next := 380769, root := ~, start := 380736, stop := 380768 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        If one or two arguments are\
 supplied, then ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "Dig\
raphClique", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", ro\
ot := ~ ) ], count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "C", next :=\
 380854, root := ~, start := 380834, stop := 380853 ), rec( content := " and\n\
        ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "DigraphMaxi\
malClique", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "C", next := \
380894, root := ~, start := 380867, stop := 380893 ), rec( content := " greedi\
ly enlarge the clique ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := \
"PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :\
= "include", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", ro\
ot := ~ ) ], count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "A", next :=\
 380937, root := ~, start := 380923, stop := 380936 ), rec( content := "\n    \
    until it can not continue.  The result is guaranteed to be a maximal\n    \
    clique. This may or may not return an answer more quickly than using\n    \
    ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", root := \
~ ), rec( attributes := rec( Func := "DigraphMaximalCliques" ), content := 0, 
                                                                          coun\
t := [ 8, 1, 3, 9 ], mathmode := "Text", name := "Ref", next := 381135, root :\
= ~, start := 381100, stop := 381134 ), rec( content := ".  with a limit of 1.\
\n      ", count := [ 8, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 8, 1, 3, 9 ], name := "Item", next := 381170, 
                                                                  root := ~, 
                                                                  start := 380\
776, stop := 381169 ), rec( attributes := rec(  ), content := [ rec( content :\
= "Three arguments", count := [ 8, 1, 3, 10 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ 8, 1, 3, 10 ], name := "Mark", next := 381205
                                                                    , 
                                                                  root := ~, 
                                                                  start := 381\
177, stop := 381204 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        If three arguments are supplied, then ", count := [ 8, 1, 3, 11 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "DigraphClique", count := [ 8, 1, 3, 11 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 11 ], mathmode \
:= "Text", name := "C", next := 381285, root := ~, start := 381265, stop := 38\
1284 ), rec( content := " greedily\n        enlarges the clique ", count := [ \
8, 1, 3, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "include", count := [ 8, 1, 3, 11\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 1\
1 ], mathmode := "Text", name := "A", next := 381337, root := ~, start := 3813\
23, stop := 381336 ), rec( content := " until it can not continue, although\n \
       this clique may not be maximal.", count := [ 8, 1, 3, 11 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :=\
 0, count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "P", next := 381417,
                                                                          root\
 := ~, start := 381413, stop := 381416 ), rec( content := "\n\n        Given t\
hree arguments, ", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "Di\
graphMaximalClique", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "C\
", next := 381477, root := ~, start := 381450, stop := 381476 ), rec( content \
:= " returns the maximal\n        clique returned by ", count := [ 8, 1, 3, 12\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
  ), content := [ rec( content := "DigraphMaximalCliques(", count := [ 8, 1, 3\
, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, \
3, 12 ], mathmode := "Text", name := "C", next := 381554, root := ~, start := \
381525, stop := 381553 ), rec( attributes := rec(  ), content := [ rec( conten\
t := "digraph", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA"\
, root := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 381568, root := ~, start := 381554, stop := 381567 ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := ",\n        ", count := [ 8, 1, 3, 12 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 12 ], 
                                                                          math\
mode := "Text", name := "C", next := 381585, root := ~, start := 381568, stop \
:= 381584 ), rec( attributes := rec(  ), content := [ rec( content := "include\
", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", root := ~ )\
 ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "A", next := 381599,
                                                                          root\
 := ~, start := 381585, stop := 381598 ), rec( attributes := rec(  ), content \
:= [ rec( content := ", ", count := [ 8, 1, 3, 12 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name\
 := "C", next := 381608, root := ~, start := 381599, stop := 381607 ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "exclude", count := [ 8, 1, 3,\
 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3\
, 12 ], mathmode := "Text", name := "A", next := 381622, root := ~, start := 3\
81608, stop := 381621 ), rec( attributes := rec(  ), content := [ rec( content\
 := ", 1)", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", ro\
ot := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "C", next :\
= 381633, root := ~, start := 381622, stop := 381632 ), rec( content := " if o\
ne exists,\n        else ", count := [ 8, 1, 3, 12 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "fail", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "K", next\
 := 381673, root := ~, start := 381662, stop := 381672 ), rec( content := ".\n\
      ", count := [ 8, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ) ], count := [ 8, 1, 3, 11 ], name := "Item", next := 381688, 
                                                                  root := ~, 
                                                                  start := 381\
212, stop := 381687 ), rec( attributes := rec(  ), content := [ rec( content :\
= "Four arguments", count := [ 8, 1, 3, 13 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 8, 1, 3, 13 ], name := "Mark", next := 381722,
                                                                  root := ~, 
                                                                  start := 381\
695, stop := 381721 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        If four arguments are supplied, then ", count := [ 8, 1, 3, 14 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "DigraphClique", count := [ 8, 1, 3, 14 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ], mathmode \
:= "Text", name := "C", next := 381801, root := ~, start := 381781, stop := 38\
1800 ), rec( content := " returns the\n        clique returned by ", count := 
                                                                            [ \
8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribu\
tes := rec(  ), content := [ rec( content := "DigraphCliques(", count := [ 8, \
1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8,\
 1, 3, 14 ], mathmode := "Text", name := "C", next := 381863, root := ~, start\
 := 381841, stop := 381862 ), rec( attributes := rec(  ), content := [ rec( co\
ntent := "digraph", count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "A"
                                                                            , 
                                                                          next\
 := 381877, root := ~, start := 381863, stop := 381876 ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := ",\n          ", count := [ 8, 1, 3, 14 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 381896, root := ~, start := 381877, stop \
:= 381895 ), rec( attributes := rec(  ), content := [ rec( content := "include\
", count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ )\
 ], count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "A", next := 381910,
                                                                          root\
 := ~, start := 381896, stop := 381909 ), rec( attributes := rec(  ), content \
:= [ rec( content := ", ", count := [ 8, 1, 3, 14 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ], mathmode := "Text", name\
 := "C", next := 381919, root := ~, start := 381910, stop := 381918 ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "exclude", count := [ 8, 1, 3,\
 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3\
, 14 ], mathmode := "Text", name := "A", next := 381933, root := ~, start := 3\
81919, stop := 381932 ), rec( attributes := rec(  ), content := [ rec( content\
 := ", 1,\n        ", count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "\
C", next := 381953, root := ~, start := 381933, stop := 381952 ), rec( attribu\
tes := rec(  ), content := [ rec( content := "size", count := [ 8, 1, 3, 14 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 14 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 381964, root := ~, start := 381953, stop \
:= 381963 ), rec( attributes := rec(  ), content := [ rec( content := ")", cou\
nt := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 1, 3, 14 ], mathmode := "Text", name := "C", next := 381972, root :=\
 ~, start := 381964, stop := 381971 ), rec( content := " if one exists, else "
                                                                            , 
                                                                          coun\
t := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "fail", count := [ 8, 1, 3, 14\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 1\
4 ], mathmode := "Text", name := "K", next := 382004, root := ~, start := 3819\
93, stop := 382003 ), rec( content := ". This clique may\n        not be maxim\
al.", count := [ 8, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", root := \
~ ), rec( attributes := rec(  ), content := 0, count := [ 8, 1, 3, 15 ], mathm\
ode := "Text", name := "P", next := 382049, root := ~, start := 382045, stop :\
= 382048 ), rec( content := " Given four arguments, ", count := [ 8, 1, 3, 15 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "DigraphMaximalClique", count := [ 8, 1, 3, 15 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], 
                                                                          math\
mode := "Text", name := "C", next := 382099, root := ~, start := 382072, stop \
:= 382098 ), rec( content := "\n        returns the maximal clique returned by\
\n        ", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "DigraphMaxi\
malCliques(", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "C", next\
 := 382184, root := ~, start := 382155, stop := 382183 ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := "digraph", count := [ 8, 1, 3, 15 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], math\
mode := "Text", name := "A", next := 382198, root := ~, start := 382184, stop \
:= 382197 ), rec( attributes := rec(  ), content := [ rec( content := ", ", co\
unt := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 1, 3, 15 ], mathmode := "Text", name := "C", next := 382207, root :=\
 ~, start := 382198, stop := 382206 ), rec( attributes := rec(  ), content := 
                                                                            [ \
rec( content := "include", count := [ 8, 1, 3, 15 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name\
 := "A", next := 382221, root := ~, start := 382207, stop := 382220 ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := ",\n        ", count := [ 8, 1\
, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, \
1, 3, 15 ], mathmode := "Text", name := "C", next := 382238, root := ~, start \
:= 382221, stop := 382237 ), rec( attributes := rec(  ), content := [ rec( con\
tent := "exclude", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "A",
                                                                          next\
 := 382252, root := ~, start := 382238, stop := 382251 ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := ", 1, ", count := [ 8, 1, 3, 15 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmo\
de := "Text", name := "C", next := 382264, root := ~, start := 382252, stop :=\
 382263 ), rec( attributes := rec(  ), content := [ rec( content := "size", co\
unt := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 1, 3, 15 ], mathmode := "Text", name := "A", next := 382275, root :=\
 ~, start := 382264, stop := 382274 ), rec( attributes := rec(  ), content := 
                                                                            [ \
rec( content := ")", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "C\
", next := 382283, root := ~, start := 382275, stop := 382282 ), rec( content \
:= " if one exists, else\n        ", count := [ 8, 1, 3, 15 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ r\
ec( content := "fail", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ 8, 1, 3, 15 ], mathmode := "Text", name := \
"K", next := 382323, root := ~, start := 382312, stop := 382322 ), rec( conten\
t := ".\n      ", count := [ 8, 1, 3, 15 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 8, 1, 3, 14 ], name := "Item", next := 382338, 
                                                                  root := ~, 
                                                                  start := 381\
729, stop := 382337 ) ], count := [ 8, 1, 3, 8 ], mathmode := "Text", 
                                                          name := "List", 
                                                          next := 382350, 
                                                          root := ~, 
                                                          start := 380723, 
                                                          stop := 382349 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 8, 1, 3, 17 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([[2, 3, 4], [1, 3], [1, 2], [1, 5], []]);\n<immutable digra\
ph with 5 vertices, 9 edges>\ngap> IsSymmetricDigraph(D);\nfalse\ngap> Digraph\
Clique(D);\n[ 5 ]\ngap> DigraphMaximalClique(D);\n[ 5 ]\ngap> DigraphClique(D,\
 [1, 2]);\n[ 1, 2, 3 ]\ngap> DigraphMaximalClique(D, [1, 3]);\n[ 1, 3, 2 ]\nga\
p> DigraphClique(D, [1], [2]);\n[ 1, 4 ]\ngap> DigraphMaximalClique(D, [1], [3\
, 4]);\nfail\ngap> DigraphClique(D, [1, 5]);\nfail\ngap> DigraphClique(D, [], \
[], 2);\n[ 1, 2 ]\ngap> D := Digraph(IsMutableDigraph,\n>                 [[2,\
 3, 4], [1, 3], [1, 2], [1, 5], []]);\n<mutable digraph with 5 vertices, 9 edg\
es>\ngap> IsSymmetricDigraph(D);\nfalse\ngap> DigraphClique(D);\n[ 5 ]", 
                                                                  count := 
                                                                    [ 8, 1, 
                                                                      3, 18 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 8, 1, 3, 18 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 383055, 
                                                          root := ~, 
                                                          start := 382356, 
                                                          stop := 383054 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 8, 1, 3, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 3, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 383072, root := ~, 
                                                  start := 379630, 
                                                  stop := 383071 ) ], 
                                          count := [ 8, 1, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 383086, root := ~, 
                                          start := 379377, stop := 383085 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 8, 1, 3, 19 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[, exclude[, limit[, size]]]]", Name := "DigraphMaximalCliques" ), 
                                                  content := 0, 
                                                  count := [ 8, 1, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 383196, root := ~, 
                                                  start := 383107, 
                                                  stop := 383195 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[, exclude[,\n    limit[, size]]]]", Name := "DigraphMaximalCliquesReps" ), 
                                                  content := 0, 
                                                  count := [ 8, 1, 4, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 383296, root := ~, 
                                                  start := 383199, 
                                                  stop := 383295 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[, exclude[,\n    limit[, size]]]]", Name := "DigraphCliques" ), 
                                                  content := 0, 
                                                  count := [ 8, 1, 4, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 383385, root := ~, 
                                                  start := 383299, 
                                                  stop := 383384 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[,\n    exclude[, limit[, size]]]]", Name := "DigraphCliquesReps" ), 
                                                  content := 0, 
                                                  count := [ 8, 1, 4, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 383478, root := ~, 
                                                  start := 383388, 
                                                  stop := 383477 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMaximalC\
liquesAttr" ), content := 0, count := [ 8, 1, 4, 10 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 383535, root := ~, 
                                                  start := 383481, 
                                                  stop := 383534 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMaximalC\
liquesRepsAttr" ), content := 0, count := [ 8, 1, 4, 12 ], mathmode := "Text",
                                                  name := "Attr", 
                                                  next := 383596, root := ~, 
                                                  start := 383538, 
                                                  stop := 383595 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An immuta\
ble list of lists of positive integers.", count := [ 8, 1, 4, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 4, 13 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 383666, root := ~, 
                                                  start := 383599, 
                                                  stop := 383665 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 383704, 
                                                          root := ~, 
                                                          start := 383690, 
                                                          stop := 383703 ), 
                                                      rec( 
                                                          content := " is digr\
aph, then these functions and attributes use ", count := [ 8, 1, 4, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Cliques\
Finder" ), content := 0, count := [ 8, 1, 4, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 383790, 
                                                          root := ~, 
                                                          start := 383757, 
                                                          stop := 383789 ), 
                                                      rec( 
                                                          content := " to retu\
rn cliques of ", count := [ 8, 1, 4, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 4, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 383826, 
                                                          root := ~, 
                                                          start := 383812, 
                                                          stop := 383825 ), 
                                                      rec( 
                                                          content := ". A\n   \
 clique is defined by the set of vertices that it contains; see ", 
                                                          count := 
                                                            [ 8, 1, 4, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsCliqu\
e" ), content := 0, count := [ 8, 1, 4, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 383925, 
                                                          root := ~, 
                                                          start := 383897, 
                                                          stop := 383924 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 1, 4, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsMaxim\
alClique" ), content := 0, count := [ 8, 1, 4, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 383959, 
                                                          root := ~, 
                                                          start := 383930, 
                                                          stop := 383958 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 8, 1, 4, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 383964, 
                                                          root := ~, 
                                                          start := 383960, 
                                                          stop := 383963 ), 
                                                      rec( 
                                                          content := "\n\n    \
The optional arguments ", count := [ 8, 1, 4, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384007, 
                                                          root := ~, 
                                                          start := 383993, 
                                                          stop := 384006 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384026, 
                                                          root := ~, 
                                                          start := 384012, 
                                                          stop := 384025 ), 
                                                      rec( 
                                                          content := " must ea\
ch be a\n    (possibly empty) list of vertices of ", count := [ 8, 1, 4, 14 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384097, 
                                                          root := ~, 
                                                          start := 384083, 
                                                          stop := 384096 ), 
                                                      rec( 
                                                          content := ", the op\
tional argument\n    ", count := [ 8, 1, 4, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
imit", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384137, 
                                                          root := ~, 
                                                          start := 384125, 
                                                          stop := 384136 ), 
                                                      rec( 
                                                          content := " must be\
 either a positive integer or ", count := [ 8, 1, 4, 14 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 384190, 
                                                          root := ~, 
                                                          start := 384175, 
                                                          stop := 384189 ), 
                                                      rec( 
                                                          content := ", and th\
e\n    optional argument ", count := [ 8, 1, 4, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384233, 
                                                          root := ~, 
                                                          start := 384222, 
                                                          stop := 384232 ), 
                                                      rec( 
                                                          content := " must be\
 a positive integer.  If not\n    specified, then ", count := [ 8, 1, 4, 14 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384304, 
                                                          root := ~, 
                                                          start := 384290, 
                                                          stop := 384303 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384323, 
                                                          root := ~, 
                                                          start := 384309, 
                                                          stop := 384322 ), 
                                                      rec( 
                                                          content := " are cho\
sen to be empty\n    lists, and ", count := [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
imit", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384374, 
                                                          root := ~, 
                                                          start := 384362, 
                                                          stop := 384373 ), 
                                                      rec( 
                                                          content := " is set \
to ", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 8, 1, 4, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 384400, 
                                                          root := ~, 
                                                          start := 384385, 
                                                          stop := 384399 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 8, 1, 4, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 384406, 
                                                          root := ~, 
                                                          start := 384402, 
                                                          stop := 384405 ), 
                                                      rec( 
                                                          content := "\n\n    \
The functions will return as many suitable cliques as possible, up to the\n   \
 number ", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
imit", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384509, 
                                                          root := ~, 
                                                          start := 384497, 
                                                          stop := 384508 ), 
                                                      rec( 
                                                          content := ".  These\
 functions will find cliques that contain all\n    of the vertices of ", 
                                                          count := 
                                                            [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384600, 
                                                          root := ~, 
                                                          start := 384586, 
                                                          stop := 384599 ), 
                                                      rec( 
                                                          content := " but do \
not contain any of the\n    vertices of ", count := [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384661, 
                                                          root := ~, 
                                                          start := 384647, 
                                                          stop := 384660 ), 
                                                      rec( 
                                                          content := ".  The a\
rgument ", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384688, 
                                                          root := ~, 
                                                          start := 384677, 
                                                          stop := 384687 ), 
                                                      rec( 
                                                          content := " restric\
ts the search\n    to those cliques that contain precisely ", 
                                                          count := 
                                                            [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 384765, 
                                                          root := ~, 
                                                          start := 384754, 
                                                          stop := 384764 ), 
                                                      rec( 
                                                          content := " vertice\
s.\n    If the function or attribute has ", count := [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "M\
aximal", count := [ 8, 1, 4, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 384827, 
                                                          root := ~, 
                                                          start := 384813, 
                                                          stop := 384826 ), 
                                                      rec( 
                                                          content := " in its \
name, then only\n    maximal cliques will be returned; otherwise non-maximal c\
liques may be\n    returned. ", count := [ 8, 1, 4, 15 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 1, 4, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 384944, 
                                                          root := ~, 
                                                          start := 384940, 
                                                          stop := 384943 ), 
                                                      rec( 
                                                          content := "\n\n    \
Let ", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 8, 1, 4, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 384962, 
                                                          root := ~, 
                                                          start := 384954, 
                                                          stop := 384961 ), 
                                                      rec( 
                                                          content := " denote \
the automorphism group of maximal symmetric subdigraph\n    of ", 
                                                          count := 
                                                            [ 8, 1, 4, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 4, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 385046, 
                                                          root := ~, 
                                                          start := 385032, 
                                                          stop := 385045 ), 
                                                      rec( 
                                                          content := " without\
 loops (see ", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := 
                                                            [ 8, 1, 4, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 385125, 
                                                          root := ~, 
                                                          start := 385066, 
                                                          stop := 385124 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 1, 4, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Maximal\
SymmetricSubdigraphWithoutLoops" ), content := 0, count := [ 8, 1, 4, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 385188, 
                                                          root := ~, 
                                                          start := 385130, 
                                                          stop := 385187 ), 
                                                      rec( 
                                                          content := ").\n\n  \
  ", count := [ 8, 1, 4, 16 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Distinct cliques", count := [ 8, 1, 4,\
 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 8, 1, 
                                                                      4, 17 ],
                                                                  name := "Mar\
k", next := 385238, root := ~, start := 385209, stop := 385237 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        ", count := [ 8, 1, 4, 18 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "DigraphMaximalCliques", count := [ 8, 1, 4, 18 ], ma\
thmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ], 
                                                                          math\
mode := "Text", name := "C", next := 385288, root := ~, start := 385260, stop \
:= 385287 ), rec( content := " and ", count := [ 8, 1, 4, 18 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ \
rec( content := "DigraphCliques", count := [ 8, 1, 4, 18 ], mathmode := "Text"\
, name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ], mathmode := "Text\
", name := "C", next := 385314, root := ~, start := 385293, stop := 385313 ), 
                                                                      rec( 
                                                                          cont\
ent := " each return a\n        duplicate-free list of at most ", count := [ 8\
, 1, 4, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := [ rec( content := "limit", count := [ 8, 1, 4, 18 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 385380, root := ~, start := 385368, stop \
:= 385379 ), rec( content := " cliques of ", count := [ 8, 1, 4, 18 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conten\
t := [ rec( content := "digraph", count := [ 8, 1, 4, 18 ], mathmode := "Text"\
, name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ], mathmode := "Text\
", name := "A", next := 385406, root := ~, start := 385392, stop := 385405 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n        that satisfy the arguments.", count := [ 8, 1, 4, 18 ], math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := 0, count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "P", next := 3\
85446, root := ~, start := 385442, stop := 385445 ), rec( content := "\n\n    \
    The computation may be significantly faster if ", count := [ 8, 1, 4, 19 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "include", count := [ 8, 1, 4, 19 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 19 ], mathmode := "Te\
xt", name := "A", next := 385517, root := ~, start := 385503, stop := 385516 )
                                                                        , 
                                                                      rec( 
                                                                          cont\
ent := " and\n        ", count := [ 8, 1, 4, 19 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "exclude", count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "A", next\
 := 385544, root := ~, start := 385530, stop := 385543 ), rec( content := " ar\
e invariant under the action of ", count := [ 8, 1, 4, 19 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec\
( content := "G", count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 8, 1, 4, 19 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 385587, root := ~, start := 385579, stop := 385586 ), rec( content := "\n \
       on sets of vertices.\n      ", count := [ 8, 1, 4, 19 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 18 ], name := "Item\
", next := 385630, root := ~, start := 385245, stop := 385629 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "Orbit representatives of cliques", 
                                                                          coun\
t := [ 8, 1, 4, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 8, 1, 
                                                                      4, 20 ],
                                                                  name := "Mar\
k", next := 385683, root := ~, start := 385638, stop := 385682 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        To use ", count := [ 8, 1, \
4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\
 rec(  ), content := [ rec( content := "DigraphMaximalCliquesReps", count := [\
 8, 1, 4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                            [ \
8, 1, 4, 21 ], mathmode := "Text", name := "C", next := 385744, root := ~, 
                                                                          star\
t := 385712, stop := 385743 ), rec( content := " or ", count := [ 8, 1, 4, 21 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "DigraphCliquesReps", count := [ 8, 1, 4, 21 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], math\
mode := "Text", name := "C", next := 385773, root := ~, start := 385748, stop \
:= 385772 ), rec( content := ",\n        the arguments ", count := [ 8, 1, 4, \
21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\
c(  ), content := [ rec( content := "include", count := [ 8, 1, 4, 21 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], math\
mode := "Text", name := "A", next := 385811, root := ~, start := 385797, stop \
:= 385810 ), rec( content := " and ", count := [ 8, 1, 4, 21 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ \
rec( content := "exclude", count := [ 8, 1, 4, 21 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], mathmode := "Text", name\
 := "A", next := 385830, root := ~, start := 385816, stop := 385829 ), 
                                                                      rec( 
                                                                          cont\
ent := " must each be invariant\n        under the action of ", count := [ 8, \
1, 4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes\
 := rec(  ), content := [ rec( content := "G", count := [ 8, 1, 4, 21 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], math\
mode := "Text", name := "C", next := 385890, root := ~, start := 385882, stop \
:= 385889 ), rec( content := " on sets of vertices.", count := [ 8, 1, 4, 21 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := 0, count := [ 8, 1, 4, 22 ], mathmode := "Text", name := "P", next := 3\
85915, root := ~, start := 385911, stop := 385914 ), rec( content := "\n\n    \
    If this is the case, then ", count := [ 8, 1, 4, 22 ], mathmode := "Text",
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "DigraphMaximalCliquesReps", count := [ 8, 1, 4, 22 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 22 ], mathmode := "Tex\
t", name := "C", next := 385983, root := ~, start := 385951, stop := 385982 ),
                                                                      rec( 
                                                                          cont\
ent := " and\n        ", count := [ 8, 1, 4, 22 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "DigraphCliquesReps", count := [ 8, 1, 4, 22 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 22 ], mathmode := "Text", name :\
= "C", next := 386021, root := ~, start := 385996, stop := 386020 ), rec( cont\
ent := " each return a duplicate-free list of at most\n        ", count := [ 8\
, 1, 4, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := [ rec( content := "limit", count := [ 8, 1, 4, 22 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 22 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 386087, root := ~, start := 386075, stop \
:= 386086 ), rec( content := " orbits representatives (under the action of ", 
                                                                          coun\
t := [ 8, 1, 4, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "G", count := [ 8, 1, 4, 22 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 22 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 386140, root := ~, start := 386132, stop \
:= 386139 ), rec( content := " on\n        sets vertices) of cliques of ", 
                                                                          coun\
t := [ 8, 1, 4, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "digraph", count := [ 8, 1, 4,\
 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4\
, 22 ], mathmode := "Text", name := "A", next := 386195, root := ~, start := 3\
86181, stop := 386194 ), rec( content := " that satisfy the\n        arguments\
.", count := [ 8, 1, 4, 22 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 8, 1, 4, 23 ], mathmode := "Text",
                                                                          name\
 := "P", next := 386235, root := ~, start := 386231, stop := 386234 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n\n        The representatives are not guaranteed to be in distinct o\
rbits.\n        However, if fewer than ", count := [ 8, 1, 4, 23 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :\
= [ rec( content := "lim", count := [ 8, 1, 4, 23 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 23 ], mathmode := "Text", name\
 := "A", next := 386351, root := ~, start := 386341, stop := 386350 ), 
                                                                      rec( 
                                                                          cont\
ent := " results are returned, then there\n        will be at least one repres\
entative from each orbit of maximal cliques.\n      ", count := [ 8, 1, 4, 23 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 4, 21 ], 
                                                                  name := "Ite\
m", next := 386478, root := ~, start := 385690, stop := 386477 ) ], 
                                                          count := 
                                                            [ 8, 1, 4, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 386490, 
                                                          root := ~, 
                                                          start := 385196, 
                                                          stop := 386489 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 8, 1, 4, 25 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := Digraph([\n> [2, 3], [1, 3], [1, 2, 4], [3, 5, 6], [4, 6], [4, 5]])\
;\n<immutable digraph with 6 vertices, 14 edges>\ngap> IsSymmetricDigraph(D);\
\ntrue\ngap> G := AutomorphismGroup(D);\nGroup([ (5,6), (1,2), (1,5)(2,6)(3,4)\
 ])\ngap> DigraphMaximalCliques(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 3, 4 ] ]\ng\
ap> DigraphMaximalCliquesReps(D);\n[ [ 1, 2, 3 ], [ 3, 4 ] ]\ngap> Orbit(G, [1\
, 2, 3], OnSets);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]\ngap> Orbit(G, [3, 4], OnSets)\
;\n[ [ 3, 4 ] ]\ngap> DigraphMaximalCliquesReps(D, [3, 4], [], 1);\n[ [ 3, 4 ]\
 ]\ngap> DigraphMaximalCliques(D, [1, 2], [5, 6], 1, 2);\n[  ]\ngap> DigraphCl\
iques(D, [1], [5, 6], infinity, 2);\n[ [ 1, 2 ], [ 1, 3 ] ]\ngap> D := Digraph\
(IsMutableDigraph, [\n> [2, 3], [1, 3], [1, 2, 4], [3, 5, 6], [4, 6], [4, 5]])\
;\n<mutable digraph with 6 vertices, 14 edges>\ngap> IsSymmetricDigraph(D);\nt\
rue\ngap> G := AutomorphismGroup(D);\nGroup([ (5,6), (1,2), (1,5)(2,6)(3,4) ])\
\ngap> DigraphMaximalCliques(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 3, 4 ] ]", 
                                                                  count := 
                                                                    [ 8, 1, 
                                                                      4, 26 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 8, 1, 4, 26 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 387505, 
                                                          root := ~, 
                                                          start := 386496, 
                                                          stop := 387504 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 8, 1, 4, 27 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 4, 13 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 387522, root := ~, 
                                                  start := 383669, 
                                                  stop := 387521 ) ], 
                                          count := [ 8, 1, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 387536, root := ~, 
                                          start := 383092, stop := 387535 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 8, 1, 4, 27 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "CliqueNumber" )
                                                    , content := 0, 
                                                  count := [ 8, 1, 5, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 387598, root := ~, 
                                                  start := 387557, 
                                                  stop := 387597 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A non-neg\
ative integer.", count := [ 8, 1, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 387643, root := ~, 
                                                  start := 387601, 
                                                  stop := 387642 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 387681, 
                                                          root := ~, 
                                                          start := 387667, 
                                                          stop := 387680 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
liqueNumber(", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "digraph", count := [ 8, 1, 5, 3 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], 
                                                                  mathmode := \
"Text", name := "A", next := 387731, root := ~, start := 387717, stop := 38773\
0 ), rec( content := ")", count := [ 8, 1, 5, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 8, 1, 5, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 387736, 
                                                          root := ~, 
                                                          start := 387701, 
                                                          stop := 387735 ), 
                                                      rec( 
                                                          content := "\n    re\
turns the largest integer ", count := [ 8, 1, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 387777, 
                                                          root := ~, 
                                                          start := 387769, 
                                                          stop := 387776 ), 
                                                      rec( 
                                                          content := " such th\
at ", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 387802, 
                                                          root := ~, 
                                                          start := 387788, 
                                                          stop := 387801 ), 
                                                      rec( 
                                                          content := " contain\
s a\n    clique with ", count := [ 8, 1, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 8, 1, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 387838, 
                                                          root := ~, 
                                                          start := 387830, 
                                                          stop := 387837 ), 
                                                      rec( 
                                                          content := " vertice\
s as an induced subdigraph.\n    ", count := [ 8, 1, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 387882, 
                                                          root := ~, 
                                                          start := 387878, 
                                                          stop := 387881 ), 
                                                      rec( 
                                                          content := "\n\n    \
A ", count := [ 8, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
lique", count := [ 8, 1, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 1, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 387903, 
                                                          root := ~, 
                                                          start := 387890, 
                                                          stop := 387902 ), 
                                                      rec( 
                                                          content := " of a di\
graph is a set of mutually adjacent vertices of the\n    digraph. Loops and mu\
ltiple edges are ignored for the purpose of\n    determining the clique number\
 of a digraph. \n    ", count := [ 8, 1, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CompleteDigraph(4);;\ngap> CliqueNumber(D);\n4\ngap> D := Digraph([\
[1, 2, 4, 4], [1, 3, 4], [2, 1], [1, 2]]);\n<immutable multidigraph with 4 ver\
tices, 11 edges>\ngap> CliqueNumber(D);\n3\ngap> D := CompleteDigraph(IsMutabl\
eDigraph, 4);;\ngap> CliqueNumber(D);\n4", count := [ 8, 1, 5, 5 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 8, 1, 5, 5 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 388381, 
                                                          root := ~, 
                                                          start := 388085, 
                                                          stop := 388380 ), 
                                                      rec( content := "\n", 
                                                          count := 
                                                            [ 8, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 1, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 388396, root := ~, 
                                                  start := 387646, 
                                                  stop := 388395 ) ], 
                                          count := [ 8, 1, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 388410, root := ~, 
                                          start := 387542, stop := 388409 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 8, 1, 5, 6 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 388424, 
                                  root := ~, start := 371912, stop := 388423 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 8, 1, 5, 6 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Finding independe\
nt sets", count := [ 8, 2, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 8, 2, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 388480, 
                                          root := ~, start := 388437, 
                                          stop := 388479 ), 
                                      rec( content := "\n    ", 
                                          count := [ 8, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, l", 
                                                      Name := "IsIndependentSe\
t" ), content := 0, count := [ 8, 2, 1, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 388548, root := ~, 
                                                  start := 388500, 
                                                  stop := 388547 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph, l", 
                                                      Name := "IsMaximalIndepe\
ndentSet" ), content := 0, count := [ 8, 2, 1, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 388606, root := ~, 
                                                  start := 388551, 
                                                  stop := 388605 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          attributes := rec(  )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 388629, 
                                                          root := ~, 
                                                          start := 388618, 
                                                          stop := 388628 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 388645, 
                                                          root := ~, 
                                                          start := 388633, 
                                                          stop := 388644 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 388656, root := ~, 
                                                  start := 388609, 
                                                  stop := 388655 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 388694, 
                                                          root := ~, 
                                                          start := 388680, 
                                                          stop := 388693 ), 
                                                      rec( 
                                                          content := " is a di\
graph and ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 388720, 
                                                          root := ~, 
                                                          start := 388712, 
                                                          stop := 388719 ), 
                                                      rec( 
                                                          content := " is a du\
plicate-free list of\n    vertices of ", count := [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 388779, 
                                                          root := ~, 
                                                          start := 388765, 
                                                          stop := 388778 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sIndependentSet(", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "C", 
                                                          next := 388814, 
                                                          root := ~, 
                                                          start := 388790, 
                                                          stop := 388813 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 388828, 
                                                          root := ~, 
                                                          start := 388814, 
                                                          stop := 388827 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ",\
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 388836, 
                                                          root := ~, 
                                                          start := 388828, 
                                                          stop := 388835 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 388844, 
                                                          root := ~, 
                                                          start := 388836, 
                                                          stop := 388843 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 388852, 
                                                          root := ~, 
                                                          start := 388844, 
                                                          stop := 388851 ), 
                                                      rec( 
                                                          content := " returns\
\n    ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 388876, 
                                                          root := ~, 
                                                          start := 388865, 
                                                          stop := 388875 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 388888, 
                                                          root := ~, 
                                                          start := 388880, 
                                                          stop := 388887 ), 
                                                      rec( 
                                                          content := " is an "
                                                            , 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
ndependent set", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 388917, 
                                                          root := ~, 
                                                          start := 388895, 
                                                          stop := 388916 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 388935, 
                                                          root := ~, 
                                                          start := 388921, 
                                                          stop := 388934 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 388956, 
                                                          root := ~, 
                                                          start := 388944, 
                                                          stop := 388955 ), 
                                                      rec( 
                                                          content := " if it i\
s not.  Similarly,\n    ", count := [ 8, 2, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sMaximalIndependentSet(", count := [ 8, 2, 1, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 389018, 
                                                          root := ~, 
                                                          start := 388987, 
                                                          stop := 389017 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 389032, 
                                                          root := ~, 
                                                          start := 389018, 
                                                          stop := 389031 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ",\
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 389040, 
                                                          root := ~, 
                                                          start := 389032, 
                                                          stop := 389039 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 389048, 
                                                          root := ~, 
                                                          start := 389040, 
                                                          stop := 389047 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ")\
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 389056, 
                                                          root := ~, 
                                                          start := 389048, 
                                                          stop := 389055 ), 
                                                      rec( 
                                                          content := "\n    re\
turns ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "t\
rue", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 389080, 
                                                          root := ~, 
                                                          start := 389069, 
                                                          stop := 389079 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 389092, 
                                                          root := ~, 
                                                          start := 389084, 
                                                          stop := 389091 ), 
                                                      rec( 
                                                          content := " is a ",
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
aximal independent set", count := [ 8, 2, 1, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 8, 2, 1, 5 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 389128, 
                                                          root := ~, 
                                                          start := 389098, 
                                                          stop := 389127 ), 
                                                      rec( 
                                                          content := " of\n   \
 ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 389150, 
                                                          root := ~, 
                                                          start := 389136, 
                                                          stop := 389149 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
alse", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 389167, 
                                                          root := ~, 
                                                          start := 389155, 
                                                          stop := 389166 ), 
                                                      rec( 
                                                          content := " if it i\
s not.  ", count := [ 8, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 389187, 
                                                          root := ~, 
                                                          start := 389183, 
                                                          stop := 389186 ), 
                                                      rec( 
                                                          content := "\n\n    \
An ", count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
ndependent set", count := [ 8, 2, 1, 6 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 389218, 
                                                          root := ~, 
                                                          start := 389196, 
                                                          stop := 389217 ), 
                                                      rec( 
                                                          content := " of a di\
graph is a set of mutually non-adjacent\n    vertices of the digraph. A ", 
                                                          count := 
                                                            [ 8, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
aximal independent set", count := [ 8, 2, 1, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 8, 2, 1, 6 ], mathmode := "Text", 
                                                          name := "E", 
                                                          next := 389327, 
                                                          root := ~, 
                                                          start := 389297, 
                                                          stop := 389326 ), 
                                                      rec( 
                                                          content := " is an i\
ndependent\n    set that is not properly contained in another independent set.\
 An\n    independent set is permitted, but not required, to contain vertices a\
t\n    which there is a loop.\n    ", count := [ 8, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(4);;\ngap> IsIndependentSet(D, [1]);\ntrue\ngap> IsMax\
imalIndependentSet(D, [1]);\nfalse\ngap> IsIndependentSet(D, [1, 4, 3]);\nfals\
e\ngap> IsIndependentSet(D, [2, 4]);\ntrue\ngap> IsMaximalIndependentSet(D, [2\
, 4]);\ntrue\ngap> D := CycleDigraph(IsMutableDigraph, 4);;\ngap> IsIndependen\
tSet(D, [1]);\ntrue", count := [ 8, 2, 1, 7 ], name := "PCDATA", root := ~ ) ]
                                                            , 
                                                          count := 
                                                            [ 8, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 389871, 
                                                          root := ~, 
                                                          start := 389522, 
                                                          stop := 389870 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 8, 2, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 389888, root := ~, 
                                                  start := 388659, 
                                                  stop := 389887 ) ], 
                                          count := [ 8, 2, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 389902, root := ~, 
                                          start := 388485, stop := 389901 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 8, 2, 1, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[, exclude[, size]]]", Name := "DigraphIndependentSet" ), content := 0, 
                                                  count := [ 8, 2, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 390007, root := ~, 
                                                  start := 389923, 
                                                  stop := 390006 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[, exclude[,\n    size]]]", Name := "DigraphMaximalIndependentSet" ), 
                                                  content := 0, 
                                                  count := [ 8, 2, 2, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 390105, root := ~, 
                                                  start := 390010, 
                                                  stop := 390104 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An immuta\
ble list of positive integers, or ", count := [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 390171, 
                                                          root := ~, 
                                                          start := 390160, 
                                                          stop := 390170 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 2, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 390182, root := ~, 
                                                  start := 390108, 
                                                  stop := 390181 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390220, 
                                                          root := ~, 
                                                          start := 390206, 
                                                          stop := 390219 ), 
                                                      rec( 
                                                          content := " is a di\
graph, then these functions returns an independent\n    set of ", 
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390304, 
                                                          root := ~, 
                                                          start := 390290, 
                                                          stop := 390303 ), 
                                                      rec( 
                                                          content := " if one \
exists that satisfies the arguments, else it\n    returns ", 
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 8, 2, 2, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 390380, 
                                                          root := ~, 
                                                          start := 390369, 
                                                          stop := 390379 ), 
                                                      rec( 
                                                          content := ".  An in\
dependent set is defined by the set of vertices\n    that it contains; see ", 
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsIndep\
endentSet" ), content := 0, count := [ 8, 2, 2, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 390492, 
                                                          root := ~, 
                                                          start := 390462, 
                                                          stop := 390491 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsMaxim\
alIndependentSet" ), content := 0, count := [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 390540, 
                                                          root := ~, 
                                                          start := 390497, 
                                                          stop := 390539 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 8, 2, 2, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 390545, 
                                                          root := ~, 
                                                          start := 390541, 
                                                          stop := 390544 ), 
                                                      rec( 
                                                          content := "\n\n    \
The optional arguments ", count := [ 8, 2, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390588, 
                                                          root := ~, 
                                                          start := 390574, 
                                                          stop := 390587 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390607, 
                                                          root := ~, 
                                                          start := 390593, 
                                                          stop := 390606 ), 
                                                      rec( 
                                                          content := " must ea\
ch be a\n    (possibly empty) duplicate-free list of vertices of ", 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390693, 
                                                          root := ~, 
                                                          start := 390679, 
                                                          stop := 390692 ), 
                                                      rec( 
                                                          content := ", and th\
e\n    optional argument ", count := [ 8, 2, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390736, 
                                                          root := ~, 
                                                          start := 390725, 
                                                          stop := 390735 ), 
                                                      rec( 
                                                          content := " must be\
 a positive integer.  By default,\n    ", count := [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390796, 
                                                          root := ~, 
                                                          start := 390782, 
                                                          stop := 390795 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390815, 
                                                          root := ~, 
                                                          start := 390801, 
                                                          stop := 390814 ), 
                                                      rec( 
                                                          content := " are emp\
ty. These functions will search\n    for an independent set of ", 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390899, 
                                                          root := ~, 
                                                          start := 390885, 
                                                          stop := 390898 ), 
                                                      rec( 
                                                          content := " that in\
cludes the vertices of\n    ", count := [ 8, 2, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 390948, 
                                                          root := ~, 
                                                          start := 390934, 
                                                          stop := 390947 ), 
                                                      rec( 
                                                          content := " but doe\
s not include any vertices in ", count := [ 8, 2, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 391000, 
                                                          root := ~, 
                                                          start := 390986, 
                                                          stop := 390999 ), 
                                                      rec( 
                                                          content := ";\n    i\
f the argument ", count := [ 8, 2, 2, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 391033, 
                                                          root := ~, 
                                                          start := 391022, 
                                                          stop := 391032 ), 
                                                      rec( 
                                                          content := " is supp\
lied, then additionally the independent\n    set will be required to contain p\
recisely ", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 391138, 
                                                          root := ~, 
                                                          start := 391127, 
                                                          stop := 391137 ), 
                                                      rec( 
                                                          content := " vertice\
s.", count := [ 8, 2, 2, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 2, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 391152, 
                                                          root := ~, 
                                                          start := 391148, 
                                                          stop := 391151 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 391175, 
                                                          root := ~, 
                                                          start := 391161, 
                                                          stop := 391174 ), 
                                                      rec( 
                                                          content := " is not \
an independent set, then these functions return\n    ", count := 
                                                            [ 8, 2, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ail", count := [ 8, 2, 2, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 2, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "K", 
                                                          next := 391246, 
                                                          root := ~, 
                                                          start := 391235, 
                                                          stop := 391245 ), 
                                                      rec( 
                                                          content := ".  Other\
wise, the functions behave in the following way,\n    depending on the number \
of arguments:\n\n    ", count := [ 8, 2, 2, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "One or two arguments", count := [ 8, 2\
, 2, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 8, 2, 
                                                                      2, 8 ], 
                                                                  name := "Mar\
k", next := 391396, root := ~, start := 391363, stop := 391395 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        If one or two arguments are\
 supplied, then ", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "Dig\
raphIndependentSet", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "C",
                                                                          next\
 := 391489, root := ~, start := 391461, stop := 391488 ), rec( content := "\n \
       and ", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "DigraphMaxi\
malIndependentSet", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 391537, root := ~, start := 391502, stop := 391536 ), rec( content := " gr\
eedily enlarge the\n        independent set ", count := [ 8, 2, 2, 9 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conte\
nt := [ rec( content := "include", count := [ 8, 2, 2, 9 ], mathmode := "Text"\
, name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 9 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "A", next := 391597, root := ~, start := 391583, stop := 391596 ), 
                                                                      rec( 
                                                                          cont\
ent := " until it can not continue.  The result\n        is guaranteed to be a\
 maximal independent set. This may or may not\n        return an answer more q\
uickly than using ", count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Func := "DigraphMaximalIndependentS\
ets" ), content := 0, count := [ 8, 2, 2, 9 ], mathmode := "Text", name := "Re\
f", next := 391814, root := ~, start := 391761, stop := 391813 ), rec( content\
 := ".  with a limit of 1.\n      ", count := [ 8, 2, 2, 9 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 9 ], name := "Item", 
                                                                  next := 3918\
49, root := ~, start := 391403, stop := 391848 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "Three arguments", count := [ 8, 2, 2, 10 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 10 ], name := "Mark", 
                                                                  next := 3918\
84, root := ~, start := 391856, stop := 391883 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n        If three arguments are supplied, then ", count := [ 8, 2, 2,\
 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := "DigraphIndependentSet", count := [ 8, 2, \
2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2,\
 2, 11 ], mathmode := "Text", name := "C", next := 391972, root := ~, start :=\
 391944, stop := 391971 ), rec( content := "\n        greedily enlarges the in\
dependent set ", count := [ 8, 2, 2, 11 ], mathmode := "Text", name := "PCDATA\
", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "incl\
ude", count := [ 8, 2, 2, 11 ], mathmode := "Text", name := "PCDATA", root := \
~ ) ], count := [ 8, 2, 2, 11 ], mathmode := "Text", name := "A", next := 3920\
33, root := ~, start := 392019, stop := 392032 ), rec( content := " until it c\
an not\n        continue, although this independent set may not be maximal.", 
                                                                          coun\
t := [ 8, 2, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 8, 2, 2, 12 ], mathmode := "Text",
                                                                          name\
 := "P", next := 392122, root := ~, start := 392118, stop := 392121 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n\n        Given three arguments, ", count := [ 8, 2, 2, 12 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), conte\
nt := [ rec( content := "DigraphMaximalIndependentSet", count := [ 8, 2, 2, 12\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 1\
2 ], mathmode := "Text", name := "C", next := 392190, root := ~, start := 3921\
55, stop := 392189 ), rec( content := " returns the\n        maximal independe\
nt set returned by\n        ", count := [ 8, 2, 2, 12 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "DigraphMaximalIndependentSets(", count := [ 8, 2, 2, 12 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 12 ], mathmode :=\
 "Text", name := "C", next := 392292, root := ~, start := 392255, stop := 3922\
91 ), rec( attributes := rec(  ), content := [ rec( content := "digraph", coun\
t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "A", next := 392306, root :=\
 ~, start := 392292, stop := 392305 ), rec( attributes := rec(  ), content := 
                                                                            [ \
rec( content := ",\n        ", count := [ 8, 2, 2, 12 ], mathmode := "Text", n\
ame := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 12 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 392323, root := ~, start := 392306, stop := 392322 ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "include", count := [ 8, 2, 2,\
 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2\
, 12 ], mathmode := "Text", name := "A", next := 392337, root := ~, start := 3\
92323, stop := 392336 ), rec( attributes := rec(  ), content := [ rec( content\
 := ", ", count := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 8, 2, 2, 12 ], mathmode := "Text", name := "C", next := \
392346, root := ~, start := 392337, stop := 392345 ), rec( attributes := rec( \
 ), content := [ rec( content := "exclude", count := [ 8, 2, 2, 12 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 12 ], mathmod\
e := "Text", name := "A", next := 392360, root := ~, start := 392346, stop := \
392359 ), rec( attributes := rec(  ), content := [ rec( content := ", 1)", cou\
nt := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "C", next := 392371, root :=\
 ~, start := 392360, stop := 392370 ), rec( content := " if one exists,\n     \
   else ", count := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "fail", coun\
t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 2, 2, 12 ], mathmode := "Text", name := "K", next := 392411, root :=\
 ~, start := 392400, stop := 392410 ), rec( content := ".\n      ", count := 
                                                                            [ \
8, 2, 2, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 8, 2, 
                                                                      2, 11 ],
                                                                  name := "Ite\
m", next := 392426, root := ~, start := 391891, stop := 392425 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "Four arguments", count := [ 8, 2, 2, \
13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 
                                                                      2, 13 ],
                                                                  name := "Mar\
k", next := 392460, root := ~, start := 392433, stop := 392459 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        If four arguments are suppl\
ied, then ", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "DigraphInde\
pendentSet", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "C", next \
:= 392547, root := ~, start := 392519, stop := 392546 ), rec( content := "\n  \
      returns the independent set returned by\n        ", count := [ 8, 2, 2, \
14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\
c(  ), content := [ rec( content := "DigraphIndependentSets(", count := [ 8, 2\
, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, \
2, 2, 14 ], mathmode := "Text", name := "C", next := 392634, root := ~, start \
:= 392604, stop := 392633 ), rec( attributes := rec(  ), content := [ rec( con\
tent := "digraph", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "A",
                                                                          next\
 := 392648, root := ~, start := 392634, stop := 392647 ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := ", ", count := [ 8, 2, 2, 14 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode \
:= "Text", name := "C", next := 392657, root := ~, start := 392648, stop := 39\
2656 ), rec( attributes := rec(  ), content := [ rec( content := "include", co\
unt := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 2, 2, 14 ], mathmode := "Text", name := "A", next := 392671, root :=\
 ~, start := 392657, stop := 392670 ), rec( attributes := rec(  ), content := 
                                                                            [ \
rec( content := ",\n        ", count := [ 8, 2, 2, 14 ], mathmode := "Text", n\
ame := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 392688, root := ~, start := 392671, stop := 392687 ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "exclude", count := [ 8, 2, 2,\
 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2\
, 14 ], mathmode := "Text", name := "A", next := 392702, root := ~, start := 3\
92688, stop := 392701 ), rec( attributes := rec(  ), content := [ rec( content\
 := ", 1, ", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "C", next \
:= 392714, root := ~, start := 392702, stop := 392713 ), rec( attributes := re\
c(  ), content := [ rec( content := "size", count := [ 8, 2, 2, 14 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 14 ], mathmod\
e := "Text", name := "A", next := 392725, root := ~, start := 392714, stop := \
392724 ), rec( attributes := rec(  ), content := [ rec( content := ")", count \
:= [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\
 := [ 8, 2, 2, 14 ], mathmode := "Text", name := "C", next := 392733, root := \
~, start := 392725, stop := 392732 ), rec( content := " if one exists, else\n \
       ", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "fail", coun\
t := [ 8, 2, 2, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 2, 2, 14 ], mathmode := "Text", name := "K", next := 392773, root :=\
 ~, start := 392762, stop := 392772 ), rec( content := ". This independent set\
 may not be maximal.", count := [ 8, 2, 2, 14 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := 0, count := [ 8, \
2, 2, 15 ], mathmode := "Text", name := "P", next := 392819, root := ~, start \
:= 392815, stop := 392818 ), rec( content := " Given four\n        arguments, \
", count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "DigraphMaximalIndependentSet"\
, count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                                             ]
                                                                            , 
                                                                          coun\
t := [ 8, 2, 2, 15 ], mathmode := "Text", name := "C", next := 392885, root :=\
 ~, start := 392850, stop := 392884 ), rec( content := " returns the maximal\n\
        independent set returned by\n        ", count := [ 8, 2, 2, 15 ], math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "DigraphMaximalIndependentSets(", count := [ 8, 2, 2,\
 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2\
, 15 ], mathmode := "Text", name := "C", next := 392987, root := ~, start := 3\
92950, stop := 392986 ), rec( attributes := rec(  ), content := [ rec( content\
 := "digraph", count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA",\
 root := ~ ) ], count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "A", 
                                                                          next\
 := 393001, root := ~, start := 392987, stop := 393000 ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := ",\n          ", count := [ 8, 2, 2, 15 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 15 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 393020, root := ~, start := 393001, stop \
:= 393019 ), rec( attributes := rec(  ), content := [ rec( content := "include\
", count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ )\
 ], count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "A", next := 393034,
                                                                          root\
 := ~, start := 393020, stop := 393033 ), rec( attributes := rec(  ), content \
:= [ rec( content := ", ", count := [ 8, 2, 2, 15 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 15 ], mathmode := "Text", name\
 := "C", next := 393043, root := ~, start := 393034, stop := 393042 ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "exclude", count := [ 8, 2, 2,\
 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2\
, 15 ], mathmode := "Text", name := "A", next := 393057, root := ~, start := 3\
93043, stop := 393056 ), rec( attributes := rec(  ), content := [ rec( content\
 := ", 1,\n        ", count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 8, 2, 2, 15 ], mathmode := "Text", name := "\
C", next := 393077, root := ~, start := 393057, stop := 393076 ), rec( attribu\
tes := rec(  ), content := [ rec( content := "size", count := [ 8, 2, 2, 15 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 15 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 393088, root := ~, start := 393077, stop \
:= 393087 ), rec( attributes := rec(  ), content := [ rec( content := ")", cou\
nt := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 2, 2, 15 ], mathmode := "Text", name := "C", next := 393096, root :=\
 ~, start := 393088, stop := 393095 ), rec( content := " if one exists, else "
                                                                            , 
                                                                          coun\
t := [ 8, 2, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "fail", count := [ 8, 2, 2, 15\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 1\
5 ], mathmode := "Text", name := "K", next := 393128, root := ~, start := 3931\
17, stop := 393127 ), rec( content := ".\n      ", count := [ 8, 2, 2, 15 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 2, 14 ], 
                                                                  name := "Ite\
m", next := 393143, root := ~, start := 392467, stop := 393142 ) ], 
                                                          count := 
                                                            [ 8, 2, 2, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 393155, 
                                                          root := ~, 
                                                          start := 391350, 
                                                          stop := 393154 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 8, 2, 2, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := ChainDigraph(6);\n<immutable chain digraph with 6 vertices>\ngap> D\
igraphIndependentSet(D);\n[ 6, 4, 2 ]\ngap> DigraphMaximalIndependentSet(D);\n\
[ 6, 4, 2 ]\ngap> DigraphIndependentSet(D, [2, 4]);\n[ 2, 4, 6 ]\ngap> Digraph\
MaximalIndependentSet(D, [1, 3]);\n[ 1, 3, 6 ]\ngap> DigraphIndependentSet(D, \
[2, 4], [6]);\n[ 2, 4 ]\ngap> DigraphMaximalIndependentSet(D, [2, 4], [6]);\nf\
ail\ngap> DigraphIndependentSet(D, [1], [], 2);\n[ 1, 3 ]\ngap> DigraphMaximal\
IndependentSet(D, [1], [], 2);\nfail\ngap> DigraphMaximalIndependentSet(D, [1]\
, [], 3);\n[ 1, 3, 5 ]\ngap> D := ChainDigraph(IsMutableDigraph, 6);\n<mutable\
 digraph with 6 vertices, 5 edges>\ngap> DigraphIndependentSet(D);\n[ 6, 4, 2 \
]\ngap> DigraphMaximalIndependentSet(D);\n[ 6, 4, 2 ]\ngap> DigraphIndependent\
Set(D, [2, 4]);\n[ 2, 4, 6 ]\ngap> DigraphMaximalIndependentSet(D, [1, 3]);\n[\
 1, 3, 6 ]\ngap> DigraphIndependentSet(D, [2, 4], [6]);\n[ 2, 4 ]\ngap> Digrap\
hMaximalIndependentSet(D, [2, 4], [6]);\nfail\ngap> DigraphIndependentSet(D, [\
1], [], 2);\n[ 1, 3 ]\ngap> DigraphMaximalIndependentSet(D, [1], [], 2);\nfail\
\ngap> DigraphMaximalIndependentSet(D, [1], [], 3);\n[ 1, 3, 5 ]", 
                                                                  count := 
                                                                    [ 8, 2, 
                                                                      2, 18 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 8, 2, 2, 18 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 394308, 
                                                          root := ~, 
                                                          start := 393160, 
                                                          stop := 394307 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 8, 2, 2, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 2, 2, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 394325, root := ~, 
                                                  start := 390185, 
                                                  stop := 394324 ) ], 
                                          count := [ 8, 2, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 394339, root := ~, 
                                          start := 389908, stop := 394338 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 8, 2, 2, 19 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[, exclude[,\n    limit[, size]]]]", Name := "DigraphMaximalIndependentSets" 
                                                     ), content := 0, 
                                                  count := [ 8, 2, 3, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 394461, root := ~, 
                                                  start := 394360, 
                                                  stop := 394460 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[,\n    exclude[, limit[, size]]]]", Name := "DigraphMaximalIndependentSetsRe\
ps" ), content := 0, count := [ 8, 2, 3, 4 ], mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 394569, root := ~, 
                                                  start := 394464, 
                                                  stop := 394568 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[,\n    exclude[, limit[, size]]]]", Name := "DigraphIndependentSets" ), 
                                                  content := 0, 
                                                  count := [ 8, 2, 3, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 394666, root := ~, 
                                                  start := 394572, 
                                                  stop := 394665 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph[, includ\
e[,\n    exclude[, limit[, size]]]]", Name := "DigraphIndependentSetsReps" ), 
                                                  content := 0, 
                                                  count := [ 8, 2, 3, 8 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 394767, root := ~, 
                                                  start := 394669, 
                                                  stop := 394766 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMaximalI\
ndependentSetsAttr" ), content := 0, count := [ 8, 2, 3, 10 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 394832, root := ~, 
                                                  start := 394770, 
                                                  stop := 394831 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DigraphMaximalI\
ndependentSetsRepsAttr" ), content := 0, count := [ 8, 2, 3, 12 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 394901, root := ~, 
                                                  start := 394835, 
                                                  stop := 394900 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An immuta\
ble list of lists of positive integers.", count := [ 8, 2, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 2, 3, 13 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 394971, root := ~, 
                                                  start := 394904, 
                                                  stop := 394970 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395009, 
                                                          root := ~, 
                                                          start := 394995, 
                                                          stop := 395008 ), 
                                                      rec( 
                                                          content := " is digr\
aph, then these functions and attributes use ", count := [ 8, 2, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Cliques\
Finder" ), content := 0, count := [ 8, 2, 3, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 395095, 
                                                          root := ~, 
                                                          start := 395062, 
                                                          stop := 395094 ), 
                                                      rec( 
                                                          content := " to retu\
rn independent sets of ", count := [ 8, 2, 3, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395140, 
                                                          root := ~, 
                                                          start := 395126, 
                                                          stop := 395139 ), 
                                                      rec( 
                                                          content := ". An\n  \
  independent set is defined by the set of vertices that it contains; see\n   \
 ", count := [ 8, 2, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsMaxim\
alIndependentSet" ), content := 0, count := [ 8, 2, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 395262, 
                                                          root := ~, 
                                                          start := 395225, 
                                                          stop := 395261 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 2, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "IsIndep\
endentSet" ), content := 0, count := [ 8, 2, 3, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 395303, 
                                                          root := ~, 
                                                          start := 395267, 
                                                          stop := 395302 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 8, 2, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 395308, 
                                                          root := ~, 
                                                          start := 395304, 
                                                          stop := 395307 ), 
                                                      rec( 
                                                          content := "\n\n    \
The optional arguments ", count := [ 8, 2, 3, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395351, 
                                                          root := ~, 
                                                          start := 395337, 
                                                          stop := 395350 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395370, 
                                                          root := ~, 
                                                          start := 395356, 
                                                          stop := 395369 ), 
                                                      rec( 
                                                          content := " must ea\
ch be a\n    (possibly empty) list of vertices of ", count := [ 8, 2, 3, 14 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395441, 
                                                          root := ~, 
                                                          start := 395427, 
                                                          stop := 395440 ), 
                                                      rec( 
                                                          content := ", the op\
tional argument\n    ", count := [ 8, 2, 3, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
imit", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395481, 
                                                          root := ~, 
                                                          start := 395469, 
                                                          stop := 395480 ), 
                                                      rec( 
                                                          content := " must be\
 either a positive integer or ", count := [ 8, 2, 3, 14 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 395534, 
                                                          root := ~, 
                                                          start := 395519, 
                                                          stop := 395533 ), 
                                                      rec( 
                                                          content := ", and th\
e\n    optional argument ", count := [ 8, 2, 3, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395577, 
                                                          root := ~, 
                                                          start := 395566, 
                                                          stop := 395576 ), 
                                                      rec( 
                                                          content := " must be\
 a positive integer.  If not\n    specified, then ", count := [ 8, 2, 3, 14 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395648, 
                                                          root := ~, 
                                                          start := 395634, 
                                                          stop := 395647 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395667, 
                                                          root := ~, 
                                                          start := 395653, 
                                                          stop := 395666 ), 
                                                      rec( 
                                                          content := " are cho\
sen to be empty\n    lists, and ", count := [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
imit", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395718, 
                                                          root := ~, 
                                                          start := 395706, 
                                                          stop := 395717 ), 
                                                      rec( 
                                                          content := " is set \
to ", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nfinity", count := [ 8, 2, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 395744, 
                                                          root := ~, 
                                                          start := 395729, 
                                                          stop := 395743 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 8, 2, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 395750, 
                                                          root := ~, 
                                                          start := 395746, 
                                                          stop := 395749 ), 
                                                      rec( 
                                                          content := "\n\n    \
The functions will return as many suitable independent sets as possible, up\n \
   to the number ", count := [ 8, 2, 3, 15 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "l\
imit", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395862, 
                                                          root := ~, 
                                                          start := 395850, 
                                                          stop := 395861 ), 
                                                      rec( 
                                                          content := ".  These\
 functions will find independent sets\n    that contain all of the vertices of\
 ", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
nclude", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 395962, 
                                                          root := ~, 
                                                          start := 395948, 
                                                          stop := 395961 ), 
                                                      rec( 
                                                          content := " but do \
not\n    contain any of the vertices of ", count := [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
xclude", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 396023, 
                                                          root := ~, 
                                                          start := 396009, 
                                                          stop := 396022 ), 
                                                      rec( 
                                                          content := " The arg\
ument ", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 396048, 
                                                          root := ~, 
                                                          start := 396037, 
                                                          stop := 396047 ), 
                                                      rec( 
                                                          content := "\n    re\
stricts the search to those cliques that contain precisely ", 
                                                          count := 
                                                            [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
ize", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 396125, 
                                                          root := ~, 
                                                          start := 396114, 
                                                          stop := 396124 ), 
                                                      rec( 
                                                          content := "\n    ve\
rtices.  If the function or attribute has ", count := [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "M\
aximal", count := [ 8, 2, 3, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 396188, 
                                                          root := ~, 
                                                          start := 396174, 
                                                          stop := 396187 ), 
                                                      rec( 
                                                          content := " in its \
name,\n    then only maximal independent sets will be returned; otherwise non-\
maximal\n    independent sets may be returned.\n    ", count := 
                                                            [ 8, 2, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 8, 2, 3, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 396327, 
                                                          root := ~, 
                                                          start := 396323, 
                                                          stop := 396326 ), 
                                                      rec( 
                                                          content := "\n\n    \
Let ", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 8, 2, 3, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 396345, 
                                                          root := ~, 
                                                          start := 396337, 
                                                          stop := 396344 ), 
                                                      rec( 
                                                          content := " denote \
the ", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := 
                                                            [ 8, 2, 3, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 396410, 
                                                          root := ~, 
                                                          start := 396357, 
                                                          stop := 396409 ), 
                                                      rec( 
                                                          content := "\n    of\
 the ", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
SymmetricClosure" ), content := 0, count := [ 8, 2, 3, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 396459, 
                                                          root := ~, 
                                                          start := 396422, 
                                                          stop := 396458 ), 
                                                      rec( 
                                                          content := " of the \
digraph formed from\n    ", count := [ 8, 2, 3, 16 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 8, 2, 3, 16 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 8, 2, 3, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 396505, 
                                                          root := ~, 
                                                          start := 396491, 
                                                          stop := 396504 ), 
                                                      rec( 
                                                          content := " by remo\
ving loops and ignoring the multiplicity of edges.\n\n    ", 
                                                          count := 
                                                            [ 8, 2, 3, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Distinct independent sets", count := 
                                                                            [ \
8, 2, 3, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 8, 2, 
                                                                      3, 17 ],
                                                                  name := "Mar\
k", next := 396620, root := ~, start := 396582, stop := 396619 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        ", count := [ 8, 2, 3, 18 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "DigraphMaximalIndependentSets", count := [ 8, 2, 3, \
18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3,\
 18 ], mathmode := "Text", name := "C", next := 396678, root := ~, start := 39\
6642, stop := 396677 ), rec( content := " and ", count := [ 8, 2, 3, 18 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "DigraphIndependentSets", count := [ 8, 2, 3, 18 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 18 ], 
                                                                          math\
mode := "Text", name := "C", next := 396712, root := ~, start := 396683, stop \
:= 396711 ), rec( content := "\n        each return a duplicate-free list of a\
t most ", count := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "limit", cou\
nt := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 2, 3, 18 ], mathmode := "Text", name := "A", next := 396778, root :=\
 ~, start := 396766, stop := 396777 ), rec( content := " independent\n        \
sets of ", count := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "digraph", c\
ount := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 2, 3, 18 ], mathmode := "Text", name := "A", next := 396821, root :=\
 ~, start := 396807, stop := 396820 ), rec( content := " that satisfy the argu\
ments.", count := [ 8, 2, 3, 18 ], mathmode := "Text", name := "PCDATA", root \
:= ~ ), rec( attributes := rec(  ), content := 0, count := [ 8, 2, 3, 19 ], 
                                                                          math\
mode := "Text", name := "P", next := 396853, root := ~, start := 396849, stop \
:= 396852 ), rec( content := "\n\n        The computation may be significantly\
 faster if ", count := [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "include", c\
ount := [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 8, 2, 3, 19 ], mathmode := "Text", name := "A", next := 396924, root :=\
 ~, start := 396910, stop := 396923 ), rec( content := " and\n        ", count\
 := [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "exclude", count := [ 8, 2, 3,\
 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3\
, 19 ], mathmode := "Text", name := "A", next := 396951, root := ~, start := 3\
96937, stop := 396950 ), rec( content := " are invariant under the action of "
                                                                            , 
                                                                          coun\
t := [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "G", count := [ 8, 2, 3, 19 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 19 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 396994, root := ~, start := 396986, stop \
:= 396993 ), rec( content := " on sets of\n        vertices.\n      ", count :\
= [ 8, 2, 3, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 8, 2, 
                                                                      3, 18 ],
                                                                  name := "Ite\
m", next := 397037, root := ~, start := 396627, stop := 397036 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "Representatives of distinct orbits of\
 independent sets", count := [ 8, 2, 3, 20 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 8, 2, 3, 20 ], name := "Mark", next := 397112,
                                                                  root := ~, 
                                                                  start := 397\
045, stop := 397111 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n        To use ", count := [ 8, 2, 3, 21 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content :=\
 "DigraphMaximalIndependentSetsReps", count := [ 8, 2, 3, 21 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmode := "\
Text", name := "C", next := 397181, root := ~, start := 397141, stop := 397180\
 ), rec( content := " or\n        ", count := [ 8, 2, 3, 21 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ r\
ec( content := "DigraphIndependentSetsReps", count := [ 8, 2, 3, 21 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmo\
de := "Text", name := "C", next := 397226, root := ~, start := 397193, stop :=\
 397225 ), rec( content := ", the arguments ", count := [ 8, 2, 3, 21 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), cont\
ent := [ rec( content := "include", count := [ 8, 2, 3, 21 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmode := "Te\
xt", name := "A", next := 397256, root := ~, start := 397242, stop := 397255 )
                                                                        , 
                                                                      rec( 
                                                                          cont\
ent := " and\n        ", count := [ 8, 2, 3, 21 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "exclude", count := [ 8, 2, 3, 21 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmode := "Text", name := "A", next\
 := 397283, root := ~, start := 397269, stop := 397282 ), rec( content := " mu\
st each be invariant under the action of ", count := [ 8, 2, 3, 21 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content\
 := [ rec( content := "G", count := [ 8, 2, 3, 21 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 21 ], mathmode := "Text", name\
 := "C", next := 397335, root := ~, start := 397327, stop := 397334 ), 
                                                                      rec( 
                                                                          cont\
ent := " on\n        sets of vertices.", count := [ 8, 2, 3, 21 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :=\
 0, count := [ 8, 2, 3, 22 ], mathmode := "Text", name := "P", next := 397368,
                                                                          root\
 := ~, start := 397364, stop := 397367 ), rec( content := "\n\n        If this\
 is the case, then ", count := [ 8, 2, 3, 22 ], mathmode := "Text", name := "P\
CDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := \
"DigraphMaximalIndependentSetsReps", count := [ 8, 2, 3, 22 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 22 ], mathmode := "T\
ext", name := "C", next := 397444, root := ~, start := 397404, stop := 397443 
                                                                         ), 
                                                                      rec( 
                                                                          cont\
ent := " and\n        ", count := [ 8, 2, 3, 22 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "DigraphIndependentSetsReps", count := [ 8, 2, 3, 22 ], mathmode := "Text",\
 name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 22 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "C", next := 397490, root := ~, start := 397457, stop := 397489 ), 
                                                                      rec( 
                                                                          cont\
ent := " each return a list of\n        at most ", count := [ 8, 2, 3, 22 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "limit", count := [ 8, 2, 3, 22 ], mathmode := "Text"\
, name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 22 ], mathmode := "Text\
", name := "A", next := 397541, root := ~, start := 397529, stop := 397540 ), 
                                                                      rec( 
                                                                          cont\
ent := " orbits representatives (under the action of\n        ", count := [ 8,\
 2, 3, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribute\
s := rec(  ), content := [ rec( content := "G", count := [ 8, 2, 3, 22 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 22 ], 
                                                                          math\
mode := "Text", name := "C", next := 397602, root := ~, start := 397594, stop \
:= 397601 ), rec( content := " on sets of vertices) of independent sets of ", 
                                                                          coun\
t := [ 8, 2, 3, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "digraph", count := [ 8, 2, 3,\
 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3\
, 22 ], mathmode := "Text", name := "A", next := 397661, root := ~, start := 3\
97647, stop := 397660 ), rec( content := "\n        that satisfy the arguments\
. ", count := [ 8, 2, 3, 22 ], mathmode := "Text", name := "PCDATA", root := ~\
 ), rec( attributes := rec(  ), content := 0, count := [ 8, 2, 3, 23 ], mathmo\
de := "Text", name := "P", next := 397702, root := ~, start := 397698, stop :=\
 397701 ), rec( content := "\n\n        The representatives are not guaranteed\
 to be in distinct orbits.\n        However, if ", count := [ 8, 2, 3, 23 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "lim", count := [ 8, 2, 3, 23 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 23 ], mathmode := "Text",
                                                                          name\
 := "A", next := 397807, root := ~, start := 397797, stop := 397806 ), 
                                                                      rec( 
                                                                          cont\
ent := " is not specified, or fewer than ", count := [ 8, 2, 3, 23 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content\
 := [ rec( content := "lim", count := [ 8, 2, 3, 23 ], mathmode := "Text", nam\
e := "PCDATA", root := ~ ) ], count := [ 8, 2, 3, 23 ], mathmode := "Text", 
                                                                          name\
 := "A", next := 397850, root := ~, start := 397840, stop := 397849 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n        results are returned, then there will be at least one repres\
entative\n        from each orbit of maximal independent sets.\n      ", count\
 := [ 8, 2, 3, 23 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 8, 2, 
                                                                      3, 21 ],
                                                                  name := "Ite\
m", next := 397994, root := ~, start := 397119, stop := 397993 ) ], 
                                                          count := 
                                                            [ 8, 2, 3, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 398006, 
                                                          root := ~, 
                                                          start := 396569, 
                                                          stop := 398005 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 8, 2, 3, 25 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(5);\n<immutable cycle digraph with 5 vertices>\ngap> D\
igraphMaximalIndependentSetsReps(D);\n[ [ 1, 3 ] ]\ngap> DigraphIndependentSet\
sReps(D);\n[ [ 1 ], [ 1, 3 ] ]\ngap> Set(DigraphMaximalIndependentSets(D));\n[\
 [ 1, 3 ], [ 1, 4 ], [ 2, 4 ], [ 2, 5 ], [ 3, 5 ] ]\ngap> DigraphMaximalIndepe\
ndentSets(D, [1]);\n[ [ 1, 3 ], [ 1, 4 ] ]\ngap> DigraphIndependentSets(D, [],\
 [4, 5]);\n[ [ 1 ], [ 2 ], [ 3 ], [ 1, 3 ] ]\ngap> DigraphIndependentSets(D, [\
], [4, 5], 1, 2);\n[ [ 1, 3 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 5);\
\n<mutable digraph with 5 vertices, 5 edges>\ngap> DigraphMaximalIndependentSe\
tsReps(D);\n[ [ 1, 3 ] ]\ngap> DigraphIndependentSetsReps(D);\n[ [ 1 ], [ 1, 3\
 ] ]\ngap> Set(DigraphMaximalIndependentSets(D));\n[ [ 1, 3 ], [ 1, 4 ], [ 2, \
4 ], [ 2, 5 ], [ 3, 5 ] ]\ngap> DigraphMaximalIndependentSets(D, [1]);\n[ [ 1,\
 3 ], [ 1, 4 ] ]\ngap> DigraphIndependentSets(D, [], [4, 5]);\n[ [ 1 ], [ 2 ],\
 [ 3 ], [ 1, 3 ] ]\ngap> DigraphIndependentSets(D, [], [4, 5], 1, 2);\n[ [ 1, \
3 ] ]", count := [ 8, 2, 3, 26 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 8, 2, 3, 26 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 399034, 
                                                          root := ~, 
                                                          start := 398012, 
                                                          stop := 399033 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 8, 2, 3, 27 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 8, 2, 3, 13 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 399051, root := ~, 
                                                  start := 394974, 
                                                  stop := 399050 ) ], 
                                          count := [ 8, 2, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 399065, root := ~, 
                                          start := 394345, stop := 399064 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 8, 2, 3, 27 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 8, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 399079, 
                                  root := ~, start := 388428, stop := 399078 )
                                , 
                              rec( content := "\n", count := [ 8, 2, 3, 27 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 8, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 399090, root := ~, start := 367151, 
                          stop := 399089 ), 
                      rec( content := "\n ", count := [ 8, 2, 3, 27 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " cliques ", count := [ 8, 2, 3, 27 ], 
                          mathmode := "Text", name := "XMLCOMMENT", root := ~ 
                         ), 
                      rec( content := "\n  ", count := [ 8, 2, 3, 27 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Label := "Visualising and IO" ),
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Visualising and IO", 
                                          count := [ 9, 0, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 9, 0, 0, 2 ], mathmode := "Text",
                                  name := "Heading", next := 399184, 
                                  root := ~, start := 399147, stop := 399183 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 9, 0, 0, 3 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Visualising a dig\
raph", count := [ 9, 1, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                                  root := ~ ) ], 
                                          count := [ 9, 1, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "Heading", next := 399237, 
                                          root := ~, start := 399197, 
                                          stop := 399236 ), 
                                      rec( content := "\n      ", 
                                          count := [ 9, 1, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "str, [opts]",
                                                      Name := "Splash" ), 
                                                  content := 0, 
                                                  count := [ 9, 1, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 399300, root := ~, 
                                                  start := 399261, 
                                                  stop := 399299 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "Nothing."
                                                            , 
                                                          count := 
                                                            [ 9, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 399332, root := ~, 
                                                  start := 399305, 
                                                  stop := 399331 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      T\
his function attempts to convert the string ", count := [ 9, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tr", count := [ 9, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 1, 1, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 399412, 
                                                          root := ~, 
                                                          start := 399402, 
                                                          stop := 399411 ), 
                                                      rec( 
                                                          content := " into a \
pdf\n      document and open this document, i.e. to splash it all over your mo\
nitor.", count := [ 9, 1, 1, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 399507, 
                                                          root := ~, 
                                                          start := 399503, 
                                                          stop := 399506 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The string ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tr", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 399536, 
                                                          root := ~, 
                                                          start := 399526, 
                                                          stop := 399535 ), 
                                                      rec( 
                                                          content := " must co\
rrespond to a valid ", count := [ 9, 1, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ot", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 399574, 
                                                          root := ~, 
                                                          start := 399564, 
                                                          stop := 399573 ), 
                                                      rec( 
                                                          content := " or\n   \
   ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
aTeX", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 399596, 
                                                          root := ~, 
                                                          start := 399584, 
                                                          stop := 399595 ), 
                                                      rec( 
                                                          content := " text fi\
le and you must have have ", count := [ 9, 1, 1, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
raphViz", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 399645, 
                                                          root := ~, 
                                                          start := 399630, 
                                                          stop := 399644 ), 
                                                      rec( 
                                                          content := " and\n  \
    ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "p\
dflatex", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 399671, 
                                                          root := ~, 
                                                          start := 399656, 
                                                          stop := 399670 ), 
                                                      rec( 
                                                          content := " install\
ed on your computer.  For details about these file\n      formats, see ", 
                                                          count := 
                                                            [ 9, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttp://www.latex-project.org", count := [ 9, 1, 1, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 1, 4 ], mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 399788, 
                                                          root := ~, 
                                                          start := 399749, 
                                                          stop := 399787 ), 
                                                      rec( 
                                                          content := " and\n  \
    ", count := [ 9, 1, 1, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttp://www.graphviz.org", count := [ 9, 1, 1, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 1, 4 ], mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 399833, 
                                                          root := ~, 
                                                          start := 399799, 
                                                          stop := 399832 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 1, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 399838, 
                                                          root := ~, 
                                                          start := 399834, 
                                                          stop := 399837 ), 
                                                      rec( 
                                                          content := "\n\n    \
  This function is provided to allow convenient, immediate viewing of the\n   \
   pictures produced by the function ", count := [ 9, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "DotDigr\
aph" ), content := 0, count := [ 9, 1, 1, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 399982, 
                                                          root := ~, 
                                                          start := 399958, 
                                                          stop := 399981 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 399987, 
                                                          root := ~, 
                                                          start := 399983, 
                                                          stop := 399986 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The optional second argument ", count := [ 9, 1, 1, 6 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
pts", count := [ 9, 1, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 400035, 
                                                          root := ~, 
                                                          start := 400024, 
                                                          stop := 400034 ), 
                                                      rec( 
                                                          content := " should \
be a record with\n      components corresponding to various options, given bel\
ow.\n\n      ", count := [ 9, 1, 1, 6 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "path", count := [ 9, 1, 1, 7 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 7 ], 
                                                                  name := "Mar\
k", next := 400163, root := ~, start := 400146, stop := 400162 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n          this should be a string r\
epresenting the path to the directory where\n          you want ", count := [ \
9, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := [ rec( content := "Splash", count := [ 9, 1, 1, 8 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 8 ],
                                                                          math\
mode := "Text", name := "C", next := 400290, root := ~, start := 400277, stop \
:= 400289 ), rec( content := " to do its work. The default value of this\n    \
      option is ", count := [ 9, 1, 1, 8 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\"~\
/\"", count := [ 9, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~\
 ) ], count := [ 9, 1, 1, 8 ], mathmode := "Text", name := "C", next := 400364
                                                                            , 
                                                                          root\
 := ~, start := 400353, stop := 400363 ), rec( content := ".\n        ", count\
 := [ 9, 1, 1, 8 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 9, 1, 
                                                                      1, 8 ], 
                                                                  name := "Ite\
m", next := 400381, root := ~, start := 400172, stop := 400380 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "directory", count := [ 9, 1, 1, 9 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 9 ], 
                                                                  name := "Mar\
k", next := 400413, root := ~, start := 400391, stop := 400412 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n          this should be a string r\
epresenting the name of the directory in\n          ", count := [ 9, 1, 1, 10 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "path", count := [ 9, 1, 1, 10 ], mathmode := "Text",\
 name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 10 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "C", next := 400526, root := ~, start := 400515, stop := 400525 ), 
                                                                      rec( 
                                                                          cont\
ent := " where you want ", count := [ 9, 1, 1, 10 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conten\
t := "Splash", count := [ 9, 1, 1, 10 ], mathmode := "Text", name := "PCDATA",\
 root := ~ ) ], count := [ 9, 1, 1, 10 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 400555, root := ~, start := 400542, stop := 400554 ), rec( content := " to\
 do its work. This function\n          will create this directory if does not \
already exist. ", count := [ 9, 1, 1, 10 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ), rec( attributes := rec(  ), content := 0, count := [ 9, 1, 1,\
 11 ], mathmode := "Text", name := "P", next := 400654, root := ~, start := 40\
0650, stop := 400653 ), rec( content := "\n\n          The default value of th\
is option is ", count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\"tmp.viz\"\
", count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ )\
 ], count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "C", next := 400718,
                                                                          root\
 := ~, start := 400702, stop := 400717 ), rec( content := " if the option\n   \
       ", count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "path", coun\
t := [ 9, 1, 1, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 9, 1, 1, 11 ], mathmode := "Text", name := "C", next := 400754, root :=\
 ~, start := 400743, stop := 400753 ), rec( content := " is present, and the r\
esult of\n          ", count := [ 9, 1, 1, 11 ], mathmode := "Text", name := "\
PCDATA", root := ~ ), rec( attributes := rec( BookName := "ref", Func := "Dire\
ctoryTemporary" ), content := 0, count := [ 9, 1, 1, 11 ], mathmode := "Text",
                                                                          name\
 := "Ref", next := 400842, root := ~, start := 400795, stop := 400841 ), 
                                                                      rec( 
                                                                          cont\
ent := " is used otherwise.\n        ", count := [ 9, 1, 1, 11 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 10 ], 
                                                                  name := "Ite\
m", next := 400877, root := ~, start := 400422, stop := 400876 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "filename", count := [ 9, 1, 1, 12 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 12 ], 
                                                                  name := "Mar\
k", next := 400908, root := ~, start := 400887, stop := 400907 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n          this should be a string r\
epresenting the name of the file where\n          ", count := [ 9, 1, 1, 13 ],
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "str", count := [ 9, 1, 1, 13 ], mathmode := "Text", \
name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 13 ], mathmode := "Text",
                                                                          name\
 := "A", next := 401018, root := ~, start := 401008, stop := 401017 ), 
                                                                      rec( 
                                                                          cont\
ent := " will be written.  The default value of this option is\n          ", 
                                                                          coun\
t := [ 9, 1, 1, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "\"vizpicture\"", count := [ 9\
, 1, 1, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ \
9, 1, 1, 13 ], mathmode := "Text", name := "C", next := 401102, root := ~, 
                                                                          star\
t := 401083, stop := 401101 ), rec( content := ".\n        ", count := [ 9, 1,\
 1, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 9, 1, 
                                                                      1, 13 ],
                                                                  name := "Ite\
m", next := 401119, root := ~, start := 400917, stop := 401118 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "viewer", count := [ 9, 1, 1, 14 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 14 ], 
                                                                  name := "Mar\
k", next := 401148, root := ~, start := 401129, stop := 401147 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n          this should be a string r\
epresenting the name of the program which\n          should open the files pro\
duced by ", count := [ 9, 1, 1, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "GraphViz", \
count := [ 9, 1, 1, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ],
                                                                          coun\
t := [ 9, 1, 1, 15 ], mathmode := "Text", name := "C", next := 401300, root :=\
 ~, start := 401285, stop := 401299 ), rec( content := " or ", count := [ 9, 1\
, 1, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes \
:= rec(  ), content := [ rec( content := "pdflatex", count := [ 9, 1, 1, 15 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 15 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 401319, root := ~, start := 401304, stop \
:= 401318 ), rec( content := ".\n        ", count := [ 9, 1, 1, 15 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 15 ], 
                                                                  name := "Ite\
m", next := 401336, root := ~, start := 401157, stop := 401335 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "type", count := [ 9, 1, 1, 16 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 16 ], 
                                                                  name := "Mar\
k", next := 401363, root := ~, start := 401346, stop := 401362 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n          this option can be used t\
o specify that the string ", count := [ 9, 1, 1, 17 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "str", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", r\
oot := ~ ) ], count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "A", next \
:= 401450, root := ~, start := 401440, stop := 401449 ), rec( content := " con\
tains\n          a ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "P\
CDATA", root := ~ ), rec( attributes := rec( Only := "LaTeX" ), content := [ r\
ec( content := "{\\LaTeX}", count := [ 9, 1, 1, 17 ], name := "PCDATA", root :\
= ~ ) ], count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "Alt", next := \
33, root := ~, start := 1, stop := 32 ), rec( attributes := rec( Not := "LaTeX\
" ), content := [ rec( content := "LaTeX", count := [ 9, 1, 1, 17 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 17 ], name := \
"Alt", next := 61, root := ~, start := 33, stop := 60 ), rec( content := " or \
", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "dot", count := [ 9, 1, 1, 17 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 17\
 ], mathmode := "Text", name := "C", next := 401493, root := ~, start := 40148\
3, stop := 401492 ), rec( content := " document. You can specify this option i\
n\n          ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "str", count\
 := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 9, 1, 1, 17 ], mathmode := "Text", name := "A", next := 401555, root :=\
 ~, start := 401545, stop := 401554 ), rec( content := " directly by making th\
e first line ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\"%latex\""\
, count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                                             ]
                                                                            , 
                                                                          coun\
t := [ 9, 1, 1, 17 ], mathmode := "Text", name := "C", next := 401605, root :=\
 ~, start := 401590, stop := 401604 ), rec( content := " or\n          ", coun\
t := [ 9, 1, 1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "\"//dot\"", count := [ 9, 1, \
1, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1,\
 1, 17 ], mathmode := "Text", name := "C", next := 401633, root := ~, start :=\
 401619, stop := 401632 ), rec( content := ".  There is no default value for t\
his option, this\n          option must be specified in ", count := [ 9, 1, 1,\
 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := 
                                                                            re\
c(  ), content := [ rec( content := "str", count := [ 9, 1, 1, 17 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 17 ], mathmode\
 := "Text", name := "A", next := 401732, root := ~, start := 401722, stop := 4\
01731 ), rec( content := " or in ", count := [ 9, 1, 1, 17 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ re\
c( content := "opt.type", count := [ 9, 1, 1, 17 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 17 ], mathmode := "Text", name \
:= "A", next := 401754, root := ~, start := 401739, stop := 401753 ), rec( 
                                                                          cont\
ent := ".\n        ", count := [ 9, 1, 1, 17 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 9, 1, 1, 17 ], name := "Item", next := 40177\
1, root := ~, start := 401372, stop := 401770 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "engine", count := [ 9, 1, 1, 18 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 9, 1, 1, 18 ], name := "Mark", next := 401800, 
                                                                  root := ~, 
                                                                  start := 401\
781, stop := 401799 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n          this option can be used to specify the GraphViz engine to use\n\
          to render a ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content \
:= "dot", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", next := \
401920, root := ~, start := 401910, stop := 401919 ), rec( content := " docume\
nt. The valid choices are ", count := [ 9, 1, 1, 19 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "\"dot\"", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 401965, root := ~, start := 401953, stop := 401964 ), rec( content := ",\n\
          ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\"neato\"",\
 count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ]
                                                                            , 
                                                                          coun\
t := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", next := 401991, root :=\
 ~, start := 401977, stop := 401990 ), rec( content := ", ", count := [ 9, 1, \
1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :=\
 rec(  ), content := [ rec( content := "\"circo\"", count := [ 9, 1, 1, 19 ], \
mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 19 ],
                                                                          math\
mode := "Text", name := "C", next := 402007, root := ~, start := 401993, stop \
:= 402006 ), rec( content := ", ", count := [ 9, 1, 1, 19 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec\
( content := "\"twopi\"", count := [ 9, 1, 1, 19 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode := "Text", name \
:= "C", next := 402023, root := ~, start := 402009, stop := 402022 ), rec( 
                                                                          cont\
ent := ", ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "\"fdp\"", c\
ount := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", next := 402037, root :=\
 ~, start := 402025, stop := 402036 ), rec( content := ",\n          ", count \
:= [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "\"sfdp\"", count := [ 9, 1, 1\
, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, \
1, 19 ], mathmode := "Text", name := "C", next := 402062, root := ~, start := \
402049, stop := 402061 ), rec( content := ", and ", count := [ 9, 1, 1, 19 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "\"patchwork\"", count := [ 9, 1, 1, 19 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode \
:= "Text", name := "C", next := 402086, root := ~, start := 402068, stop := 40\
2085 ), rec( content := ". Please refer to the\n          GraphViz documentati\
on for details on these engines.\n          The default value for this option \
is ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := \
~ ), rec( attributes := rec(  ), content := [ rec( content := "\"dot\"", count\
 := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], coun\
t := [ 9, 1, 1, 19 ], mathmode := "Text", name := "C", next := 402230, root :=\
 ~, start := 402218, stop := 402229 ), rec( content := ", and it\n          mu\
st be specified in ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "P\
CDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := \
"opt.engine", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", \
root := ~ ) ], count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "A", next\
 := 402287, root := ~, start := 402270, stop := 402286 ), rec( content := ".\n\
        ", count := [ 9, 1, 1, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 9, 1, 1, 19 ], name := "Item", next := 402304, 
                                                                  root := ~, 
                                                                  start := 401\
809, stop := 402303 ), rec( attributes := rec(  ), content := [ rec( content :\
= "filetype", count := [ 9, 1, 1, 20 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 9, 1, 1, 20 ], name := "Mark", next := 402335, 
                                                                  root := ~, 
                                                                  start := 402\
314, stop := 402334 ), rec( attributes := rec(  ), content := [ rec( content :\
= "\n          this should be a string representing the type of file which\n  \
        ", count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "Splash", co\
unt := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                          coun\
t := [ 9, 1, 1, 21 ], mathmode := "Text", name := "C", next := 402444, root :=\
 ~, start := 402431, stop := 402443 ), rec( content := " should produce. For "
                                                                            , 
                                                                          coun\
t := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec( Only := "LaTeX" ), content := [ rec( content := "{\\LaTeX}", co\
unt := [ 9, 1, 1, 21 ], name := "PCDATA", root := ~ ) ], count := [ 9, 1, 1, 2\
1 ], mathmode := "Text", name := "Alt", next := 33, root := ~, start := 1, 
                                                                          stop\
 := 32 ), rec( attributes := rec( Not := "LaTeX" ), content := [ rec( content \
:= "LaTeX", count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA", ro\
ot := ~ ) ], count := [ 9, 1, 1, 21 ], name := "Alt", next := 61, root := ~, 
                                                                          star\
t := 33, stop := 60 ), rec( content := " files, this option is\n          igno\
red and the default value ", count := [ 9, 1, 1, 21 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "\"pdf\"", count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "C", 
                                                                          next\
 := 402547, root := ~, start := 402535, stop := 402546 ), rec( content := " is\
 used.\n        ", count := [ 9, 1, 1, 21 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 1, 1, 21 ], name := "Item", next := 402572, 
                                                                  root := ~, 
                                                                  start := 402\
344, stop := 402571 ) ], count := [ 9, 1, 1, 7 ], mathmode := "Text", 
                                                          name := "List", 
                                                          next := 402586, 
                                                          root := ~, 
                                                          start := 400131, 
                                                          stop := 402585 ), 
                                                      rec( 
                                                          content := "\n\n    \
  This function was written by Attila Egri-Nagy and Manuel Delgado with some\n\
      minor changes by J. D. Mitchell.", count := [ 9, 1, 1, 23 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 1, 24 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 402711, 
                                                          root := ~, 
                                                          start := 402707, 
                                                          stop := 402710 ), 
                                                      rec( 
                                                          content := "\n      \
", count := [ 9, 1, 1, 24 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> Splash(DotDigraph(RandomDigraph(4)));\n", count := [ 9, 1, 1, 25 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 1, 25 ], mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 402785, 
                                                          root := ~, 
                                                          start := 402718, 
                                                          stop := 402784 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 1, 1, 26 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 1, 1, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 402804, root := ~, 
                                                  start := 399337, 
                                                  stop := 402803 ) ], 
                                          count := [ 9, 1, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 402820, root := ~, 
                                          start := 399244, stop := 402819 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 9, 1, 1, 26 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DotDigraph" ), 
                                                  content := 0, 
                                                  count := [ 9, 1, 2, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 402884, root := ~, 
                                                  start := 402845, 
                                                  stop := 402883 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vert, e\
dge", Name := "DotColoredDigraph" ), content := 0, count := [ 9, 1, 2, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 402947, root := ~, 
                                                  start := 402889, 
                                                  stop := 402946 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DotVertexLabell\
edDigraph" ), content := 0, count := [ 9, 1, 2, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 403005, root := ~, 
                                                  start := 402952, 
                                                  stop := 403004 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vert", 
                                                      Name := "DotVertexColore\
dDigraph" ), content := 0, count := [ 9, 1, 2, 8 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 403068, root := ~, 
                                                  start := 403010, 
                                                  stop := 403067 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edge", 
                                                      Name := "DotEdgeColoredD\
igraph" ), content := 0, count := [ 9, 1, 2, 10 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 403129, root := ~, 
                                                  start := 403073, 
                                                  stop := 403128 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A string.\
", count := [ 9, 1, 2, 11 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 9, 1, 2, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 403162, root := ~, 
                                                  start := 403134, 
                                                  stop := 403161 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      "
                                                            , 
                                                          count := 
                                                            [ 9, 1, 2, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otDigraph", count := [ 9, 1, 2, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 403204, 
                                                          root := ~, 
                                                          start := 403187, 
                                                          stop := 403203 ), 
                                                      rec( 
                                                          content := " produce\
s a graphical representation of the digraph\n      ", count := [ 9, 1, 2, 11 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 2, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 403276, 
                                                          root := ~, 
                                                          start := 403262, 
                                                          stop := 403275 ), 
                                                      rec( 
                                                          content := ". Vertic\
es are displayed as circles, numbered consistently\n      with ", 
                                                          count := 
                                                            [ 9, 1, 2, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 2, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 403360, 
                                                          root := ~, 
                                                          start := 403346, 
                                                          stop := 403359 ), 
                                                      rec( 
                                                          content := ". Edges \
are displayed as arrowed lines between\n      vertices, with the arrowhead of \
each line pointing towards the range\n      of the edge.", 
                                                          count := 
                                                            [ 9, 1, 2, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 2, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 403504, 
                                                          root := ~, 
                                                          start := 403500, 
                                                          stop := 403503 ), 
                                                      rec( 
                                                          content := "\n\n    \
  ", count := [ 9, 1, 2, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otColoredDigraph", count := [ 9, 1, 2, 12 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 1, 2, 12 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 403536, 
                                                          root := ~, 
                                                          start := 403512, 
                                                          stop := 403535 ), 
                                                      rec( 
                                                          content := " differs\
 from ", count := [ 9, 1, 2, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otDigraph", count := [ 9, 1, 2, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 403567, 
                                                          root := ~, 
                                                          start := 403550, 
                                                          stop := 403566 ), 
                                                      rec( 
                                                          content := " only in\
\n      that the values in given in the two lists are used to color the vertic\
es and\n      edges of the graph when displayed. The list for vertex colours s\
hould be\n      a list of length equal to the number of vertices, containing s\
trings that\n      are accepted by the graphviz software, which is the one use\
d for graph\n      representation. The list for edge colours should be a list \
of lists\n      with the same shape of the outneighbours of the digraph that c\
ontains strings \n      that correspond to colours accepted by the graphviz so\
ftware. If the lists \n      are not the appropriate size, or have holes then \
the function will return\n      an error.", count := [ 9, 1, 2, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 2, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 404235, 
                                                          root := ~, 
                                                          start := 404231, 
                                                          stop := 404234 ), 
                                                      rec( 
                                                          content := "\n\n    \
  ", count := [ 9, 1, 2, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otVertexColoredDigraph", count := [ 9, 1, 2, 13 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 2, 13 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 404273, 
                                                          root := ~, 
                                                          start := 404243, 
                                                          stop := 404272 ), 
                                                      rec( 
                                                          content := " differs\
 from ", count := [ 9, 1, 2, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otDigraph", count := [ 9, 1, 2, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 404304, 
                                                          root := ~, 
                                                          start := 404287, 
                                                          stop := 404303 ), 
                                                      rec( 
                                                          content := " only in\
\n      that the values in given in the list are used to color the vertices\n \
     of the graph when displayed. The list for vertex colours should be\n     \
 a list of length equal to the number of vertices, containing strings that\n  \
    are accepted by the graphviz software, which is the one used for graph\n  \
    representation. If the list is not the appropriate size, or has holes \n  \
    then the function will return an error.", count := [ 9, 1, 2, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 2, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 404743, 
                                                          root := ~, 
                                                          start := 404739, 
                                                          stop := 404742 ), 
                                                      rec( 
                                                          content := "\n\n    \
  ", count := [ 9, 1, 2, 14 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otEdgeColoredDigraph", count := [ 9, 1, 2, 14 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 2, 14 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 404779, 
                                                          root := ~, 
                                                          start := 404751, 
                                                          stop := 404778 ), 
                                                      rec( 
                                                          content := " differs\
 from ", count := [ 9, 1, 2, 14 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otDigraph", count := [ 9, 1, 2, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 404810, 
                                                          root := ~, 
                                                          start := 404793, 
                                                          stop := 404809 ), 
                                                      rec( 
                                                          content := " only in\
\n      that the values in given in the list are used to color the vertices an\
d\n      edges of the graph when displayed. The list for edge colours should b\
e a list\n      of lists with the same shape of the outneighbours of the digra\
ph that contains\n      strings that correspond to colours accepted by the gra\
phviz software. If the \n      list is not the appropriate size, or has holes \
then the function will return\n      an error.", count := [ 9, 1, 2, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 2, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 405252, 
                                                          root := ~, 
                                                          start := 405248, 
                                                          stop := 405251 ), 
                                                      rec( 
                                                          content := "\n\n    \
  ", count := [ 9, 1, 2, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otVertexLabelledDigraph", count := [ 9, 1, 2, 15 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 2, 15 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 405291, 
                                                          root := ~, 
                                                          start := 405260, 
                                                          stop := 405290 ), 
                                                      rec( 
                                                          content := " differs\
 from ", count := [ 9, 1, 2, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otDigraph", count := [ 9, 1, 2, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 405322, 
                                                          root := ~, 
                                                          start := 405305, 
                                                          stop := 405321 ), 
                                                      rec( 
                                                          content := " only in\
\n      that the values in ", count := [ 9, 1, 2, 15 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 9, 1, 2, 15 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 405389, 
                                                          root := ~, 
                                                          start := 405356, 
                                                          stop := 405388 ), 
                                                      rec( 
                                                          content := " are use\
d to label\n      the vertices in the produced picture rather than the numbers\
 ", count := [ 9, 1, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 9, 1, 2, 15 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 1, 2, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 405483, 
                                                          root := ~, 
                                                          start := 405475, 
                                                          stop := 405482 ), 
                                                      rec( 
                                                          content := " to\n   \
   the number of vertices of the digraph. ", count := [ 9, 1, 2, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 2, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 405536, 
                                                          root := ~, 
                                                          start := 405532, 
                                                          stop := 405535 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The output is in ", count := [ 9, 1, 2, 16 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ot", count := [ 9, 1, 2, 16 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 405571, 
                                                          root := ~, 
                                                          start := 405561, 
                                                          stop := 405570 ), 
                                                      rec( 
                                                          content := " format \
(also known as ", count := [ 9, 1, 2, 16 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
raphViz", count := [ 9, 1, 2, 16 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 405609, 
                                                          root := ~, 
                                                          start := 405594, 
                                                          stop := 405608 ), 
                                                      rec( 
                                                          content := ")\n     \
 format. For details about this file format, and information about how to\n   \
   display or edit this format see ", count := [ 9, 1, 2, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttp://www.graphviz.org", count := [ 9, 1, 2, 16 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 2, 16 ], mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 405762, 
                                                          root := ~, 
                                                          start := 405728, 
                                                          stop := 405761 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 9, 1, 2, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 2, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 405768, 
                                                          root := ~, 
                                                          start := 405764, 
                                                          stop := 405767 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The string returned by ", count := [ 9, 1, 2, 17 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otDigraph", count := [ 9, 1, 2, 17 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 405816, 
                                                          root := ~, 
                                                          start := 405799, 
                                                          stop := 405815 ), 
                                                      rec( 
                                                          content := " or\n   \
   ", count := [ 9, 1, 2, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otVertexLabelledDigraph", count := [ 9, 1, 2, 17 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 2, 17 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 405857, 
                                                          root := ~, 
                                                          start := 405826, 
                                                          stop := 405856 ), 
                                                      rec( 
                                                          content := " can be \
written to a file using\n      the command ", count := [ 9, 1, 2, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "GAP\
Doc", Func := "FileString" ), content := 0, count := [ 9, 1, 2, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 405949, 
                                                          root := ~, 
                                                          start := 405907, 
                                                          stop := 405948 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 2, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 2, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 405954, 
                                                          root := ~, 
                                                          start := 405950, 
                                                          stop := 405953 ), 
                                                      rec( 
                                                          content := "\n      \
", count := [ 9, 1, 2, 18 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> adj := List([1 .. 4], x -> [1, 1, 1, 1]);\n[ [ 1, 1, 1, 1 ], [ 1, 1, 1, \
1 ], [ 1, 1, 1, 1 ], [ 1, 1, 1, 1 ] ]\ngap> adj[1][3] := 0;\n0\ngap> gr := Dig\
raphByAdjacencyMatrix(adj);\n<immutable digraph with 4 vertices, 15 edges>\nga\
p> D := CompleteDigraph(4);\n<immutable complete digraph with 4 vertices>\ngap\
> vertcolors := [];;\ngap> vertcolors[1] := \"blue\";; vertcolors[2] := \"red\
\";; \ngap> vertcolors[3] := \"green\";; vertcolors[4] := \"yellow\";;\ngap> e\
dgecolors := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [];;\ngap> edge\
colors[3] := [];; edgecolors[4] := [];; \ngap> edgecolors[1][2] := \"lightblue\
\";;\ngap> edgecolors[1][3] := \"pink\";;\ngap> edgecolors[1][4] := \"purple\"\
;;\ngap> edgecolors[2][1] := \"lightblue\";;\ngap> edgecolors[2][3] := \"pink\
\";; \ngap> edgecolors[2][4] := \"purple\";; \ngap> edgecolors[3][1] := \"ligh\
tblue\";; \ngap> edgecolors[3][2] := \"pink\";; \ngap> edgecolors[3][4] := \"p\
urple\";;\ngap> edgecolors[4][1] := \"lightblue\";; \ngap> edgecolors[4][2] :=\
 \"pink\";;\ngap> edgecolors[4][3] := \"purple\";;\ngap> Print(DotColoredDigra\
ph(D, vertcolors, edgecolors));\n//dot\ndigraph hgn{\nnode [shape=circle]\n1[c\
olor=blue, style=filled]\n2[color=red, style=filled]\n3[color=green, style=fil\
led]\n4[color=yellow, style=filled]\n1 -> 2[color=lightblue]\n1 -> 3[color=pin\
k]\n1 -> 4[color=purple]\n2 -> 1[color=lightblue]\n2 -> 3[color=pink]\n2 -> 4[\
color=purple]\n3 -> 1[color=lightblue]\n3 -> 2[color=pink]\n3 -> 4[color=purpl\
e]\n4 -> 1[color=lightblue]\n4 -> 2[color=pink]\n4 -> 3[color=purple]\n}\ngap>\
 D := EmptyDigraph(3);\n<immutable empty digraph with 3 vertices>\ngap> vertco\
lors := [];;\ngap> vertcolors[1] := \"blue\";; vertcolors[2] := \"red\";;\ngap\
> vertcolors[3] := \"green\";;\ngap> edgecolors := [];;\ngap> edgecolors[1] :=\
 [];; edgecolors[2] := [];; \ngap> edgecolors[3] := [];;\ngap> Print(DotColore\
dDigraph(D, vertcolors, edgecolors));\n//dot\ndigraph hgn{\nnode [shape=circle\
]\n1[color=blue, style=filled]\n2[color=red, style=filled]\n3[color=green, sty\
le=filled]\n}\ngap> D := Digraph([[2], [1, 3], [2]]);\n<immutable digraph with\
 3 vertices, 4 edges>\ngap> vertcolors := [];;\ngap> vertcolors[1] := \"blue\"\
;;\ngap> vertcolors[2] := \"pink\";;\ngap> vertcolors[3] := \"purple\";;\ngap>\
 edgecolors := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [];;\ngap> ed\
gecolors[3] := [];;\ngap> edgecolors[1][2] := \"green\";; edgecolors[2][1] := \
\"green\";;\ngap> edgecolors[2][3] := \"red\";; edgecolors[3][2] := \"red\";;\
\ngap> Print(DotSymmetricColoredDigraph(D, vertcolors, edgecolors));\n//dot\ng\
raph hgn{\nnode [shape=circle]\n\n1[color=blue, style=filled]\n2[color=pink, s\
tyle=filled]\n3[color=purple, style=filled]\n1 -- 2[color=green]\n2 -- 3[color\
=red]\n}\ngap> D := Digraph([[2, 3], [1, 3], [1]]);\n<immutable digraph with 3\
 vertices, 5 edges>\ngap> vertcolors := [];;\ngap> vertcolors[1] := \"blue\";;\
 vertcolors[2] := \"red\";;\ngap> vertcolors[3] := \"green\";;\ngap> edgecolor\
s := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [];;\ngap> edgecolors[3\
] := [];;\ngap> edgecolors[1][2] := \"orange\";; edgecolors[1][3] := \"yellow\
\";;\ngap> edgecolors[2][1] := \"orange\";; edgecolors[2][3] := \"pink\";;\nga\
p> edgecolors[3][1] := \"yellow\";;\ngap> Print(DotColoredDigraph(D, vertcolor\
s, edgecolors));;\n//dot\ndigraph hgn{\nnode [shape=circle]\n1[color=blue, sty\
le=filled]\n2[color=red, style=filled]\n3[color=green, style=filled]\n1 -> 2[c\
olor=orange]\n1 -> 3[color=yellow]\n2 -> 1[color=orange]\n2 -> 3[color=pink]\n\
3 -> 1[color=yellow]\n}\ngap> D := Digraph(IsMutableDigraph, [[2, 3], [1, 3], \
[1]]);\n<mutable digraph with 3 vertices, 5 edges>\ngap> vertcolors := [];;\ng\
ap> vertcolors[1] := \"blue\";; vertcolors[2] := \"red\";;\ngap> vertcolors[3]\
 := \"green\";;\ngap> edgecolors := [];;\ngap> edgecolors[1] := [];; edgecolor\
s[2] := [];;\ngap> edgecolors[3] := [];;\ngap> edgecolors[1][2] := \"orange\";\
; edgecolors[1][3] := \"yellow\";;\ngap> edgecolors[2][1] := \"orange\";; edge\
colors[2][3] := \"pink\";;\ngap> edgecolors[3][1] := \"yellow\";;\ngap> Print(\
DotColoredDigraph(D, vertcolors, edgecolors));;\n//dot\ndigraph hgn{\nnode [sh\
ape=circle]\n1[color=blue, style=filled]\n2[color=red, style=filled]\n3[color=\
green, style=filled]\n1 -> 2[color=orange]\n1 -> 3[color=yellow]\n2 -> 1[color\
=orange]\n2 -> 3[color=pink]\n3 -> 1[color=yellow]\n}\ngap> D;\n<mutable digra\
ph with 3 vertices, 5 edges>\ngap> DotSymmetricDigraph(gr2){[12 .. 70]};\n\" h\
gn{\\nnode [shape=circle]\\n\\n1\\n2\\n3\\n4\\n1 -- 2\\n2 -- 3\\n3 -- 3\\n3 -\
\"\ngap> DotSymmetricDigraph(gr1);\nError, the argument <D> must be a symmetri\
c digraph,\ngap> D := CompleteDigraph(4);\n<immutable complete digraph with 4 \
vertices>\ngap> vertcolors := [];;\ngap> vertcolors[1] := \"blue\";; vertcolor\
s[2] := \"red\";; \ngap> vertcolors[3] := \"green\";; vertcolors[4] := \"yello\
w\";;\ngap> Print(DotVertexColoredDigraph(D, vertcolors));\n//dot\ndigraph hgn\
{\nnode [shape=circle]\n1[color=blue, style=filled]\n2[color=red, style=filled\
]\n3[color=green, style=filled]\n4[color=yellow, style=filled]\n1 -> 2\n1 -> 3\
\n1 -> 4\n2 -> 1\n2 -> 3\n2 -> 4\n3 -> 1\n3 -> 2\n3 -> 4\n4 -> 1\n4 -> 2\n4 ->\
 3\n}\ngap> D := CompleteDigraph(4);\n<immutable complete digraph with 4 verti\
ces>\ngap> edgecolors := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [];\
;\ngap> edgecolors[3] := [];; edgecolors[4] := [];; \ngap> edgecolors[1][2] :=\
 \"lightblue\";;\ngap> edgecolors[1][3] := \"pink\";;\ngap> edgecolors[1][4] :\
= \"purple\";;\ngap> edgecolors[2][1] := \"lightblue\";;\ngap> edgecolors[2][3\
] := \"pink\";; \ngap> edgecolors[2][4] := \"purple\";; \ngap> edgecolors[3][1\
] := \"lightblue\";; \ngap> edgecolors[3][2] := \"pink\";; \ngap> edgecolors[3\
][4] := \"purple\";;\ngap> edgecolors[4][1] := \"lightblue\";; \ngap> edgecolo\
rs[4][2] := \"pink\";;\ngap> edgecolors[4][3] := \"purple\";;\ngap> Print(DotE\
dgeColoredDigraph(D, edgecolors));\n//dot\ndigraph hgn{\nnode [shape=circle]\n\
1\n2\n3\n4\n1 -> 2[color=lightblue]\n1 -> 3[color=pink]\n1 -> 4[color=purple]\
\n2 -> 1[color=lightblue]\n2 -> 3[color=pink]\n2 -> 4[color=purple]\n3 -> 1[co\
lor=lightblue]\n3 -> 2[color=pink]\n3 -> 4[color=purple]\n4 -> 1[color=lightbl\
ue]\n4 -> 2[color=pink]\n4 -> 3[color=purple]\n}\ngap> FileString(\"dot/k4.dot\
\", DotDigraph(gr));\n154", count := [ 9, 1, 2, 19 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 2, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 411909, 
                                                          root := ~, 
                                                          start := 405961, 
                                                          stop := 411908 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 1, 2, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 1, 2, 11 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 411928, root := ~, 
                                                  start := 403167, 
                                                  stop := 411927 ) ], 
                                          count := [ 9, 1, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 411944, root := ~, 
                                          start := 402828, stop := 411943 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 9, 1, 2, 20 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DotSymmetricDig\
raph" ), content := 0, count := [ 9, 1, 3, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 412017, root := ~, 
                                                  start := 411969, 
                                                  stop := 412016 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vert, e\
dge", Name := "DotSymmetricColoredDigraph" ), content := 0, 
                                                  count := [ 9, 1, 3, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 412089, root := ~, 
                                                  start := 412022, 
                                                  stop := 412088 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, vert", 
                                                      Name := "DotSymmetricVer\
texColoredDigraph" ), content := 0, count := [ 9, 1, 3, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 412161, root := ~, 
                                                  start := 412094, 
                                                  stop := 412160 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, edge", 
                                                      Name := "DotSymmetricEdg\
eColoredDigraph" ), content := 0, count := [ 9, 1, 3, 8 ], mathmode := "Text",
                                                  name := "Oper", 
                                                  next := 412231, root := ~, 
                                                  start := 412166, 
                                                  stop := 412230 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A string.\
", count := [ 9, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 9, 1, 3, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 412264, root := ~, 
                                                  start := 412236, 
                                                  stop := 412263 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      T\
his function produces a graphical representation of the symmetric\n      digra\
ph ", count := [ 9, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 412384, 
                                                          root := ~, 
                                                          start := 412370, 
                                                          stop := 412383 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 9, 1, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otSymmetricDigraph", count := [ 9, 1, 3, 9 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 3, 9 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 412412, 
                                                          root := ~, 
                                                          start := 412386, 
                                                          stop := 412411 ), 
                                                      rec( 
                                                          content := " will re\
turn an\n      error if ", count := [ 9, 1, 3, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 412457, 
                                                          root := ~, 
                                                          start := 412443, 
                                                          stop := 412456 ), 
                                                      rec( 
                                                          content := " is not \
a symmetric digraph. See\n      ", count := [ 9, 1, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsSymme\
tricDigraph" ), content := 0, count := [ 9, 1, 3, 9 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 412528, 
                                                          root := ~, 
                                                          start := 412496, 
                                                          stop := 412527 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 412533, 
                                                          root := ~, 
                                                          start := 412529, 
                                                          stop := 412532 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The function ", count := [ 9, 1, 3, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otSymmetricColoredDigraph", count := [ 9, 1, 3, 10 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 3, 10 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 412587, 
                                                          root := ~, 
                                                          start := 412554, 
                                                          stop := 412586 ), 
                                                      rec( 
                                                          content := " differs\
 from ", count := [ 9, 1, 3, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otDigraph", count := [ 9, 1, 3, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 412618, 
                                                          root := ~, 
                                                          start := 412601, 
                                                          stop := 412617 ), 
                                                      rec( 
                                                          content := "\n      \
only in that the values given in the two lists are used to color the vertices\
\n      and edges of the graph when displayed. The list for vertex colours sho\
uld be\n      a list of length equal to the number of vertices, containing str\
ings that\n      are accepted by the graphviz software, which is the one used \
for graph\n      representation.  The list for edge colours should be a list o\
f lists\n      with the same shape of the outneighbours of the digraph that co\
ntains strings \n      that correspond to colours accepted by the graphviz sof\
tware.\n      If the list is not the appropriate size, or has holes then the f\
unction\n      will return an error.  ", count := [ 9, 1, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 3, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 413282, 
                                                          root := ~, 
                                                          start := 413278, 
                                                          stop := 413281 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The function ", count := [ 9, 1, 3, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otSymmetricVertexColoredDigraph", count := [ 9, 1, 3, 11 ], mathmode := "Text"
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 3, 11 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 413342, 
                                                          root := ~, 
                                                          start := 413303, 
                                                          stop := 413341 ), 
                                                      rec( 
                                                          content := " differs\
 from ", count := [ 9, 1, 3, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otDigraph", count := [ 9, 1, 3, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 3, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 413373, 
                                                          root := ~, 
                                                          start := 413356, 
                                                          stop := 413372 ), 
                                                      rec( 
                                                          content := "\n      \
only in that the values in given in the list is used to color the vertices\n  \
    of the graph when displayed. The list for vertex colours should be\n      \
a list of length equal to the number of vertices, containing strings that\n   \
   are accepted by the graphviz software, which is the one used for graph\n   \
   representation. If the list is not the appropriate size, or has holes \n   \
   then the function will return an error.  ", count := [ 9, 1, 3, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 3, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 413813, 
                                                          root := ~, 
                                                          start := 413809, 
                                                          stop := 413812 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The function ", count := [ 9, 1, 3, 12 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otSymmetricEdgeColoredDigraph", count := [ 9, 1, 3, 12 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 3, 12 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 413871, 
                                                          root := ~, 
                                                          start := 413834, 
                                                          stop := 413870 ), 
                                                      rec( 
                                                          content := " differs\
 from ", count := [ 9, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otDigraph", count := [ 9, 1, 3, 12 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 3, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 413902, 
                                                          root := ~, 
                                                          start := 413885, 
                                                          stop := 413901 ), 
                                                      rec( 
                                                          content := "\n      \
only in that the values given in the list are used to color the edges\n      o\
f the graph when displayed. The list for edge colours should be\n      a list \
of lists with the same shape of the outneighbours, containing strings that\n  \
    are accepted by the graphviz software, which is the one used for graph\n  \
    representation. If the list is not the appropriate size, or has holes \n  \
    then the function will return an error.  ", count := [ 9, 1, 3, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 414343, 
                                                          root := ~, 
                                                          start := 414339, 
                                                          stop := 414342 ), 
                                                      rec( 
                                                          content := "\n\n    \
  Vertices are displayed as circles, numbered consistently with\n      ", 
                                                          count := 
                                                            [ 9, 1, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 3, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 414433, 
                                                          root := ~, 
                                                          start := 414419, 
                                                          stop := 414432 ), 
                                                      rec( 
                                                          content := ". Since \
", count := [ 9, 1, 3, 13 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 3, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 414455, 
                                                          root := ~, 
                                                          start := 414441, 
                                                          stop := 414454 ), 
                                                      rec( 
                                                          content := " is symm\
etric, for every non-loop\n      edge there is a complementary edge with oppos\
ite source and range.\n      ", count := [ 9, 1, 3, 13 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otSymmetricDigraph", count := [ 9, 1, 3, 13 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 3, 13 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 414594, 
                                                          root := ~, 
                                                          start := 414568, 
                                                          stop := 414593 ), 
                                                      rec( 
                                                          content := " display\
s each pair of complementary edges\n      as a single line between the relevan\
t vertices, with no arrowhead.", count := [ 9, 1, 3, 13 ], mathmode := "Text",
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 414713, 
                                                          root := ~, 
                                                          start := 414709, 
                                                          stop := 414712 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The output is in ", count := [ 9, 1, 3, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ot", count := [ 9, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 414748, 
                                                          root := ~, 
                                                          start := 414738, 
                                                          stop := 414747 ), 
                                                      rec( 
                                                          content := " format \
(also known as ", count := [ 9, 1, 3, 14 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
raphViz", count := [ 9, 1, 3, 14 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 414786, 
                                                          root := ~, 
                                                          start := 414771, 
                                                          stop := 414785 ), 
                                                      rec( 
                                                          content := ")\n     \
 format. For details about this file format, and information about how\n      \
to display or edit this format see\n      ", count := [ 9, 1, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttp://www.graphviz.org", count := [ 9, 1, 3, 14 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 3, 14 ], mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 414945, 
                                                          root := ~, 
                                                          start := 414911, 
                                                          stop := 414944 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 9, 1, 3, 14 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 414951, 
                                                          root := ~, 
                                                          start := 414947, 
                                                          stop := 414950 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The string returned by ", count := [ 9, 1, 3, 15 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otSymmetricDigraph", count := [ 9, 1, 3, 15 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 3, 15 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 415008, 
                                                          root := ~, 
                                                          start := 414982, 
                                                          stop := 415007 ), 
                                                      rec( 
                                                          content := " can be \
written to a\n      file using the command ", count := [ 9, 1, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "GAP\
Doc", Func := "FileString" ), content := 0, count := [ 9, 1, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 415100, 
                                                          root := ~, 
                                                          start := 415058, 
                                                          stop := 415099 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 3, 15 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 3, 16 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 415105, 
                                                          root := ~, 
                                                          start := 415101, 
                                                          stop := 415104 ), 
                                                      rec( 
                                                          content := "\n\n    \
  ", count := [ 9, 1, 3, 16 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> star := Digraph([[2, 2, 3, 4], [1, 1], [1], [1, 4]]);\n<immutable multid\
igraph with 4 vertices, 9 edges>\ngap> IsSymmetricDigraph(star);\ntrue\ngap> F\
ileString(\"dot/star.dot\", DotSymmetricDigraph(gr));\ngap> D := Digraph([[2],\
 [1, 3], [2]]);\n<immutable digraph with 3 vertices, 4 edges>\ngap> vertcolors\
 := [];;\ngap> vertcolors[1] := \"blue\";;\ngap> vertcolors[2] := \"pink\";;\n\
gap> vertcolors[3] := \"purple\";;\ngap> edgecolors := [];;\ngap> edgecolors[1\
] := [];; edgecolors[2] := [];;\ngap> edgecolors[3] := [];;\ngap> edgecolors[1\
][2] := \"green\";; edgecolors[2][1] := \"green\";;\ngap> edgecolors[2][3] := \
\"red\";; edgecolors[3][2] := \"red\";;\ngap> Print(DotSymmetricColoredDigraph\
(D, vertcolors, edgecolors));\n//dot\ngraph hgn{\nnode [shape=circle]\n\n1[col\
or=blue, style=filled]\n2[color=pink, style=filled]\n3[color=purple, style=fil\
led]\n1 -- 2[color=green]\n2 -- 3[color=red]\n}\ngap> D := Digraph([[2], [1, 3\
], [2]]);\n<immutable digraph with 3 vertices, 4 edges>\ngap> vertcolors := []\
;;\ngap> vertcolors[1] := \"blue\";;\ngap> vertcolors[2] := \"pink\";;\ngap> v\
ertcolors[3] := \"purple\";;\ngap> Print(DotSymmetricVertexColoredDigraph(D, v\
ertcolors));\n//dot\ngraph hgn{\nnode [shape=circle]\n\n1[color=blue, style=fi\
lled]\n2[color=pink, style=filled]\n3[color=purple, style=filled]\n1 -- 2\n2 -\
- 3\n}\ngap> D := Digraph([[2], [1, 3], [2]]);\n<immutable digraph with 3 vert\
ices, 4 edges>\ngap> edgecolors := [];;\ngap> edgecolors[1] := [];; edgecolors\
[2] := [];;\ngap> edgecolors[3] := [];;\ngap> edgecolors[1][2] := \"green\";; \
edgecolors[2][1] := \"green\";;\ngap> edgecolors[2][3] := \"red\";; edgecolors\
[3][2] := \"red\";;\ngap> Print(DotSymmetricEdgeColoredDigraph(D, edgecolors))\
;\n//dot\ngraph hgn{\nnode [shape=circle]\n\n1\n2\n3\n1 -- 2[color=green]\n2 -\
- 3[color=red]\n}\n83", count := [ 9, 1, 3, 17 ], name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 1, 3, 17 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 416859, 
                                                          root := ~, 
                                                          start := 415113, 
                                                          stop := 416858 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 1, 3, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 1, 3, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 416878, root := ~, 
                                                  start := 412269, 
                                                  stop := 416877 ) ], 
                                          count := [ 9, 1, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 416894, root := ~, 
                                          start := 411952, stop := 416893 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 9, 1, 3, 18 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DotPartialOrder\
Digraph" ), content := 0, count := [ 9, 1, 4, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 416970, root := ~, 
                                                  start := 416919, 
                                                  stop := 416969 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A string.\
", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 9, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 417003, root := ~, 
                                                  start := 416975, 
                                                  stop := 417002 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      T\
his function produces a graphical representation of a partial order\n      dig\
raph ", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 417125, 
                                                          root := ~, 
                                                          start := 417111, 
                                                          stop := 417124 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 9, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otPartialOrderDigraph", count := [ 9, 1, 4, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 4, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 417156, 
                                                          root := ~, 
                                                          start := 417127, 
                                                          stop := 417155 ), 
                                                      rec( 
                                                          content := " will re\
turn an error\n      if ", count := [ 9, 1, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 417201, 
                                                          root := ~, 
                                                          start := 417187, 
                                                          stop := 417200 ), 
                                                      rec( 
                                                          content := " is not \
a partial order digraph. See ", count := [ 9, 1, 4, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsParti\
alOrderDigraph" ), content := 0, count := [ 9, 1, 4, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 417281, 
                                                          root := ~, 
                                                          start := 417238, 
                                                          stop := 417280 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 417286, 
                                                          root := ~, 
                                                          start := 417282, 
                                                          stop := 417285 ), 
                                                      rec( 
                                                          content := "\n\n    \
  Since ", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 417314, 
                                                          root := ~, 
                                                          start := 417300, 
                                                          stop := 417313 ), 
                                                      rec( 
                                                          content := " is a pa\
rtial order, it is both reflexive and\n      transitive. The output of ", 
                                                          count := 
                                                            [ 9, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otPartialOrderDigraph", count := [ 9, 1, 4, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 4, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 417421, 
                                                          root := ~, 
                                                          start := 417392, 
                                                          stop := 417420 ), 
                                                      rec( 
                                                          content := " is the\\
n      ", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "DotDigr\
aph" ), content := 0, count := [ 9, 1, 4, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 417459, 
                                                          root := ~, 
                                                          start := 417435, 
                                                          stop := 417458 ), 
                                                      rec( 
                                                          content := " of the\\
n      ", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
ReflexiveTransitiveReduction" ), content := 0, count := [ 9, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 417522, 
                                                          root := ~, 
                                                          start := 417473, 
                                                          stop := 417521 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 9, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 417540, 
                                                          root := ~, 
                                                          start := 417526, 
                                                          stop := 417539 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 417545, 
                                                          root := ~, 
                                                          start := 417541, 
                                                          stop := 417544 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The output is in ", count := [ 9, 1, 4, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ot", count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 417580, 
                                                          root := ~, 
                                                          start := 417570, 
                                                          stop := 417579 ), 
                                                      rec( 
                                                          content := " format \
(also known as ", count := [ 9, 1, 4, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
raphViz", count := [ 9, 1, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 417618, 
                                                          root := ~, 
                                                          start := 417603, 
                                                          stop := 417617 ), 
                                                      rec( 
                                                          content := ")\n     \
 format. For details about this file format, and information about how\n      \
to display or edit this format see\n      ", count := [ 9, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttp://www.graphviz.org", count := [ 9, 1, 4, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 4, 5 ], mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 417777, 
                                                          root := ~, 
                                                          start := 417743, 
                                                          stop := 417776 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 9, 1, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 417783, 
                                                          root := ~, 
                                                          start := 417779, 
                                                          stop := 417782 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The string returned by ", count := [ 9, 1, 4, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otPartialOrderDigraph", count := [ 9, 1, 4, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 4, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 417843, 
                                                          root := ~, 
                                                          start := 417814, 
                                                          stop := 417842 ), 
                                                      rec( 
                                                          content := " can be \
written to a\n      file using the command ", count := [ 9, 1, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "GAP\
Doc", Func := "FileString" ), content := 0, count := [ 9, 1, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 417935, 
                                                          root := ~, 
                                                          start := 417893, 
                                                          stop := 417934 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 417940, 
                                                          root := ~, 
                                                          start := 417936, 
                                                          stop := 417939 ), 
                                                      rec( 
                                                          content := "\n\n    \
  ", count := [ 9, 1, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> poset := Digraph([[1, 4], [2], [2, 3, 4], [4]);\ngap> IsPartialOrderDigr\
aph(gr);\ntrue\ngap> FileString(\"dot/poset.dot\", DotPartialOrderDigraph(gr))\
;\n83", count := [ 9, 1, 4, 8 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 9, 1, 4, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 418126, 
                                                          root := ~, 
                                                          start := 417948, 
                                                          stop := 418125 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 1, 4, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 1, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 418145, root := ~, 
                                                  start := 417008, 
                                                  stop := 418144 ) ], 
                                          count := [ 9, 1, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 418161, root := ~, 
                                          start := 416902, stop := 418160 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 9, 1, 4, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DotPreorderDigr\
aph" ), content := 0, count := [ 9, 1, 5, 2 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 418233, root := ~, 
                                                  start := 418186, 
                                                  stop := 418232 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DotQuasiorderDi\
graph" ), content := 0, count := [ 9, 1, 5, 4 ], mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 418287, root := ~, 
                                                  start := 418238, 
                                                  stop := 418286 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A string.\
", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 9, 1, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 418320, root := ~, 
                                                  start := 418292, 
                                                  stop := 418319 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      T\
his function produces a graphical representation of a preorder\n      digraph \
", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 418437, 
                                                          root := ~, 
                                                          start := 418423, 
                                                          stop := 418436 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 9, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otPreorderDigraph", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "C", 
                                                          next := 418464, 
                                                          root := ~, 
                                                          start := 418439, 
                                                          stop := 418463 ), 
                                                      rec( 
                                                          content := " will re\
turn an error\n      if ", count := [ 9, 1, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 418509, 
                                                          root := ~, 
                                                          start := 418495, 
                                                          stop := 418508 ), 
                                                      rec( 
                                                          content := " is not \
a preorder digraph. See ", count := [ 9, 1, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsPreor\
derDigraph" ), content := 0, count := [ 9, 1, 5, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 418580, 
                                                          root := ~, 
                                                          start := 418541, 
                                                          stop := 418579 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 418585, 
                                                          root := ~, 
                                                          start := 418581, 
                                                          stop := 418584 ), 
                                                      rec( 
                                                          content := "\n\n    \
  A preorder digraph is reflexive and transitive but in general it is\n      n\
ot anti-symmetric and may have strongly connected components\n      containing\
 more than one vertex. The ", count := [ 9, 1, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Quotien\
tDigraph" ), content := 0, count := [ 9, 1, 5, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 418801, 
                                                          root := ~, 
                                                          start := 418772, 
                                                          stop := 418800 ), 
                                                      rec( 
                                                          content := "\n      \
", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "Q\
", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 418816, 
                                                          root := ~, 
                                                          start := 418808, 
                                                          stop := 418815 ), 
                                                      rec( 
                                                          content := " obtaine\
d by forming the quotient of ", count := [ 9, 1, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 418867, 
                                                          root := ~, 
                                                          start := 418853, 
                                                          stop := 418866 ), 
                                                      rec( 
                                                          content := " by the\\
n      partition of its vertices into the strongly connected components\n     \
 satisfies ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsParti\
alOrderDigraph" ), content := 0, count := [ 9, 1, 5, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 418997, 
                                                          root := ~, 
                                                          start := 418962, 
                                                          stop := 418996 ), 
                                                      rec( 
                                                          content := ". Thus e\
very vertex of\n      ", count := [ 9, 1, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "Q\
", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 419034, 
                                                          root := ~, 
                                                          start := 419026, 
                                                          stop := 419033 ), 
                                                      rec( 
                                                          content := " corresp\
onds to a strongly connected component of ", count := [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 419098, 
                                                          root := ~, 
                                                          start := 419084, 
                                                          stop := 419097 ), 
                                                      rec( 
                                                          content := ".\n     \
 The output of ", count := [ 9, 1, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otPreorderDigraph", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "C", 
                                                          next := 419145, 
                                                          root := ~, 
                                                          start := 419120, 
                                                          stop := 419144 ), 
                                                      rec( 
                                                          content := " display\
s the \n      ", count := [ 9, 1, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
ReflexiveTransitiveReduction" ), content := 0, count := [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 419215, 
                                                          root := ~, 
                                                          start := 419166, 
                                                          stop := 419214 ), 
                                                      rec( content := " of ", 
                                                          count := 
                                                            [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "Q\
", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 419227, 
                                                          root := ~, 
                                                          start := 419219, 
                                                          stop := 419226 ), 
                                                      rec( 
                                                          content := " with\n \
     vertices displayed as rounded rectangles labelled by all of the vertices\
\n      of ", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 419335, 
                                                          root := ~, 
                                                          start := 419321, 
                                                          stop := 419334 ), 
                                                      rec( 
                                                          content := " in the \
corresponding strongly connected component. ", count := [ 9, 1, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 419391, 
                                                          root := ~, 
                                                          start := 419387, 
                                                          stop := 419390 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The output is in ", count := [ 9, 1, 5, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ot", count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 1, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 419426, 
                                                          root := ~, 
                                                          start := 419416, 
                                                          stop := 419425 ), 
                                                      rec( 
                                                          content := " format \
(also known as ", count := [ 9, 1, 5, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
raphViz", count := [ 9, 1, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 419464, 
                                                          root := ~, 
                                                          start := 419449, 
                                                          stop := 419463 ), 
                                                      rec( 
                                                          content := ")\n     \
 format. For details about this file format, and information about how\n      \
to display or edit this format see\n      ", count := [ 9, 1, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttp://www.graphviz.org", count := [ 9, 1, 5, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 5, 7 ], mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 419623, 
                                                          root := ~, 
                                                          start := 419589, 
                                                          stop := 419622 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 9, 1, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 419629, 
                                                          root := ~, 
                                                          start := 419625, 
                                                          stop := 419628 ), 
                                                      rec( 
                                                          content := "\n\n    \
  The string returned by ", count := [ 9, 1, 5, 8 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otPreorderDigraph", count := [ 9, 1, 5, 8 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 1, 5, 8 ], mathmode := "Text", name := "C", 
                                                          next := 419685, 
                                                          root := ~, 
                                                          start := 419660, 
                                                          stop := 419684 ), 
                                                      rec( 
                                                          content := " can be \
written to a\n      file using the command ", count := [ 9, 1, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "GAP\
Doc", Func := "FileString" ), content := 0, count := [ 9, 1, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 419777, 
                                                          root := ~, 
                                                          start := 419735, 
                                                          stop := 419776 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 1, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 5, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 419782, 
                                                          root := ~, 
                                                          start := 419778, 
                                                          stop := 419781 ), 
                                                      rec( 
                                                          content := "\n\n    \
  ", count := [ 9, 1, 5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> preset := Digraph([[1, 2, 4, 5], [1, 2, 4, 5], [3, 4], [4], [1, 2, 4, 5]\
);\ngap> IsPreorderDigraph(gr);\ntrue\ngap> FileString(\"dot/preset.dot\", Dot\
ProrderDigraph(gr));\n83", count := [ 9, 1, 5, 10 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 5, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 419987, 
                                                          root := ~, 
                                                          start := 419790, 
                                                          stop := 419986 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 1, 5, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 1, 5, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 420006, root := ~, 
                                                  start := 418325, 
                                                  stop := 420005 ) ], 
                                          count := [ 9, 1, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 420022, root := ~, 
                                          start := 418169, stop := 420021 ), 
                                      rec( content := "\n\n      ", 
                                          count := [ 9, 1, 5, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "digraph, verts [\
, colour1, colour2]", Name := "DotHighlightedDigraph" ), content := 0, 
                                                  count := [ 9, 1, 6, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 420125, root := ~, 
                                                  start := 420047, 
                                                  stop := 420124 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A string.\
", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 9, 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 420158, root := ~, 
                                                  start := 420130, 
                                                  stop := 420157 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n      "
                                                            , 
                                                          count := 
                                                            [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otHighlightedDigraph", count := [ 9, 1, 6, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 420211, 
                                                          root := ~, 
                                                          start := 420183, 
                                                          stop := 420210 ), 
                                                      rec( 
                                                          content := " produce\
s a graphical represenation of the\n      digraph ", count := [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 420282, 
                                                          root := ~, 
                                                          start := 420268, 
                                                          stop := 420281 ), 
                                                      rec( 
                                                          content := ", where \
the vertices in the list ", count := [ 9, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
erts", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 420327, 
                                                          root := ~, 
                                                          start := 420315, 
                                                          stop := 420326 ), 
                                                      rec( 
                                                          content := ", and\n \
     edges between them, are drawn with colour ", count := [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olour1", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 420395, 
                                                          root := ~, 
                                                          start := 420381, 
                                                          stop := 420394 ), 
                                                      rec( 
                                                          content := " and all\
 other\n      vertices and edges in ", count := [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 420452, 
                                                          root := ~, 
                                                          start := 420438, 
                                                          stop := 420451 ), 
                                                      rec( 
                                                          content := " are dra\
wn with colour ", count := [ 9, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olour2", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 420489, 
                                                          root := ~, 
                                                          start := 420475, 
                                                          stop := 420488 ), 
                                                      rec( 
                                                          content := ".\n     \
 If ", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olour1", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 420514, 
                                                          root := ~, 
                                                          start := 420500, 
                                                          stop := 420513 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olour2", count := [ 9, 1, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 420533, 
                                                          root := ~, 
                                                          start := 420519, 
                                                          stop := 420532 ), 
                                                      rec( 
                                                          content := " are not\
 given then\n      ", count := [ 9, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otHighlightedDigraph", count := [ 9, 1, 6, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 420587, 
                                                          root := ~, 
                                                          start := 420559, 
                                                          stop := 420586 ), 
                                                      rec( 
                                                          content := " uses bl\
ack and grey respectively. ", count := [ 9, 1, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 420626, 
                                                          root := ~, 
                                                          start := 420622, 
                                                          stop := 420625 ), 
                                                      rec( 
                                                          content := "\n\n    \
  Note that ", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
otHighlightedDigraph", count := [ 9, 1, 6, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 6, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 420672, 
                                                          root := ~, 
                                                          start := 420644, 
                                                          stop := 420671 ), 
                                                      rec( 
                                                          content := " does no\
t validate the colours\n      ", count := [ 9, 1, 6, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olour1", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 420723, 
                                                          root := ~, 
                                                          start := 420709, 
                                                          stop := 420722 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 9, 1, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
olour2", count := [ 9, 1, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 1, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 420742, 
                                                          root := ~, 
                                                          start := 420728, 
                                                          stop := 420741 ), 
                                                      rec( 
                                                          content := " - consu\
lt the GraphViz documentation to\n      see what is available.\n\n      See ",
                                                          count := 
                                                            [ 9, 1, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "DotDigr\
aph" ), content := 0, count := [ 9, 1, 6, 4 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 420847, 
                                                          root := ~, 
                                                          start := 420823, 
                                                          stop := 420846 ), 
                                                      rec( 
                                                          content := " for mor\
e details on the output.", count := [ 9, 1, 6, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 1, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 420883, 
                                                          root := ~, 
                                                          start := 420879, 
                                                          stop := 420882 ), 
                                                      rec( 
                                                          content := "\n\n    \
  ", count := [ 9, 1, 6, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> digraph := Digraph([[2, 3], [2], [1, 3]]);\n<digraph with 3 vertices, 5 \
edges>\ngap> FileString(\"dot/my_digraph.dot\",\n> DotHighlightedDigraph(digra\
ph, [1, 2], \"red\", \"black\"));\n264", count := [ 9, 1, 6, 6 ], name := "PCD\
ATA", root := ~ ) ], count := [ 9, 1, 6, 6 ], mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 421098, 
                                                          root := ~, 
                                                          start := 420891, 
                                                          stop := 421097 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 1, 6, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 1, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 421117, root := ~, 
                                                  start := 420163, 
                                                  stop := 421116 ) ], 
                                          count := [ 9, 1, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 421133, root := ~, 
                                          start := 420030, stop := 421132 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 9, 1, 6, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 9, 1, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 421147, 
                                  root := ~, start := 399188, stop := 421146 )
                                , 
                              rec( content := "\n\n  ", 
                                  count := [ 9, 1, 6, 7 ], mathmode := "Text",
                                  name := "PCDATA", root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "Reading and writi\
ng digraphs to a file", count := [ 9, 2, 0, 2 ], mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 9, 2, 0, 2 ],
                                          mathmode := "Text", 
                                          name := "Heading", next := 421217, 
                                          root := ~, start := 421160, 
                                          stop := 421216 ), 
                                      rec( 
                                          content := "\n    This section descr\
ibes different ways to store and read graphs\n    from a file in the ", 
                                          count := [ 9, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( content := "Digraphs", 
                                                  count := [ 9, 2, 0, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "PCDATA", root := ~ 
                                                 ) ], count := [ 9, 2, 0, 3 ],
                                          mathmode := "Text", 
                                          name := "Package", next := 28, 
                                          root := ~, start := 1, stop := 27 ),
                                      rec( content := " package.\n    ", 
                                          count := [ 9, 2, 0, 3 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " Graph6 "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 0, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 0, 4 ], 
                                                  name := "Mark", 
                                                  next := 421366, root := ~, 
                                                  start := 421345, 
                                                  stop := 421365 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n\t", 
                                                          count := 
                                                            [ 9, 2, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
Graph6 ", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 421396, 
                                                          root := ~, 
                                                          start := 421381, 
                                                          stop := 421395 ), 
                                                      rec( 
                                                          content := " is a gr\
aph data format for storing undirected graphs\n\twith no multiple edges nor lo\
ops of size up to ", count := [ 9, 2, 0, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
2^{36} - 1 ", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 421517, 
                                                          root := ~, 
                                                          start := 421498, 
                                                          stop := 421516 ), 
                                                      rec( 
                                                          content := " in\n\tp\
rintable chracters. The format consists of two parts. The first part\n\tuses o\
ne to eight bytes to store the number of vertices. And the second\n\tpart is t\
he upper half of the adjacency matrix converted into ASCII\n\tcharacters. For \
a more detail description see ", count := [ 9, 2, 0, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Text := "Graph6"\
 ), content := [ rec( content := "\n\thttp://cs.anu.edu.au/~bdm/data/formats.t\
xt", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 421850, 
                                                          root := ~, 
                                                          start := 421781, 
                                                          stop := 421849 ), 
                                                      rec( 
                                                          content := ".\n     \
 ", count := [ 9, 2, 0, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 9, 2, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 421865, root := ~, 
                                                  start := 421373, 
                                                  stop := 421864 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " Sparse6 \
", count := [ 9, 2, 0, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 9, 2, 0, 6 ], 
                                                  name := "Mark", 
                                                  next := 421895, root := ~, 
                                                  start := 421873, 
                                                  stop := 421894 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n\t", 
                                                          count := 
                                                            [ 9, 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
Sparse6 ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 421926, 
                                                          root := ~, 
                                                          start := 421910, 
                                                          stop := 421925 ), 
                                                      rec( 
                                                          content := " is a gr\
aph data format for storing undirected graphs\n\twith possibly multiple edges \
or loops. The maximal number of vertices\n\tallowed is ", count := 
                                                            [ 9, 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
2^{36} - 1 ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "M", 
                                                          next := 422082, 
                                                          root := ~, 
                                                          start := 422063, 
                                                          stop := 422081 ), 
                                                      rec( 
                                                          content := ". The fo\
rmat consists of two parts. The\n\tfirst part uses one to eight bytes to store\
 the number of vertices.\n\tAnd the second part only stores information about \
the edges.\n\tTherefore, the ", count := [ 9, 2, 0, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
Sparse6 ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 422285, 
                                                          root := ~, 
                                                          start := 422269, 
                                                          stop := 422284 ), 
                                                      rec( 
                                                          content := " format \
return a more compact encoding\n\tthen ", count := [ 9, 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
Graph6 ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 422345, 
                                                          root := ~, 
                                                          start := 422330, 
                                                          stop := 422344 ), 
                                                      rec( 
                                                          content := " for spa\
rse graph, i.e.  graphs where the number\n\tof edges is much less than the num\
ber of vertices squared.  For a more\n\tdetail description see ", 
                                                          count := 
                                                            [ 9, 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Text := "Sparse6\
" ), content := [ rec( content := "\n        http://cs.anu.edu.au/~bdm/data/fo\
rmats.txt", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 422567, 
                                                          root := ~, 
                                                          start := 422490, 
                                                          stop := 422566 ), 
                                                      rec( 
                                                          content := ".\n     \
 ", count := [ 9, 2, 0, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 9, 2, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 422582, root := ~, 
                                                  start := 421902, 
                                                  stop := 422581 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " Digraph6\
 ", count := [ 9, 2, 0, 8 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 9, 2, 0, 8 ], 
                                                  name := "Mark", 
                                                  next := 422613, root := ~, 
                                                  start := 422590, 
                                                  stop := 422612 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n\t", 
                                                          count := 
                                                            [ 9, 2, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraph6", count := [ 9, 2, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 422643, 
                                                          root := ~, 
                                                          start := 422628, 
                                                          stop := 422642 ), 
                                                      rec( 
                                                          content := " is a ne\
w format based on ", count := [ 9, 2, 0, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
Graph6 ", count := [ 9, 2, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 422684, 
                                                          root := ~, 
                                                          start := 422669, 
                                                          stop := 422683 ), 
                                                      rec( 
                                                          content := ", but de\
signed\n\tfor digraphs. The entire adjacency matrix is stored, and\n\ttherefor\
e there is support for directed edges and single-vertex loops.\n\tHowever, mul\
tiple edges are not supported.\n      ", count := [ 9, 2, 0, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 422886, root := ~, 
                                                  start := 422620, 
                                                  stop := 422885 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := " DiSparse\
6 ", count := [ 9, 2, 0, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 0, 10 ], 
                                                  name := "Mark", 
                                                  next := 422918, root := ~, 
                                                  start := 422894, 
                                                  stop := 422917 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n\t", 
                                                          count := 
                                                            [ 9, 2, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
iSparse6", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 422949, 
                                                          root := ~, 
                                                          start := 422933, 
                                                          stop := 422948 ), 
                                                      rec( 
                                                          content := " is a ne\
w format based on ", count := [ 9, 2, 0, 11 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
Sparse6 ", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 422991, 
                                                          root := ~, 
                                                          start := 422975, 
                                                          stop := 422990 ), 
                                                      rec( 
                                                          content := ", but\n\\
tdesigned for digraphs. In this format the list of edges is\n\tpartitioned int\
o inceasing and decreasing edges, depending whether the\n\tedge has its source\
 bigger than the range. Then both sets of edges are\n\twritten separetly in ",
                                                          count := 
                                                            [ 9, 2, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := " \
Sparse6 ", count := [ 9, 2, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 423239, 
                                                          root := ~, 
                                                          start := 423223, 
                                                          stop := 423238 ), 
                                                      rec( 
                                                          content := " format \
with a separation symbol\n\tin between.\n      ", count := [ 9, 2, 0, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 423298, root := ~, 
                                                  start := 422925, 
                                                  stop := 423297 ) ], 
                                          count := [ 9, 2, 0, 4 ], 
                                          mathmode := "Text", name := "List", 
                                          next := 423310, root := ~, 
                                          start := 421332, stop := 423309 ), 
                                      rec( content := "\n    ", 
                                          count := [ 9, 2, 0, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "String" ), 
                                                  content := 0, 
                                                  count := [ 9, 2, 1, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Attr", 
                                                  next := 423365, root := ~, 
                                                  start := 423330, 
                                                  stop := 423364 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "PrintString" ),
                                                  content := 0, 
                                                  count := [ 9, 2, 1, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 423408, root := ~, 
                                                  start := 423368, 
                                                  stop := 423407 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A string.\
", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 9, 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 423439, root := ~, 
                                                  start := 423411, 
                                                  stop := 423438 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Ret\
urns a string ", count := [ 9, 2, 1, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tring", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 423490, 
                                                          root := ~, 
                                                          start := 423477, 
                                                          stop := 423489 ), 
                                                      rec( 
                                                          content := " such th\
at ", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "E\
valString(string)", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "C", 
                                                          next := 423526, 
                                                          root := ~, 
                                                          start := 423501, 
                                                          stop := 423525 ), 
                                                      rec( 
                                                          content := "\n    is\
 equal to ", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 2, 1, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 423557, 
                                                          root := ~, 
                                                          start := 423543, 
                                                          stop := 423556 ), 
                                                      rec( 
                                                          content := ", and ha\
s the same mutability.\n    See ", count := [ 9, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Func := "EvalString" ), content := 0, count := [ 9, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 423636, 
                                                          root := ~, 
                                                          start := 423596, 
                                                          stop := 423635 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 1, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 423646, 
                                                          root := ~, 
                                                          start := 423642, 
                                                          stop := 423645 ), 
                                                      rec( 
                                                          content := "\n\n    \
The methods installed for ", count := [ 9, 2, 1, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
tring", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 423691, 
                                                          root := ~, 
                                                          start := 423678, 
                                                          stop := 423690 ), 
                                                      rec( 
                                                          content := " make so\
me attempts to\n    ensure that ", count := [ 9, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tring", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 423743, 
                                                          root := ~, 
                                                          start := 423730, 
                                                          stop := 423742 ), 
                                                      rec( 
                                                          content := " has as \
short a length as possible, but\n    there may exist shorter strings that also\
 evaluate to ", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 2, 1, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 423855, 
                                                          root := ~, 
                                                          start := 423841, 
                                                          stop := 423854 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 1, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 423865, 
                                                          root := ~, 
                                                          start := 423861, 
                                                          stop := 423864 ), 
                                                      rec( 
                                                          content := "\n\n    \
It is possible that ", count := [ 9, 2, 1, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tring", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 423904, 
                                                          root := ~, 
                                                          start := 423891, 
                                                          stop := 423903 ), 
                                                      rec( 
                                                          content := " may con\
tain escaped special\n    characters. To obtain a representation of ", 
                                                          count := 
                                                            [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 423993, 
                                                          root := ~, 
                                                          start := 423979, 
                                                          stop := 423992 ), 
                                                      rec( 
                                                          content := " that\n \
   can be entered as GAP input, please use\n    ", count := [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Func := "Print" ), content := 0, count := [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 424082, 
                                                          root := ~, 
                                                          start := 424047, 
                                                          stop := 424081 ), 
                                                      rec( 
                                                          content := ".\n    N\
ote that ", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "P\
rint", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 424110, 
                                                          root := ~, 
                                                          start := 424098, 
                                                          stop := 424109 ), 
                                                      rec( 
                                                          content := " for a d\
igraph  delegates to\n    ", count := [ 9, 2, 1, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "P\
rintString", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 424161, 
                                                          root := ~, 
                                                          start := 424143, 
                                                          stop := 424160 ), 
                                                      rec( 
                                                          content := ", which \
delegates to ", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
tring", count := [ 9, 2, 1, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 424195, 
                                                          root := ~, 
                                                          start := 424182, 
                                                          stop := 424194 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 1, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> D := CycleDigraph(3);\n<immutable cycle digraph with 3 vertices>\ngap> P\
rint(D);\nCycleDigraph(3);\ngap> G := PetersenGraph(IsMutableDigraph);\n<mutab\
le digraph with 10 vertices, 30 edges>\ngap> String(G);\n\"DigraphFromGraph6St\
ring(IsMutableDigraph, \\\"IheA@GUAo\\\");\"\ngap> Print(last);\nDigraphFromGr\
aph6String(IsMutableDigraph, \"IheA@GUAo\");\ngap> DigraphFromGraph6String(IsM\
utableDigraph, \"IheA@GUAo\");\n<mutable digraph with 10 vertices, 30 edges>\n\
", count := [ 9, 2, 1, 8 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 9, 2, 1, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Log", 
                                                          next := 424670, 
                                                          root := ~, 
                                                          start := 424201, 
                                                          stop := 424669 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 1, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 1, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 424687, root := ~, 
                                                  start := 423442, 
                                                  stop := 424686 ) ], 
                                          count := [ 9, 2, 1, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 424701, root := ~, 
                                          start := 423315, stop := 424700 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 1, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]str",
                                                      Name := "DigraphFromGrap\
h6String" ), content := 0, count := [ 9, 2, 2, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 424781, root := ~, 
                                                  start := 424722, 
                                                  stop := 424780 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]str",
                                                      Name := "DigraphFromDigr\
aph6String" ), content := 0, count := [ 9, 2, 2, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 424843, root := ~, 
                                                  start := 424784, 
                                                  stop := 424842 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]str",
                                                      Name := "DigraphFromSpar\
se6String" ), content := 0, count := [ 9, 2, 2, 6 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 424905, root := ~, 
                                                  start := 424846, 
                                                  stop := 424904 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "[filt, ]str",
                                                      Name := "DigraphFromDiSp\
arse6String" ), content := 0, count := [ 9, 2, 2, 8 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 424967, root := ~, 
                                                  start := 424908, 
                                                  stop := 424966 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 9, 2, 2, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 424999, root := ~, 
                                                  start := 424970, 
                                                  stop := 424998 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tr", count := [ 9, 2, 2, 9 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 2, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 425033, 
                                                          root := ~, 
                                                          start := 425023, 
                                                          stop := 425032 ), 
                                                      rec( 
                                                          content := " is a st\
ring encoding a graph in Graph6, Digraph6, Sparse6 or\n    DiSparse6 format, t\
hen the corresponding function returns a digraph. In the\n    case of either G\
raph6 or Sparse6, formats which do not support directed\n    edges, this will \
be a digraph such that for every edge, the edge going in\n    the opposite dir\
ection is also present.", count := [ 9, 2, 2, 9 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 425376, 
                                                          root := ~, 
                                                          start := 425372, 
                                                          stop := 425375 ), 
                                                      rec( 
                                                          content := "\n\n    \
Each of these functions takes an optional first argument ", 
                                                          count := 
                                                            [ 9, 2, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilt", count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 2, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 425450, 
                                                          root := ~, 
                                                          start := 425439, 
                                                          stop := 425449 ), 
                                                      rec( 
                                                          content := ",\n    w\
hich should be either ", count := [ 9, 2, 2, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 9, 2, 2, 10 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 425509, 
                                                          root := ~, 
                                                          start := 425479, 
                                                          stop := 425508 ), 
                                                      rec( 
                                                          content := "\n    or\
 ", count := [ 9, 2, 2, 10 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 9, 2, 2, 10 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 425549, 
                                                          root := ~, 
                                                          start := 425517, 
                                                          stop := 425548 ), 
                                                      rec( 
                                                          content := ",\n    a\
nd which specifies whether the output digraph shall\n    be mutable or immutab\
le.\n    If no first argument is provided, then an immutable\n    digraph is r\
eturned by default.\n    ", count := [ 9, 2, 2, 10 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> DigraphFromGraph6String(\"?\");\n<immutable empty digraph with 0 vertice\
s>\ngap> DigraphFromGraph6String(\"C]\");\n<immutable digraph with 4 vertices,\
 8 edges>\ngap> DigraphFromGraph6String(\"H?AAEM{\");\n<immutable digraph with\
 9 vertices, 22 edges>\ngap> DigraphFromDigraph6String(\"&?\");\n<immutable em\
pty digraph with 0 vertices>\ngap> DigraphFromDigraph6String(IsMutableDigraph,\
 \"&DOOOW?\");\n<mutable digraph with 5 vertices, 5 edges>\ngap> DigraphFromDi\
graph6String(\"&CQFG\");\n<immutable digraph with 4 vertices, 6 edges>\ngap> D\
igraphFromDigraph6String(\"&IM[SrKLc~lhesbU[F_\");\n<immutable digraph with 10\
 vertices, 51 edges>\ngap> DigraphFromDiSparse6String(\".CaWBGA?b\");\n<immuta\
ble multidigraph with 4 vertices, 9 edges>\n", count := [ 9, 2, 2, 11 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 2, 11 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 426478, 
                                                          root := ~, 
                                                          start := 425733, 
                                                          stop := 426477 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 2, 2, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 2, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 426497, root := ~, 
                                                  start := 425002, 
                                                  stop := 426496 ) ], 
                                          count := [ 9, 2, 2, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 426511, root := ~, 
                                          start := 424707, stop := 426510 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 2, 12 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "Graph6String" )
                                                    , content := 0, 
                                                  count := [ 9, 2, 3, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 426573, root := ~, 
                                                  start := 426532, 
                                                  stop := 426572 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "Digraph6String"\
 ), content := 0, count := [ 9, 2, 3, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 426619, root := ~, 
                                                  start := 426576, 
                                                  stop := 426618 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "Sparse6String" 
                                                     ), content := 0, 
                                                  count := [ 9, 2, 3, 6 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 426664, root := ~, 
                                                  start := 426622, 
                                                  stop := 426663 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "DiSparse6String\
" ), content := 0, count := [ 9, 2, 3, 8 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 426711, root := ~, 
                                                  start := 426667, 
                                                  stop := 426710 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A string.\
", count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 9, 2, 3, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 426742, root := ~, 
                                                  start := 426714, 
                                                  stop := 426741 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
se four functions return a highly compressed string fully describing the\n    \
digraph ", count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 2, 3, 9 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 426865, 
                                                          root := ~, 
                                                          start := 426851, 
                                                          stop := 426864 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 9, 2, 3, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 426871, 
                                                          root := ~, 
                                                          start := 426867, 
                                                          stop := 426870 ), 
                                                      rec( 
                                                          content := "\n\n    \
Graph6 and Digraph6 are formats best used on small, dense graphs, if\n    appl\
icable. For larger, sparse graphs use ", count := [ 9, 2, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
parse6", count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 427006, 
                                                          root := ~, 
                                                          start := 426992, 
                                                          stop := 427005 ), 
                                                      rec( 
                                                          content := " and\n  \
  ", count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
isparse6", count := [ 9, 2, 3, 10 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "E", 
                                                          next := 427031, 
                                                          root := ~, 
                                                          start := 427015, 
                                                          stop := 427030 ), 
                                                      rec( 
                                                          content := " (this l\
atter also preserves multiple edges). ", count := [ 9, 2, 3, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 3, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 427081, 
                                                          root := ~, 
                                                          start := 427077, 
                                                          stop := 427080 ), 
                                                      rec( 
                                                          content := "\n\n    \
See ", count := [ 9, 2, 3, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "WriteDi\
graphs" ), content := 0, count := [ 9, 2, 3, 11 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 427118, 
                                                          root := ~, 
                                                          start := 427091, 
                                                          stop := 427117 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 3, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[2, 3], [1], [1]]);\n<immutable digraph with 3 vertices, \
4 edges>\ngap> Sparse6String(gr);\n\":Bc\"\ngap> DiSparse6String(gr);\n\".Bc{f\
\"\n", count := [ 9, 2, 3, 12 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 9, 2, 3, 12 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 427305, 
                                                          root := ~, 
                                                          start := 427124, 
                                                          stop := 427304 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 3, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 3, 9 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 427322, root := ~, 
                                                  start := 426745, 
                                                  stop := 427321 ) ], 
                                          count := [ 9, 2, 3, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 427336, root := ~, 
                                          start := 426517, stop := 427335 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 3, 13 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filename [, code\
r][, mode]", Name := "DigraphFile" ), content := 0, count := [ 9, 2, 4, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 427416, root := ~, 
                                                  start := 427357, 
                                                  stop := 427415 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An IO fil\
e object.", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 427456, root := ~, 
                                                  start := 427419, 
                                                  stop := 427455 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 427495, 
                                                          root := ~, 
                                                          start := 427480, 
                                                          stop := 427494 ), 
                                                      rec( 
                                                          content := " is a st\
ring representing the name of a file, then\n    ", count := [ 9, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphFile", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 427568, 
                                                          root := ~, 
                                                          start := 427550, 
                                                          stop := 427567 ), 
                                                      rec( 
                                                          content := " returns\
 an ", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "IO" ), content := [ rec( content := "\n     http://gap-packages\
.github.io/io/\n", count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 9, 2, 4, 3 ], mathmode := "Text", name := "URL",
                                                                  next := 78, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 77 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 4, 3 ], 
                                                          name := "Alt", 
                                                          next := 84, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 83 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "IO", count := [ 9, 2, 4, 3 ], name := \
"PCDATA", root := ~ ) ], count := [ 9, 2, 4, 3 ], name := "Package", 
                                                                  next := 122,
                                                                  root := ~, 
                                                                  start := 101
                                                                    , 
                                                                  stop := 121 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 128, 
                                                          root := ~, 
                                                          start := 84, 
                                                          stop := 127 ), 
                                                      rec( 
                                                          content := " package\
 file object for that file.\n    ", count := [ 9, 2, 4, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 427628, 
                                                          root := ~, 
                                                          start := 427624, 
                                                          stop := 427627 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional argument ", count := [ 9, 2, 4, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
oder", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 427671, 
                                                          root := ~, 
                                                          start := 427659, 
                                                          stop := 427670 ), 
                                                      rec( 
                                                          content := " is spec\
ified\n    and is a function which either encodes a digraph as a string, or de\
codes a\n    string into a digraph, then this function will be used when readi\
ng or\n    writing to the returned file object. If the optional argument ", 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "c\
oder", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 427917, 
                                                          root := ~, 
                                                          start := 427905, 
                                                          stop := 427916 ), 
                                                      rec( 
                                                          content := "\n    is\
 not specified, then the encoding of the digraphs in the returned file\n    ob\
ject must be specified in the the file extension. The file extension must\n   \
 be one of: ", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
g6", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428100, 
                                                          root := ~, 
                                                          start := 428090, 
                                                          stop := 428099 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
s6", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428112, 
                                                          root := ~, 
                                                          start := 428102, 
                                                          stop := 428111 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
d6", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428124, 
                                                          root := ~, 
                                                          start := 428114, 
                                                          stop := 428123 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
ds6", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428137, 
                                                          root := ~, 
                                                          start := 428126, 
                                                          stop := 428136 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
txt", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428150, 
                                                          root := ~, 
                                                          start := 428139, 
                                                          stop := 428149 ), 
                                                      rec( 
                                                          content := ",\n    "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
p", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428165, 
                                                          root := ~, 
                                                          start := 428156, 
                                                          stop := 428164 ), 
                                                      rec( content := ", or ",
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
pickle", count := [ 9, 2, 4, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428184, 
                                                          root := ~, 
                                                          start := 428170, 
                                                          stop := 428183 ), 
                                                      rec( 
                                                          content := "; more d\
etails of these file formats is given\n    below. ", count := [ 9, 2, 4, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 428245, 
                                                          root := ~, 
                                                          start := 428241, 
                                                          stop := 428244 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional argument ", count := [ 9, 2, 4, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
ode", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 428287, 
                                                          root := ~, 
                                                          start := 428276, 
                                                          stop := 428286 ), 
                                                      rec( 
                                                          content := " is spec\
ified, then it must be one of:\n    ", count := [ 9, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
"w\"", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428340, 
                                                          root := ~, 
                                                          start := 428330, 
                                                          stop := 428339 ), 
                                                      rec( 
                                                          content := " (for wr\
ite), ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
"a\"", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428364, 
                                                          root := ~, 
                                                          start := 428354, 
                                                          stop := 428363 ), 
                                                      rec( 
                                                          content := " (for ap\
pend), or ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
"r\"", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428392, 
                                                          root := ~, 
                                                          start := 428382, 
                                                          stop := 428391 ), 
                                                      rec( 
                                                          content := " (for re\
ad).\n    If ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "m\
ode", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 428423, 
                                                          root := ~, 
                                                          start := 428412, 
                                                          stop := 428422 ), 
                                                      rec( 
                                                          content := " is not \
specified, then ", count := [ 9, 2, 4, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
"r\"", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428457, 
                                                          root := ~, 
                                                          start := 428447, 
                                                          stop := 428456 ), 
                                                      rec( 
                                                          content := " is used\
 by default. ", count := [ 9, 2, 4, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 428482, 
                                                          root := ~, 
                                                          start := 428478, 
                                                          stop := 428481 ), 
                                                      rec( 
                                                          content := "\n\n    \
If ", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 428506, 
                                                          root := ~, 
                                                          start := 428491, 
                                                          stop := 428505 ), 
                                                      rec( 
                                                          content := " ends in\
 one of: ", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
gz", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428533, 
                                                          root := ~, 
                                                          start := 428523, 
                                                          stop := 428532 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 9, 2, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
bz2", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428546, 
                                                          root := ~, 
                                                          start := 428535, 
                                                          stop := 428545 ), 
                                                      rec( 
                                                          content := ", or\n  \
  ", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
xz", count := [ 9, 2, 4, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428565, 
                                                          root := ~, 
                                                          start := 428555, 
                                                          stop := 428564 ), 
                                                      rec( 
                                                          content := ", then t\
he digraphs which are read from, or written to, the\n    returned file object \
are decompressed, or compressed, appropriately.\n    ", count := 
                                                            [ 9, 2, 4, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 428706, 
                                                          root := ~, 
                                                          start := 428702, 
                                                          stop := 428705 ), 
                                                      rec( 
                                                          content := "\n\n    \
The file object returned by ", count := [ 9, 2, 4, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphFile", count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 428758, 
                                                          root := ~, 
                                                          start := 428740, 
                                                          stop := 428757 ), 
                                                      rec( 
                                                          content := " can be \
given as the first\n    argument for either of the functions ", 
                                                          count := 
                                                            [ 9, 2, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "ReadDig\
raphs" ), content := 0, count := [ 9, 2, 4, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 428852, 
                                                          root := ~, 
                                                          start := 428826, 
                                                          stop := 428851 ), 
                                                      rec( content := " or ", 
                                                          count := 
                                                            [ 9, 2, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "WriteDi\
graphs" ), content := 0, count := [ 9, 2, 4, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 428889, 
                                                          root := ~, 
                                                          start := 428856, 
                                                          stop := 428888 ), 
                                                      rec( 
                                                          content := ". The pu\
rpose of this is to reduce the overhead of\n    recreating the file object ins\
ide the functions ", count := [ 9, 2, 4, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "ReadDig\
raphs" ), content := 0, count := [ 9, 2, 4, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 429018, 
                                                          root := ~, 
                                                          start := 428992, 
                                                          stop := 429017 ), 
                                                      rec( 
                                                          content := "\n    or\
 ", count := [ 9, 2, 4, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "WriteDi\
graphs" ), content := 0, count := [ 9, 2, 4, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 429053, 
                                                          root := ~, 
                                                          start := 429026, 
                                                          stop := 429052 ), 
                                                      rec( 
                                                          content := " when, f\
or example, reading or writing many\n    digraphs in a loop.\n    ", 
                                                          count := 
                                                            [ 9, 2, 4, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 4, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 429129, 
                                                          root := ~, 
                                                          start := 429125, 
                                                          stop := 429128 ), 
                                                      rec( 
                                                          content := "\n\n    \
The currently supported file formats, and associated filename extensions,\n   \
 are:\n    ", count := [ 9, 2, 4, 8 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "graph6 (.g6)", count := [ 9, 2, 4, 9 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 9 ], 
                                                                  name := "Mar\
k", next := 429260, root := ~, start := 429235, stop := 429259 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n\tA standard and widely-used format\
 for undirected graphs, with no support\n\tfor loops or multiple edges.  Only \
symmetric graphs are allowed -- each\n\tedge is combined with its converse edg\
e to produce a single undirected\n\tedge.  This format is best used for \"dens\
e\" graphs -- those with many\n\tedges per vertex.\n      ", count := [ 9, 2, \
4, 10 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 9, 2, 
                                                                      4, 10 ],
                                                                  name := "Ite\
m", next := 429596, root := ~, start := 429267, stop := 429595 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "sparse6 (.s6)", count := [ 9, 2, 4, 1\
1 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 
                                                                      11 ], 
                                                                  name := "Mar\
k", next := 429629, root := ~, start := 429603, stop := 429628 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n\tUnlike graph6, sparse6 has suppor\
t for loops and multiple edges.\n\tHowever, its use is still limited to symmet\
ric graphs.  This format is\n\tbetter-suited to \"sparse\" graphs -- those wit\
h few edges per vertex.\n      ", count := [ 9, 2, 4, 12 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 12 ], name := "Item", 
                                                                  next := 4298\
64, root := ~, start := 429636, stop := 429863 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph6 (.d6)", count := [ 9, 2, 4, 13 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 13 ], name := "Mark", 
                                                                  next := 4298\
98, root := ~, start := 429871, stop := 429897 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n\tThis format is based on graph6, but stores direction information -\
\n\ttherefore is not limited to symmetric graphs.  Loops are allowed, but\n\tm\
ultiple edges are not.  Best compression with \"dense\" graphs.\n      ", coun\
t := [ 9, 2, 4, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 9, 2, 
                                                                      4, 14 ],
                                                                  name := "Ite\
m", next := 430128, root := ~, start := 429905, stop := 430127 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "disparse6 (.ds6)", count := [ 9, 2, 4\
, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 9, 2, 
                                                                      4, 15 ],
                                                                  name := "Mar\
k", next := 430164, root := ~, start := 430135, stop := 430163 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n\tAny type of digraph can be encode\
d in disparse6: directions, loops, and\n\tmultiple edges are all allowed.  Sim\
ilar to sparse6, this has the best\n\tcompression rate with \"sparse\" graphs.\
\n      ", count := [ 9, 2, 4, 16 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 9, 2, 4, 16 ], name := "Item", next := 430376, 
                                                                  root := ~, 
                                                                  start := 430\
171, stop := 430375 ), rec( attributes := rec(  ), content := [ rec( content :\
= "plain text (.txt)", count := [ 9, 2, 4, 17 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ 9, 2, 4, 17 ], name := "Mark", next := 4304\
13, root := ~, start := 430383, stop := 430412 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n\tThis is a human-readable format which stores graphs in the form\n \
       ", count := [ 9, 2, 4, 18 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "0 7  0 8  1\
 7  2 8  3 8  4 8  5 8  6 8", count := [ 9, 2, 4, 18 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 18 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 430545, root := ~, start := 430500, stop := 430544 ), 
                                                                      rec( 
                                                                          cont\
ent := " i.e. pairs of vertices\n        describing edges in a graph. More spe\
cifically, the vertices making up\n        one edge must be separated by a sin\
gle space, and pairs of vertices must\n        be separated by two spaces. ", 
                                                                          coun\
t := [ 9, 2, 4, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 9, 2, 4, 19 ], mathmode := "Text",
                                                                          name\
 := "P", next := 430769, root := ~, start := 430765, stop := 430768 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n\n        See ", count := [ 9, 2, 4, 19 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ), rec( attributes := rec( Oper := "ReadPlainTextDigrap\
h" ), content := 0, count := [ 9, 2, 4, 19 ], mathmode := "Text", name := "Ref\
", next := 430817, root := ~, start := 430783, stop := 430816 ), rec( content \
:= " for a more flexible way to store\n        digraphs in a plain text file. \
", count := [ 9, 2, 4, 19 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 9, 2, 4, 20 ], mathmode := "Text",
                                                                          name\
 := "P", next := 430894, root := ~, start := 430890, stop := 430893 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n      ", count := [ 9, 2, 4, 20 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 2, 4, 18 ], name := "Item", next := 430908, 
                                                                  root := ~, 
                                                                  start := 430\
420, stop := 430907 ), rec( attributes := rec(  ), content := [ rec( content :\
= "pickled (", count := [ 9, 2, 4, 21 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := ".p", count \
:= [ 9, 2, 4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\
 := [ 9, 2, 4, 21 ], mathmode := "Text", name := "F", next := 430940, root := \
~, start := 430931, stop := 430939 ), rec( content := " or ", count := [ 9, 2,\
 4, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( content := ".pickle", count := [ 9, 2, 4, 21 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 21 ], 
                                                                          math\
mode := "Text", name := "F", next := 430958, root := ~, start := 430944, stop \
:= 430957 ), rec( content := ")", count := [ 9, 2, 4, 21 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 21 ], name := "Mark", 
                                                                  next := 4309\
66, root := ~, start := 430916, stop := 430965 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n        Digraphs are pickled using the ", count := [ 9, 2, 4, 22 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := \
"Text" ), content := [ rec( attributes := rec( Text := "IO" ), content := [ re\
c( content := "\n     http://gap-packages.github.io/io/\n", count := [ 9, 2, 4\
, 22 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, \
4, 22 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17\
, stop := 77 ) ], count := [ 9, 2, 4, 22 ], name := "Alt", next := 84, root :=\
 ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ), conten\
t := [ rec( attributes := rec(  ), content := [ rec( content := "IO", count :=\
 [ 9, 2, 4, 22 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 4, 22 ], n\
ame := "Package", next := 122, root := ~, start := 101, stop := 121 ) ], count\
 := [ 9, 2, 4, 22 ], mathmode := "Text", name := "Alt", next := 128, root := ~
                                                                            , 
                                                                          star\
t := 84, stop := 127 ), rec( content := " package. This is particularly good\n\
        when the ", count := [ 9, 2, 4, 22 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphGroup" ), content :\
= 0, count := [ 9, 2, 4, 22 ], mathmode := "Text", name := "Ref", next := 4311\
02, root := ~, start := 431076, stop := 431101 ), rec( content := " is non-tri\
vial.\n      ", count := [ 9, 2, 4, 22 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 9, 2, 4, 22 ], name := "Item", next := 431132, 
                                                                  root := ~, 
                                                                  start := 430\
973, stop := 431131 ) ], count := [ 9, 2, 4, 9 ], mathmode := "Text", 
                                                          name := "List", 
                                                          next := 431144, 
                                                          root := ~, 
                                                          start := 429222, 
                                                          stop := 431143 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 9, 2, 4, 24 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> filename := Concatenation(DIGRAPHS_Dir(), \"/tst/out/man.d6.gz\");;\ngap\
> file := DigraphFile(filename, \"w\");;\ngap> for i in [1 .. 10] do\n> WriteD\
igraphs(file, Digraph([[1, 3], [2], [1, 2]]));\n> od;\ngap> IO_Close(file);;\n\
gap> file := DigraphFile(filename, \"r\");;\ngap> ReadDigraphs(file, 9);\n<imm\
utable digraph with 3 vertices, 5 edges>\ngap> IO_Close(file);;\n", 
                                                                  count := 
                                                                    [ 9, 2, 
                                                                      4, 25 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 4, 25 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 431542, 
                                                          root := ~, 
                                                          start := 431150, 
                                                          stop := 431541 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 2, 4, 26 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 4, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 431561, root := ~, 
                                                  start := 427459, 
                                                  stop := 431560 ) ], 
                                          count := [ 9, 2, 4, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 431575, root := ~, 
                                          start := 427342, stop := 431574 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 4, 26 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filename[, decod\
er][, n]", Name := "ReadDigraphs" ), content := 0, count := [ 9, 2, 5, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 431654, root := ~, 
                                                  start := 431596, 
                                                  stop := 431653 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
, or a list of digraphs.", count := [ 9, 2, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 431709, root := ~, 
                                                  start := 431657, 
                                                  stop := 431708 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 431748, 
                                                          root := ~, 
                                                          start := 431733, 
                                                          stop := 431747 ), 
                                                      rec( 
                                                          content := " is a st\
ring containing the name of a file containing\n    encoded digraphs or an ", 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "IO" ), content := [ rec( content := "\n     http://gap-packages\
.github.io/io/\n", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "URL",
                                                                  next := 78, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 77 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          name := "Alt", 
                                                          next := 84, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 83 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "IO", count := [ 9, 2, 5, 3 ], name := \
"PCDATA", root := ~ ) ], count := [ 9, 2, 5, 3 ], name := "Package", 
                                                                  next := 122,
                                                                  root := ~, 
                                                                  start := 101
                                                                    , 
                                                                  stop := 121 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 128, 
                                                          root := ~, 
                                                          start := 84, 
                                                          stop := 127 ), 
                                                      rec( 
                                                          content := " file ob\
ject created using ", count := [ 9, 2, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
File" ), content := 0, count := [ 9, 2, 5, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 431891, 
                                                          root := ~, 
                                                          start := 431860, 
                                                          stop := 431890 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
eadDigraphs", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 431917, 
                                                          root := ~, 
                                                          start := 431898, 
                                                          stop := 431916 ), 
                                                      rec( 
                                                          content := " returns\
 the digraphs\n    encoded in the file as a list.  Note that if ", 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432003, 
                                                          root := ~, 
                                                          start := 431988, 
                                                          stop := 432002 ), 
                                                      rec( 
                                                          content := " is a\n \
   compressed file, which has been compressed appropriately to give a filename\
\n    extension of ", count := [ 9, 2, 5, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
gz", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432116, 
                                                          root := ~, 
                                                          start := 432106, 
                                                          stop := 432115 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
bz2", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432129, 
                                                          root := ~, 
                                                          start := 432118, 
                                                          stop := 432128 ), 
                                                      rec( content := ", or ",
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
xz", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432144, 
                                                          root := ~, 
                                                          start := 432134, 
                                                          stop := 432143 ), 
                                                      rec( 
                                                          content := ", then\n\
    ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
eadDigraphs", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432174, 
                                                          root := ~, 
                                                          start := 432155, 
                                                          stop := 432173 ), 
                                                      rec( 
                                                          content := " can rea\
d ", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 5, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432199, 
                                                          root := ~, 
                                                          start := 432184, 
                                                          stop := 432198 ), 
                                                      rec( 
                                                          content := " without\
 it first needing to be\n    decompressed.\n    ", count := [ 9, 2, 5, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 432257, 
                                                          root := ~, 
                                                          start := 432253, 
                                                          stop := 432256 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional argument ", count := [ 9, 2, 5, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ecoder", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432302, 
                                                          root := ~, 
                                                          start := 432288, 
                                                          stop := 432301 ), 
                                                      rec( 
                                                          content := " is spec\
ified\n    and is a function which decodes a string into a digraph,\n    then \
", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
eadDigraphs", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432405, 
                                                          root := ~, 
                                                          start := 432386, 
                                                          stop := 432404 ), 
                                                      rec( 
                                                          content := " will us\
e ", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ecoder", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432429, 
                                                          root := ~, 
                                                          start := 432415, 
                                                          stop := 432428 ), 
                                                      rec( 
                                                          content := " to deco\
de the digraphs\n    contained in ", count := [ 9, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 5, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432485, 
                                                          root := ~, 
                                                          start := 432470, 
                                                          stop := 432484 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 2, 5, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 432490, 
                                                          root := ~, 
                                                          start := 432486, 
                                                          stop := 432489 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional argument ", count := [ 9, 2, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432529, 
                                                          root := ~, 
                                                          start := 432521, 
                                                          stop := 432528 ), 
                                                      rec( 
                                                          content := " is spec\
ified, then ", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
eadDigraphs", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432568, 
                                                          root := ~, 
                                                          start := 432549, 
                                                          stop := 432567 ), 
                                                      rec( 
                                                          content := "\n    re\
turns the ", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432593, 
                                                          root := ~, 
                                                          start := 432585, 
                                                          stop := 432592 ), 
                                                      rec( 
                                                          content := "th digra\
ph encoded in the file ", count := [ 9, 2, 5, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 5, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432639, 
                                                          root := ~, 
                                                          start := 432624, 
                                                          stop := 432638 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 5, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 432649, 
                                                          root := ~, 
                                                          start := 432645, 
                                                          stop := 432648 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional argument ", count := [ 9, 2, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ecoder", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432694, 
                                                          root := ~, 
                                                          start := 432680, 
                                                          stop := 432693 ), 
                                                      rec( 
                                                          content := " is not \
specified, then\n    ", count := [ 9, 2, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
eadDigraphs", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432741, 
                                                          root := ~, 
                                                          start := 432722, 
                                                          stop := 432740 ), 
                                                      rec( 
                                                          content := " will de\
duce which decoder to use based on the filename\n    extension of ", 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 432829, 
                                                          root := ~, 
                                                          start := 432814, 
                                                          stop := 432828 ), 
                                                      rec( 
                                                          content := " (after \
removing the compression-related\n    filename extensions ", 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
gz", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432904, 
                                                          root := ~, 
                                                          start := 432894, 
                                                          stop := 432903 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
bz2", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432917, 
                                                          root := ~, 
                                                          start := 432906, 
                                                          stop := 432916 ), 
                                                      rec( 
                                                          content := ", and ",
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
xz", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432933, 
                                                          root := ~, 
                                                          start := 432923, 
                                                          stop := 432932 ), 
                                                      rec( 
                                                          content := ").  For \
example,\n    if the filename extension is ", count := [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
g6", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 432993, 
                                                          root := ~, 
                                                          start := 432983, 
                                                          stop := 432992 ), 
                                                      rec( 
                                                          content := ", then "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
eadDigraphs", count := [ 9, 2, 5, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 433019, 
                                                          root := ~, 
                                                          start := 433000, 
                                                          stop := 433018 ), 
                                                      rec( 
                                                          content := " will us\
e\n    the graph6 decoder ", count := [ 9, 2, 5, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
FromGraph6String" ), content := 0, count := [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 433089, 
                                                          root := ~, 
                                                          start := 433052, 
                                                          stop := 433088 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 5, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 5, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 433099, 
                                                          root := ~, 
                                                          start := 433095, 
                                                          stop := 433098 ), 
                                                      rec( 
                                                          content := "\n\n    \
The currently supported file formats, and associated filename extensions,\n   \
 are:\n    ", count := [ 9, 2, 5, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "graph6 (.g6)", count := [ 9, 2, 5, 8 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 8 ], 
                                                                  name := "Mar\
k", next := 433230, root := ~, start := 433205, stop := 433229 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n\tA standard and widely-used format\
 for undirected graphs, with no support\n\tfor loops or multiple edges.  Only \
symmetric graphs are allowed -- each\n\tedge is combined with its converse edg\
e to produce a single undirected\n\tedge.  This format is best used for \"dens\
e\" graphs -- those with many\n\tedges per vertex.\n      ", count := [ 9, 2, \
5, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 9, 2, 
                                                                      5, 9 ], 
                                                                  name := "Ite\
m", next := 433566, root := ~, start := 433237, stop := 433565 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "sparse6 (.s6)", count := [ 9, 2, 5, 1\
0 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 
                                                                      10 ], 
                                                                  name := "Mar\
k", next := 433599, root := ~, start := 433573, stop := 433598 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n\tUnlike graph6, sparse6 has suppor\
t for loops and multiple edges.\n\tHowever, its use is still limited to symmet\
ric graphs.  This format is\n\tbetter-suited to \"sparse\" graphs -- those wit\
h few edges per vertex.\n      ", count := [ 9, 2, 5, 11 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 11 ], name := "Item", 
                                                                  next := 4338\
34, root := ~, start := 433606, stop := 433833 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph6 (.d6)", count := [ 9, 2, 5, 12 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 12 ], name := "Mark", 
                                                                  next := 4338\
68, root := ~, start := 433841, stop := 433867 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n\tThis format is based on graph6, but stores direction information -\
\n\ttherefore is not limited to symmetric graphs.  Loops are allowed, but\n\tm\
ultiple edges are not.  Best compression with \"dense\" graphs.\n      ", coun\
t := [ 9, 2, 5, 13 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 9, 2, 
                                                                      5, 13 ],
                                                                  name := "Ite\
m", next := 434098, root := ~, start := 433875, stop := 434097 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "disparse6 (.ds6)", count := [ 9, 2, 5\
, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 9, 2, 
                                                                      5, 14 ],
                                                                  name := "Mar\
k", next := 434134, root := ~, start := 434105, stop := 434133 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n\tAny type of digraph can be encode\
d in disparse6: directions, loops, and\n\tmultiple edges are all allowed.  Sim\
ilar to sparse6, this has the best\n\tcompression rate with \"sparse\" graphs.\
\n      ", count := [ 9, 2, 5, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 9, 2, 5, 15 ], name := "Item", next := 434346, 
                                                                  root := ~, 
                                                                  start := 434\
141, stop := 434345 ), rec( attributes := rec(  ), content := [ rec( content :\
= "plain text (.txt)", count := [ 9, 2, 5, 16 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ 9, 2, 5, 16 ], name := "Mark", next := 4343\
83, root := ~, start := 434353, stop := 434382 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n\tThis is a human-readable format which stores graphs in the form\n \
       ", count := [ 9, 2, 5, 17 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "0 7  0 8  1\
 7  2 8  3 8  4 8  5 8  6 8", count := [ 9, 2, 5, 17 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 17 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 434515, root := ~, start := 434470, stop := 434514 ), 
                                                                      rec( 
                                                                          cont\
ent := " i.e. pairs of vertices\n        describing edges in a graph. More spe\
cifically, the vertices making up\n        one edge must be separated by a sin\
gle space, and pairs of vertices must\n        be separated by two spaces. ", 
                                                                          coun\
t := [ 9, 2, 5, 17 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 9, 2, 5, 18 ], mathmode := "Text",
                                                                          name\
 := "P", next := 434739, root := ~, start := 434735, stop := 434738 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n\n        See ", count := [ 9, 2, 5, 18 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ), rec( attributes := rec( Oper := "ReadPlainTextDigrap\
h" ), content := 0, count := [ 9, 2, 5, 18 ], mathmode := "Text", name := "Ref\
", next := 434787, root := ~, start := 434753, stop := 434786 ), rec( content \
:= " for a more flexible way to store\n        digraphs in a plain text file. \
", count := [ 9, 2, 5, 18 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 9, 2, 5, 19 ], mathmode := "Text",
                                                                          name\
 := "P", next := 434864, root := ~, start := 434860, stop := 434863 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n", count := [ 9, 2, 5, 19 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( content := "\n        Just so I remember:\n        <C>ReadPlainT\
extDigraph(\"data-local/soc-Epinions1.txt.gz\", \"\\t\", 1,\n        '#');</C>\
\n", count := [ 9, 2, 5, 19 ], mathmode := "Text", name := "XMLCOMMENT", root \
:= ~ ), rec( content := "\n      ", count := [ 9, 2, 5, 19 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 17 ], name := "Item",
                                                                  next := 4350\
09, root := ~, start := 434390, stop := 435008 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "pickled (", count := [ 9, 2, 5, 20 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := ".\
p", count := [ 9, 2, 5, 20 ], mathmode := "Text", name := "PCDATA", root := ~ \
) ], count := [ 9, 2, 5, 20 ], mathmode := "Text", name := "F", next := 435041
                                                                            , 
                                                                          root\
 := ~, start := 435032, stop := 435040 ), rec( content := " or ", count := [ 9\
, 2, 5, 20 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := [ rec( content := ".pickle", count := [ 9, 2, 5, 20 \
], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 20\
 ], mathmode := "Text", name := "F", next := 435059, root := ~, start := 43504\
5, stop := 435058 ), rec( content := ")", count := [ 9, 2, 5, 20 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 20 ], 
                                                                  name := "Mar\
k", next := 435067, root := ~, start := 435017, stop := 435066 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        Digraphs are pickled using \
the ", count := [ 9, 2, 5, 21 ], mathmode := "Text", name := "PCDATA", root :=\
 ~ ), rec( attributes := rec( Not := "Text" ), content := [ rec( attributes :=\
 rec( Text := "IO" ), content := [ rec( content := "\n     http://gap-packages\
.github.io/io/\n", count := [ 9, 2, 5, 21 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 2, 5, 21 ], mathmode := "Text", name := "URL\
", next := 78, root := ~, start := 17, stop := 77 ) ], count := [ 9, 2, 5, 21 
                                                                             ]
                                                                            , 
                                                                          name\
 := "Alt", next := 84, root := ~, start := 1, stop := 83 ), rec( attributes :=\
 rec( Only := "Text" ), content := [ rec( attributes := rec(  ), content := [ \
rec( content := "IO", count := [ 9, 2, 5, 21 ], name := "PCDATA", root := ~ ) \
], count := [ 9, 2, 5, 21 ], name := "Package", next := 122, root := ~, start \
:= 101, stop := 121 ) ], count := [ 9, 2, 5, 21 ], mathmode := "Text", name :=\
 "Alt", next := 128, root := ~, start := 84, stop := 127 ), rec( content := " \
package. This is particularly good\n        when the ", count := [ 9, 2, 5, 21\
 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(\
 Attr := "DigraphGroup" ), content := 0, count := [ 9, 2, 5, 21 ], mathmode :=\
 "Text", name := "Ref", next := 435203, root := ~, start := 435177, stop := 43\
5202 ), rec( content := " is non-trivial.\n      ", count := [ 9, 2, 5, 21 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 5, 21 ], 
                                                                  name := "Ite\
m", next := 435233, root := ~, start := 435074, stop := 435232 ) ], 
                                                          count := 
                                                            [ 9, 2, 5, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 435245, 
                                                          root := ~, 
                                                          start := 433192, 
                                                          stop := 435244 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 9, 2, 5, 23 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> ReadDigraphs(\n> Concatenation(DIGRAPHS_Dir(), \"/data/graph5.g6.gz\"), \
10);\n<immutable digraph with 5 vertices, 8 edges>\ngap> ReadDigraphs(\n> Conc\
atenation(DIGRAPHS_Dir(), \"/data/graph5.g6.gz\"), 17);\n<immutable digraph wi\
th 5 vertices, 12 edges>\ngap> ReadDigraphs(\n> Concatenation(DIGRAPHS_Dir(), \
\"/data/tree9.4.txt\"));\n[ <immutable digraph with 9 vertices, 8 edges>, \n  \
<immutable digraph with 9 vertices, 8 edges>, \n  <immutable digraph with 9 ve\
rtices, 8 edges>, \n  <immutable digraph with 9 vertices, 8 edges>, \n  <immut\
able digraph with 9 vertices, 8 edges>, \n  <immutable digraph with 9 vertices\
, 8 edges>, \n  <immutable digraph with 9 vertices, 8 edges>, \n  <immutable d\
igraph with 9 vertices, 8 edges>, \n  <immutable digraph with 9 vertices, 8 ed\
ges>, \n  <immutable digraph with 9 vertices, 8 edges>, \n  <immutable digraph\
 with 9 vertices, 8 edges>, \n  <immutable digraph with 9 vertices, 8 edges>, \
\n  <immutable digraph with 9 vertices, 8 edges>, \n  <immutable digraph with \
9 vertices, 8 edges> ]", count := [ 9, 2, 5, 24 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 5, 24 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 436291, 
                                                          root := ~, 
                                                          start := 435251, 
                                                          stop := 436290 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 2, 5, 25 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 5, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 436310, root := ~, 
                                                  start := 431712, 
                                                  stop := 436309 ) ], 
                                          count := [ 9, 2, 5, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 436324, root := ~, 
                                          start := 431581, stop := 436323 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 5, 25 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filename, digrap\
hs[, encoder] [, mode]", Name := "WriteDigraphs" ), content := 0, 
                                                  count := [ 9, 2, 6, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 436418, root := ~, 
                                                  start := 436345, 
                                                  stop := 436417 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraphs", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 436457, 
                                                          root := ~, 
                                                          start := 436442, 
                                                          stop := 436456 ), 
                                                      rec( 
                                                          content := " is a li\
st of digraphs or a digraph and ", count := [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 436512, 
                                                          root := ~, 
                                                          start := 436497, 
                                                          stop := 436511 ), 
                                                      rec( 
                                                          content := "\n    is\
 a string or an ", count := [ 9, 2, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "IO" ), content := [ rec( content := "\n     http://gap-packages\
.github.io/io/\n", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "URL",
                                                                  next := 78, 
                                                                  root := ~, 
                                                                  start := 17,
                                                                  stop := 77 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          name := "Alt", 
                                                          next := 84, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 83 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "IO", count := [ 9, 2, 6, 3 ], name := \
"PCDATA", root := ~ ) ], count := [ 9, 2, 6, 3 ], name := "Package", 
                                                                  next := 122,
                                                                  root := ~, 
                                                                  start := 101
                                                                    , 
                                                                  stop := 121 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 128, 
                                                          root := ~, 
                                                          start := 84, 
                                                          stop := 127 ), 
                                                      rec( 
                                                          content := " file ob\
ject created using ", count := [ 9, 2, 6, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
File" ), content := 0, count := [ 9, 2, 6, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 436591, 
                                                          root := ~, 
                                                          start := 436566, 
                                                          stop := 436590 ), 
                                                      rec( 
                                                          content := ",\n    t\
hen ", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "W\
riteDigraphs", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 436622, 
                                                          root := ~, 
                                                          start := 436602, 
                                                          stop := 436621 ), 
                                                      rec( 
                                                          content := " writes \
the digraphs to the file represented by\n    ", count := [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 436689, 
                                                          root := ~, 
                                                          start := 436674, 
                                                          stop := 436688 ), 
                                                      rec( 
                                                          content := ".  If th\
e supplied filename ends in one of the extensions\n    ", count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
gz", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 436761, 
                                                          root := ~, 
                                                          start := 436751, 
                                                          stop := 436760 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
bz2", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 436774, 
                                                          root := ~, 
                                                          start := 436763, 
                                                          stop := 436773 ), 
                                                      rec( content := ", or ",
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
xz", count := [ 9, 2, 6, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 436789, 
                                                          root := ~, 
                                                          start := 436779, 
                                                          stop := 436788 ), 
                                                      rec( 
                                                          content := ", then t\
he file will be compressed\n    appropriately.  Excluding these extensions, if\
 the file ends with an\n    extension in the list below, the corresponding gra\
ph format will be used to\n    encode it.  If such an extension is not include\
d, an appropriate format\n    will be chosen intelligently, and an extension a\
ppended, to minimise file\n    size.\n    ", count := [ 9, 2, 6, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 437149, 
                                                          root := ~, 
                                                          start := 437145, 
                                                          stop := 437148 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          content := " TODO: e\
ncode and mode. ", count := [ 9, 2, 6, 4 ], mathmode := "Text", 
                                                          name := "XMLCOMMENT"
                                                            , root := ~ ), 
                                                      rec( 
                                                          content := "\n\n    \
For more verbose information on the progress of the function, set the info\n  \
  level of ", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
nfoDigraphs", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 437299, 
                                                          root := ~, 
                                                          start := 437280, 
                                                          stop := 437298 ), 
                                                      rec( 
                                                          content := " to 1 or\
 higher, using ", count := [ 9, 2, 6, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
etInfoLevel", count := [ 9, 2, 6, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 437341, 
                                                          root := ~, 
                                                          start := 437322, 
                                                          stop := 437340 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 2, 6, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 437346, 
                                                          root := ~, 
                                                          start := 437342, 
                                                          stop := 437345 ), 
                                                      rec( 
                                                          content := "\n\n    \
The currently supported file formats are:\n    ", count := [ 9, 2, 6, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "graph6 (.g6)", count := [ 9, 2, 6, 6 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 6 ], 
                                                                  name := "Mar\
k", next := 437436, root := ~, start := 437411, stop := 437435 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n\tA standard and widely-used format\
 for undirected graphs, with no support\n\tfor loops or multiple edges.  Only \
symmetric graphs are allowed -- each\n\tedge is combined with its converse edg\
e to produce a single undirected\n\tedge.  This format is best used for \"dens\
e\" graphs -- those with many\n\tedges per vertex.\n      ", count := [ 9, 2, \
6, 7 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 9, 2, 
                                                                      6, 7 ], 
                                                                  name := "Ite\
m", next := 437772, root := ~, start := 437443, stop := 437771 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "sparse6 (.s6)", count := [ 9, 2, 6, 8\
 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 
                                                                      8 ], 
                                                                  name := "Mar\
k", next := 437805, root := ~, start := 437779, stop := 437804 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n\tUnlike graph6, sparse6 has suppor\
t for loops and multiple edges.\n\tHowever, its use is still limited to symmet\
ric graphs.  This format is\n\tbetter-suited to \"sparse\" graphs -- those wit\
h few edges per vertex.\n      ", count := [ 9, 2, 6, 9 ], mathmode := "Text",
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 9 ], name := "Item", 
                                                                  next := 4380\
40, root := ~, start := 437812, stop := 438039 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph6 (.d6)", count := [ 9, 2, 6, 10 ], mathmode := "Text", name :=\
 "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 10 ], name := "Mark", 
                                                                  next := 4380\
74, root := ~, start := 438047, stop := 438073 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n\tThis format is based on graph6, but stores direction information -\
\n\ttherefore is not limited to symmetric graphs.  Loops are allowed, but\n\tm\
ultiple edges are not.  Best compression with \"dense\" graphs.\n      ", coun\
t := [ 9, 2, 6, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ 9, 2, 
                                                                      6, 11 ],
                                                                  name := "Ite\
m", next := 438304, root := ~, start := 438081, stop := 438303 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "disparse6 (.ds6)", count := [ 9, 2, 6\
, 12 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                    [ 9, 2, 
                                                                      6, 12 ],
                                                                  name := "Mar\
k", next := 438340, root := ~, start := 438311, stop := 438339 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n\tAny type of digraph can be encode\
d in disparse6: directions, loops, and\n\tmultiple edges are all allowed.  Sim\
ilar to sparse6, this has the best\n\tcompression rate with \"sparse\" graphs.\
\n      ", count := [ 9, 2, 6, 13 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ) ], count := [ 9, 2, 6, 13 ], name := "Item", next := 438552, 
                                                                  root := ~, 
                                                                  start := 438\
347, stop := 438551 ), rec( attributes := rec(  ), content := [ rec( content :\
= "plain text (.txt)", count := [ 9, 2, 6, 14 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ 9, 2, 6, 14 ], name := "Mark", next := 4385\
90, root := ~, start := 438560, stop := 438589 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n\tThis is a human-readable format which stores graphs in the form\n \
       ", count := [ 9, 2, 6, 15 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "0 7  0 8  1\
 7  2 8  3 8  4 8  5 8  6 8", count := [ 9, 2, 6, 15 ], mathmode := "Text", na\
me := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 15 ], mathmode := "Text", 
                                                                          name\
 := "C", next := 438722, root := ~, start := 438677, stop := 438721 ), 
                                                                      rec( 
                                                                          cont\
ent := " i.e. pairs of vertices\n        describing edges in a graph. More spe\
cifically, the vertices making up\n        one edge must be separated by a sin\
gle space, and pairs of vertices must\n        be separated by two spaces. ", 
                                                                          coun\
t := [ 9, 2, 6, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 9, 2, 6, 16 ], mathmode := "Text",
                                                                          name\
 := "P", next := 438946, root := ~, start := 438942, stop := 438945 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n\n        See ", count := [ 9, 2, 6, 16 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ), rec( attributes := rec( Oper := "ReadPlainTextDigrap\
h" ), content := 0, count := [ 9, 2, 6, 16 ], mathmode := "Text", name := "Ref\
", next := 438994, root := ~, start := 438960, stop := 438993 ), rec( content \
:= " for a more flexible way to store\n        digraphs in a plain text file. \
", count := [ 9, 2, 6, 16 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                                        , 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 9, 2, 6, 17 ], mathmode := "Text",
                                                                          name\
 := "P", next := 439071, root := ~, start := 439067, stop := 439070 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n", count := [ 9, 2, 6, 17 ], mathmode := "Text", name := "PCDATA", 
                                                                          root\
 := ~ ), rec( content := "\n        Just so I remember:\n        <C>ReadPlainT\
extDigraph(\"data-local/soc-Epinions1.txt.gz\", \"\\t\", 1, '#');</C>\n", coun\
t := [ 9, 2, 6, 17 ], mathmode := "Text", name := "XMLCOMMENT", root := ~ ), 
                                                                      rec( 
                                                                          cont\
ent := "\n      ", count := [ 9, 2, 6, 17 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 2, 6, 15 ], name := "Item", next := 439208, 
                                                                  root := ~, 
                                                                  start := 438\
597, stop := 439207 ), rec( attributes := rec(  ), content := [ rec( content :\
= "pickled (", count := [ 9, 2, 6, 18 ], mathmode := "Text", name := "PCDATA",
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := ".p", count \
:= [ 9, 2, 6, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\
 := [ 9, 2, 6, 18 ], mathmode := "Text", name := "F", next := 439239, root := \
~, start := 439230, stop := 439238 ), rec( content := " or ", count := [ 9, 2,\
 6, 18 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes :\
= rec(  ), content := [ rec( content := ".pickle", count := [ 9, 2, 6, 18 ], m\
athmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 18 ], 
                                                                          math\
mode := "Text", name := "F", next := 439257, root := ~, start := 439243, stop \
:= 439256 ), rec( content := ")", count := [ 9, 2, 6, 18 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 18 ], name := "Mark", 
                                                                  next := 4392\
65, root := ~, start := 439215, stop := 439264 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n        Digraphs are pickled using the ", count := [ 9, 2, 6, 19 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := \
"Text" ), content := [ rec( attributes := rec( Text := "IO" ), content := [ re\
c( content := "\n     http://gap-packages.github.io/io/\n", count := [ 9, 2, 6\
, 19 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, \
6, 19 ], mathmode := "Text", name := "URL", next := 78, root := ~, start := 17\
, stop := 77 ) ], count := [ 9, 2, 6, 19 ], name := "Alt", next := 84, root :=\
 ~, start := 1, stop := 83 ), rec( attributes := rec( Only := "Text" ), conten\
t := [ rec( attributes := rec(  ), content := [ rec( content := "IO", count :=\
 [ 9, 2, 6, 19 ], name := "PCDATA", root := ~ ) ], count := [ 9, 2, 6, 19 ], n\
ame := "Package", next := 122, root := ~, start := 101, stop := 121 ) ], count\
 := [ 9, 2, 6, 19 ], mathmode := "Text", name := "Alt", next := 128, root := ~
                                                                            , 
                                                                          star\
t := 84, stop := 127 ), rec( content := " package. This is particularly good\n\
        when the ", count := [ 9, 2, 6, 19 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphGroup" ), content :\
= 0, count := [ 9, 2, 6, 19 ], mathmode := "Text", name := "Ref", next := 4394\
01, root := ~, start := 439375, stop := 439400 ), rec( content := " is non-tri\
vial.\n      ", count := [ 9, 2, 6, 19 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ 9, 2, 6, 19 ], name := "Item", next := 439431, 
                                                                  root := ~, 
                                                                  start := 439\
272, stop := 439430 ) ], count := [ 9, 2, 6, 6 ], mathmode := "Text", 
                                                          name := "List", 
                                                          next := 439443, 
                                                          root := ~, 
                                                          start := 437398, 
                                                          stop := 439442 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 9, 2, 6, 21 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> grs := [];;\ngap> grs[1] := Digraph([]);\n<immutable empty digraph with \
0 vertices>\ngap> grs[2] := Digraph([[1, 3], [2], [1, 2]]);\n<immutable digrap\
h with 3 vertices, 5 edges>\ngap> grs[3] := Digraph([\n> [6, 7], [6, 9], [1, 3\
, 4, 5, 8, 9],\n> [1, 2, 3, 4, 5, 6, 7, 10], [1, 5, 6, 7, 10], [2, 4, 5, 9, 10\
],\n> [3, 4, 5, 6, 7, 8, 9, 10], [1, 3, 5, 7, 8, 9], [1, 2, 5],\n> [1, 2, 4, 6\
, 7, 8]]);\n<immutable digraph with 10 vertices, 51 edges>\ngap> filename := C\
oncatenation(DIGRAPHS_Dir(), \"/tst/out/man.d6.gz\");;\ngap> WriteDigraphs(fil\
ename, grs, \"w\");\nIO_OK\ngap> ReadDigraphs(filename);\n[ <immutable empty d\
igraph with 0 vertices>, \n  <immutable digraph with 3 vertices, 5 edges>, \n \
 <immutable digraph with 10 vertices, 51 edges> ]", count := [ 9, 2, 6, 22 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 6, 22 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 440210, 
                                                          root := ~, 
                                                          start := 439449, 
                                                          stop := 440209 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 2, 6, 23 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 6, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 440229, root := ~, 
                                                  start := 436421, 
                                                  stop := 440228 ) ], 
                                          count := [ 9, 2, 6, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 440243, root := ~, 
                                          start := 436330, stop := 440242 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 6, 23 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filename [, deco\
der]", Name := "IteratorFromDigraphFile" ), content := 0, 
                                                  count := [ 9, 2, 7, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 440329, root := ~, 
                                                  start := 440264, 
                                                  stop := 440328 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "An iterat\
or.", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 440363, root := ~, 
                                                  start := 440332, 
                                                  stop := 440362 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 7, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 440402, 
                                                          root := ~, 
                                                          start := 440387, 
                                                          stop := 440401 ), 
                                                      rec( 
                                                          content := " is a st\
ring representing the name of a file containing\n    encoded digraphs, then ",
                                                          count := 
                                                            [ 9, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
teratorFromDigraphFile", count := [ 9, 2, 7, 3 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 7, 3 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 440515, 
                                                          root := ~, 
                                                          start := 440485, 
                                                          stop := 440514 ), 
                                                      rec( 
                                                          content := " returns\
 an iterator\n    for which the value of ", count := [ 9, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              BookName := "ref\
", Oper := "NextIterator" ), content := 0, count := [ 9, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 440604, 
                                                          root := ~, 
                                                          start := 440563, 
                                                          stop := 440603 ), 
                                                      rec( 
                                                          content := " is the\\
n    next digraph encoded in the file.\n    ", count := [ 9, 2, 7, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 440658, 
                                                          root := ~, 
                                                          start := 440654, 
                                                          stop := 440657 ), 
                                                      rec( 
                                                          content := "\n\n    \
If the optional argument ", count := [ 9, 2, 7, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ecoder", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 440703, 
                                                          root := ~, 
                                                          start := 440689, 
                                                          stop := 440702 ), 
                                                      rec( 
                                                          content := " is spec\
ified and is a function\n    which decodes a string into a digraph, then ", 
                                                          count := 
                                                            [ 9, 2, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
teratorFromDigraphFile", count := [ 9, 2, 7, 4 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 7, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 440813, 
                                                          root := ~, 
                                                          start := 440783, 
                                                          stop := 440812 ), 
                                                      rec( 
                                                          content := "\n    wi\
ll use ", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
ecoder", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 440841, 
                                                          root := ~, 
                                                          start := 440827, 
                                                          stop := 440840 ), 
                                                      rec( 
                                                          content := " to deco\
de the digraphs contained in ", count := [ 9, 2, 7, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 7, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 440893, 
                                                          root := ~, 
                                                          start := 440878, 
                                                          stop := 440892 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 7, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 7, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 440903, 
                                                          root := ~, 
                                                          start := 440899, 
                                                          stop := 440902 ), 
                                                      rec( 
                                                          content := "\n\n    \
The purpose of this function is to easily allow looping over digraphs\n    enc\
oded in a file when loading all of the encoded digraphs would require\n    too\
 much memory. ", count := [ 9, 2, 7, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 441081, 
                                                          root := ~, 
                                                          start := 441077, 
                                                          stop := 441080 ), 
                                                      rec( 
                                                          content := "\n\n    \
To see what file types are available, see ", count := [ 9, 2, 7, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "WriteDi\
graphs" ), content := 0, count := [ 9, 2, 7, 6 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 441156, 
                                                          root := ~, 
                                                          start := 441129, 
                                                          stop := 441155 ), 
                                                      rec( 
                                                          content := ".\n\n   \
 ", count := [ 9, 2, 7, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> filename := Concatenation(DIGRAPHS_Dir(), \"/tst/out/man.d6.gz\");;\ngap\
> file := DigraphFile(filename, \"w\");;\ngap> for i in [1 .. 10] do\n>   Writ\
eDigraphs(file, Digraph([[1, 3], [2], [1, 2]]));\n> od;\ngap> IO_Close(file);;\
\ngap> iter := IteratorFromDigraphFile(filename);\n<iterator>\ngap> for x in i\
ter do od;\n", count := [ 9, 2, 7, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 9, 2, 7, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 441505, 
                                                          root := ~, 
                                                          start := 441163, 
                                                          stop := 441504 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 7, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 7, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 441522, root := ~, 
                                                  start := 440366, 
                                                  stop := 441521 ) ], 
                                          count := [ 9, 2, 7, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 441536, root := ~, 
                                          start := 440249, stop := 441535 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 7, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "delimiter1, [del\
imiter2,] offset", Name := "DigraphPlainTextLineEncoder" ), content := 0, 
                                                  count := [ 9, 2, 8, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 441638, root := ~, 
                                                  start := 441557, 
                                                  stop := 441637 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "delimiter1, [del\
imiter2,] offset", Name := "DigraphPlainTextLineDecoder" ), content := 0, 
                                                  count := [ 9, 2, 8, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 441722, root := ~, 
                                                  start := 441641, 
                                                  stop := 441721 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A string.\
", count := [ 9, 2, 8, 5 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                     ], 
                                                  count := [ 9, 2, 8, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 441753, root := ~, 
                                                  start := 441725, 
                                                  stop := 441752 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
se two functions return a function which encodes or decodes a digraph in\n    \
a plain text format.", count := [ 9, 2, 8, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 441878, 
                                                          root := ~, 
                                                          start := 441874, 
                                                          stop := 441877 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ),
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphPlainTextLineEncoder", count := [ 9, 2, 8, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 8, 6 ], mathmode := "Text", 
                                                          name := "A", 
                                                          next := 441918, 
                                                          root := ~, 
                                                          start := 441884, 
                                                          stop := 441917 ), 
                                                      rec( 
                                                          content := " returns\
 a function which takes a single\n    digraph as an argument.  The function re\
turns a string describing the edges\n    of that digraph; each edge is written\
 as a pair of integers separated by the\n    string ", count := [ 9, 2, 8, 6 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
elimiter2", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 442148, 
                                                          root := ~, 
                                                          start := 442131, 
                                                          stop := 442147 ), 
                                                      rec( 
                                                          content := ", and th\
e edges themselves are separated by the\n    string ", count := [ 9, 2, 8, 6 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
elimiter1", count := [ 9, 2, 8, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 442224, 
                                                          root := ~, 
                                                          start := 442207, 
                                                          stop := 442223 ), 
                                                      rec( content := ".  ", 
                                                          count := 
                                                            [ 9, 2, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphPlainTextLineDecoder", count := [ 9, 2, 8, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 8, 6 ], mathmode := "Text", 
                                                          name := "A", 
                                                          next := 442261, 
                                                          root := ~, 
                                                          start := 442227, 
                                                          stop := 442260 ), 
                                                      rec( 
                                                          content := " returns\
 the\n    corresponding decoder function, which takes a string argument in thi\
s format\n    and returns a digraph.", count := [ 9, 2, 8, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 442385, 
                                                          root := ~, 
                                                          start := 442381, 
                                                          stop := 442384 ), 
                                                      rec( 
                                                          content := "\n\n    \
If only one delimiter is passed as an argument to\n    ", count := 
                                                            [ 9, 2, 8, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphPlainTextLineDecoder", count := [ 9, 2, 8, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 8, 7 ], mathmode := "Text", 
                                                          name := "A", 
                                                          next := 442479, 
                                                          root := ~, 
                                                          start := 442445, 
                                                          stop := 442478 ), 
                                                      rec( 
                                                          content := ", it wil\
l return a function which decodes\n    a single edge, returning its contents a\
s a list of integers.", count := [ 9, 2, 8, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 442589, 
                                                          root := ~, 
                                                          start := 442585, 
                                                          stop := 442588 ), 
                                                      rec( 
                                                          content := "\n\n    \
The argument ", count := [ 9, 2, 8, 8 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ffset", count := [ 9, 2, 8, 8 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 442621, 
                                                          root := ~, 
                                                          start := 442608, 
                                                          stop := 442620 ), 
                                                      rec( 
                                                          content := " should \
be an integer, which will describe a\n    number to be added to each vertex be\
fore it is encoded, or after it is\n    decoded.  This may be used, for exampl\
e, to label vertices starting at 0\n    instead of 1.", count := 
                                                            [ 9, 2, 8, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 8, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 442839, 
                                                          root := ~, 
                                                          start := 442835, 
                                                          stop := 442838 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that the number of vertices of a digraph is not stored, and so vertices\n\
    which are not connected to any edge may be lost.\n\n    ", 
                                                          count := 
                                                            [ 9, 2, 8, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[2, 3], [1], [1]]);\n<immutable digraph with 3 vertices, \
4 edges>\ngap> enc := DigraphPlainTextLineEncoder(\"  \", \" \", -1);;\ngap> d\
ec := DigraphPlainTextLineDecoder(\"  \", \" \", 1);;\ngap> enc(gr);\n\"0 1  0\
 2  1 0  2 0\"\ngap> dec(last);\n<immutable digraph with 3 vertices, 4 edges>\
\n", count := [ 9, 2, 8, 10 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 9, 2, 8, 10 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 443306, 
                                                          root := ~, 
                                                          start := 442980, 
                                                          stop := 443305 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 8, 11 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 8, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 443323, root := ~, 
                                                  start := 441756, 
                                                  stop := 443322 ) ], 
                                          count := [ 9, 2, 8, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 443337, root := ~, 
                                          start := 441542, stop := 443336 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 8, 11 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "str", 
                                                      Name := "TournamentLineD\
ecoder" ), content := 0, count := [ 9, 2, 9, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 443404, root := ~, 
                                                  start := 443358, 
                                                  stop := 443403 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 9, 2, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 443436, root := ~, 
                                                  start := 443407, 
                                                  stop := 443435 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function takes a string ", count := [ 9, 2, 9, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tr", count := [ 9, 2, 9, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 443496, 
                                                          root := ~, 
                                                          start := 443486, 
                                                          stop := 443495 ), 
                                                      rec( 
                                                          content := ", decode\
s it, and then returns the\n    tournament [see ", count := [ 9, 2, 9, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsTourn\
ament" ), content := 0, count := [ 9, 2, 9, 3 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 443577, 
                                                          root := ~, 
                                                          start := 443551, 
                                                          stop := 443576 ), 
                                                      rec( 
                                                          content := "] which \
it defines, according to\n    the following rules. ", count := [ 9, 2, 9, 3 ],
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 443639, 
                                                          root := ~, 
                                                          start := 443635, 
                                                          stop := 443638 ), 
                                                      rec( 
                                                          content := "\n\n    \
The characters of the string ", count := [ 9, 2, 9, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tr", count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 443684, 
                                                          root := ~, 
                                                          start := 443674, 
                                                          stop := 443683 ), 
                                                      rec( 
                                                          content := " represe\
nt the entries in the upper\n    triangle of a tournament's adjacency matrix. \
The number of vertices\n    ", count := [ 9, 2, 9, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 443804, 
                                                          root := ~, 
                                                          start := 443796, 
                                                          stop := 443803 ), 
                                                      rec( 
                                                          content := " will be\
 detected from the length of the string and will be as\n    large as possible.\
  ", count := [ 9, 2, 9, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 443895, 
                                                          root := ~, 
                                                          start := 443891, 
                                                          stop := 443894 ), 
                                                      rec( 
                                                          content := "\n\n    \
The first character represents the possible edge ", count := [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
 -> 2", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 443963, 
                                                          root := ~, 
                                                          start := 443950, 
                                                          stop := 443962 ), 
                                                      rec( 
                                                          content := ", the se\
cond\n    represents ", count := [ 9, 2, 9, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
 -> 3", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 444004, 
                                                          root := ~, 
                                                          start := 443991, 
                                                          stop := 444003 ), 
                                                      rec( 
                                                          content := " and so \
on until ", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
 -> n", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 444034, 
                                                          root := ~, 
                                                          start := 444021, 
                                                          stop := 444033 ), 
                                                      rec( 
                                                          content := "; then t\
he following\n    character represents ", count := [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
 -> 3", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 444093, 
                                                          root := ~, 
                                                          start := 444080, 
                                                          stop := 444092 ), 
                                                      rec( 
                                                          content := ", and so\
 on up to the character which\n    represents the edge ", count := 
                                                            [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
-1 -> n", count := [ 9, 2, 9, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 444170, 
                                                          root := ~, 
                                                          start := 444155, 
                                                          stop := 444169 ), 
                                                      rec( content := ". ", 
                                                          count := 
                                                            [ 9, 2, 9, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 444176, 
                                                          root := ~, 
                                                          start := 444172, 
                                                          stop := 444175 ), 
                                                      rec( 
                                                          content := "\n\n    \
If a character of the string with corresponding edge ", count := 
                                                            [ 9, 2, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 -> j", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 444248, 
                                                          root := ~, 
                                                          start := 444235, 
                                                          stop := 444247 ), 
                                                      rec( 
                                                          content := " is equa\
l\n    to ", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 444273, 
                                                          root := ~, 
                                                          start := 444265, 
                                                          stop := 444272 ), 
                                                      rec( 
                                                          content := ", then t\
he edge ", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 -> j", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 444302, 
                                                          root := ~, 
                                                          start := 444289, 
                                                          stop := 444301 ), 
                                                      rec( 
                                                          content := " is pres\
ent in the tournament.\n    Otherwise, the edge ", count := [ 9, 2, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 -> j", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 9, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 444370, 
                                                          root := ~, 
                                                          start := 444357, 
                                                          stop := 444369 ), 
                                                      rec( 
                                                          content := " is pres\
ent instead.  In this way, all the\n    possible edges are encoded one-by-one.\
\n\n    ", count := [ 9, 2, 9, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := TournamentLineDecoder(\"100001\");\n<immutable digraph with 4 vert\
ices, 6 edges>\ngap> OutNeighbours(gr);\n[ [ 2 ], [  ], [ 1, 2, 4 ], [ 1, 2 ] \
]\n", count := [ 9, 2, 9, 7 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ 9, 2, 9, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 444645, 
                                                          root := ~, 
                                                          start := 444461, 
                                                          stop := 444644 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 9, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 9, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 444662, root := ~, 
                                                  start := 443439, 
                                                  stop := 444661 ) ], 
                                          count := [ 9, 2, 9, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 444676, root := ~, 
                                          start := 443343, stop := 444675 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 9, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "str", 
                                                      Name := "AdjacencyMatrix\
UpperTriangleLineDecoder" ), content := 0, count := [ 9, 2, 10, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 444761, root := ~, 
                                                  start := 444697, 
                                                  stop := 444760 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 9, 2, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 444793, root := ~, 
                                                  start := 444764, 
                                                  stop := 444792 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    Thi\
s function takes a string ", count := [ 9, 2, 10, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tr", count := [ 9, 2, 10, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 444853, 
                                                          root := ~, 
                                                          start := 444843, 
                                                          stop := 444852 ), 
                                                      rec( 
                                                          content := ", decode\
s it, and then returns the\n    topologically sorted digraph [see ", 
                                                          count := 
                                                            [ 9, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
TopologicalSort" ), content := 0, count := [ 9, 2, 10, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 444962, 
                                                          root := ~, 
                                                          start := 444926, 
                                                          stop := 444961 ), 
                                                      rec( 
                                                          content := "]\n    w\
hich it defines, according to the following rules. ", count := [ 9, 2, 10, 3 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 445024, 
                                                          root := ~, 
                                                          start := 445020, 
                                                          stop := 445023 ), 
                                                      rec( 
                                                          content := "\n\n    \
The characters of the string ", count := [ 9, 2, 10, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tr", count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 445069, 
                                                          root := ~, 
                                                          start := 445059, 
                                                          stop := 445068 ), 
                                                      rec( 
                                                          content := " represe\
nt the entries in the upper\n    triangle of a digraph's adjacency matrix. The\
 number of vertices ", count := [ 9, 2, 10, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
", count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 10, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 445182, 
                                                          root := ~, 
                                                          start := 445174, 
                                                          stop := 445181 ), 
                                                      rec( 
                                                          content := "\n    wi\
ll be detected from the length of the string and will be as large as\n    poss\
ible.  ", count := [ 9, 2, 10, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 445277, 
                                                          root := ~, 
                                                          start := 445273, 
                                                          stop := 445276 ), 
                                                      rec( 
                                                          content := "\n\n    \
The first character represents the possible edge ", count := [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
 -> 2", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 445345, 
                                                          root := ~, 
                                                          start := 445332, 
                                                          stop := 445344 ), 
                                                      rec( 
                                                          content := ", the se\
cond\n    represents ", count := [ 9, 2, 10, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
 -> 3", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 445386, 
                                                          root := ~, 
                                                          start := 445373, 
                                                          stop := 445385 ), 
                                                      rec( 
                                                          content := " and so \
on until ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
 -> n", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 445416, 
                                                          root := ~, 
                                                          start := 445403, 
                                                          stop := 445415 ), 
                                                      rec( 
                                                          content := "; then t\
he following\n    character represents ", count := [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
 -> 3", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 445475, 
                                                          root := ~, 
                                                          start := 445462, 
                                                          stop := 445474 ), 
                                                      rec( 
                                                          content := ", and so\
 on up to the character which\n    represents the edge ", count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "n\
-1 -> n", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 445552, 
                                                          root := ~, 
                                                          start := 445537, 
                                                          stop := 445551 ), 
                                                      rec( 
                                                          content := ".  If a \
character of the string with\n    corresponding edge ", count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
 -> j", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 445625, 
                                                          root := ~, 
                                                          start := 445612, 
                                                          stop := 445624 ), 
                                                      rec( 
                                                          content := " is equa\
l to ", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 9, 2, 10, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 445646, 
                                                          root := ~, 
                                                          start := 445638, 
                                                          stop := 445645 ), 
                                                      rec( 
                                                          content := ", then t\
his edge is\n    present in the digraph. Otherwise, it is not present.  In thi\
s way, all the\n    possible edges are encoded one-by-one. ", 
                                                          count := 
                                                            [ 9, 2, 10, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 445793, 
                                                          root := ~, 
                                                          start := 445789, 
                                                          stop := 445792 ), 
                                                      rec( 
                                                          content := "\n\n    \
In particular, note that there exists no edge ", count := [ 9, 2, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
i, j]", count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 445858, 
                                                          root := ~, 
                                                          start := 445845, 
                                                          stop := 445857 ), 
                                                      rec( content := " if ", 
                                                          count := 
                                                            [ 9, 2, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "j\
 \\leq\n      i", count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ 9, 2, 10, 6 ], mathmode := "Text", name := "M", 
                                                          next := 445883, 
                                                          root := ~, 
                                                          start := 445862, 
                                                          stop := 445882 ), 
                                                      rec( 
                                                          content := ".  In or\
der words, the digraph will be topologically sorted.\n\n    ", 
                                                          count := 
                                                            [ 9, 2, 10, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := AdjacencyMatrixUpperTriangleLineDecoder(\"100001\");\n<immutable d\
igraph with 4 vertices, 2 edges>\ngap> OutNeighbours(gr);\n[ [ 2 ], [  ], [ 4 \
], [  ] ]\ngap> gr := AdjacencyMatrixUpperTriangleLineDecoder(\"111111x111\");\
\n<immutable digraph with 5 vertices, 9 edges>\ngap> OutNeighbours(gr);\n[ [ 2\
, 3, 4, 5 ], [ 3, 4 ], [ 4, 5 ], [ 5 ], [  ] ]\n", count := [ 9, 2, 10, 7 ], 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 10, 7 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 446328, 
                                                          root := ~, 
                                                          start := 445949, 
                                                          stop := 446327 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 10, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 10, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 446345, root := ~, 
                                                  start := 444796, 
                                                  stop := 446344 ) ], 
                                          count := [ 9, 2, 10, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 446359, root := ~, 
                                          start := 444682, stop := 446358 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 10, 8 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "str", 
                                                      Name := "TCodeDecoder" )
                                                    , content := 0, 
                                                  count := [ 9, 2, 11, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 446417, root := ~, 
                                                  start := 446380, 
                                                  stop := 446416 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A digraph\
.", count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 9, 2, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 446449, root := ~, 
                                                  start := 446420, 
                                                  stop := 446448 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    If \
", count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tr", count := [ 9, 2, 11, 3 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 11, 3 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 446483, 
                                                          root := ~, 
                                                          start := 446473, 
                                                          stop := 446482 ), 
                                                      rec( 
                                                          content := " is a st\
ring consisting of at least two non-negative integers\n    separated by spaces\
, then this function will attempt to return the digraph\n    which it defines \
as a TCode string. ", count := [ 9, 2, 11, 3 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 446668, 
                                                          root := ~, 
                                                          start := 446664, 
                                                          stop := 446667 ), 
                                                      rec( 
                                                          content := "\n\n    \
The first integer of the string defines the number of vertices ", 
                                                          count := 
                                                            [ 9, 2, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "v\
", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 446745, 
                                                          root := ~, 
                                                          start := 446737, 
                                                          stop := 446744 ), 
                                                      rec( 
                                                          content := " in\n   \
 the digraph, and the second defines the number of edges ", 
                                                          count := 
                                                            [ 9, 2, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "e\
", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 446817, 
                                                          root := ~, 
                                                          start := 446809, 
                                                          stop := 446816 ), 
                                                      rec( 
                                                          content := ".  The\n\
    following ", count := [ 9, 2, 11, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
e", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 446847, 
                                                          root := ~, 
                                                          start := 446838, 
                                                          stop := 446846 ), 
                                                      rec( 
                                                          content := " integer\
s should be vertex numbers in the range ", count := [ 9, 2, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
0 ..\n      v-1]", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ 9, 2, 11, 4 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 446918, 
                                                          root := ~, 
                                                          start := 446895, 
                                                          stop := 446917 ), 
                                                      rec( 
                                                          content := ". These \
integers are read in pairs and define the digraph's\n    edges.  This function\
 will return an error if ", count := [ 9, 2, 11, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "s\
tr", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 447038, 
                                                          root := ~, 
                                                          start := 447028, 
                                                          stop := 447037 ), 
                                                      rec( 
                                                          content := " has few\
er than\n    ", count := [ 9, 2, 11, 4 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "2\
e+2", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 11, 4 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 447069, 
                                                          root := ~, 
                                                          start := 447058, 
                                                          stop := 447068 ), 
                                                      rec( 
                                                          content := " entries\
. ", count := [ 9, 2, 11, 4 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 447083, 
                                                          root := ~, 
                                                          start := 447079, 
                                                          stop := 447082 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that the vertex numbers will be incremented by 1 in the digraph\n    retu\
rned.  Hence the string fragment ", count := [ 9, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "0\
 6", count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 447209, 
                                                          root := ~, 
                                                          start := 447199, 
                                                          stop := 447208 ), 
                                                      rec( 
                                                          content := " will de\
scribe the edge\n    ", count := [ 9, 2, 11, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "[\
1,7]", count := [ 9, 2, 11, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 447249, 
                                                          root := ~, 
                                                          start := 447237, 
                                                          stop := 447248 ), 
                                                      rec( 
                                                          content := ".\n    "
                                                            , 
                                                          count := 
                                                            [ 9, 2, 11, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := TCodeDecoder(\"3 2 0 2 2 1\");\n<immutable digraph with 3 vertices\
, 2 edges>\ngap> OutNeighbours(gr);\n[ [ 3 ], [  ], [ 2 ] ]\ngap> gr := TCodeD\
ecoder(\"12 3 0 10 5 2 8 8\");\n<immutable digraph with 12 vertices, 3 edges>\
\ngap> OutNeighbours(gr);\n[ [ 11 ], [  ], [  ], [  ], [  ], [ 3 ], [  ], [  ]\
, [ 9 ], [  ], \n  [  ], [  ] ]\n", count := [ 9, 2, 11, 6 ], name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 11, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 447617, 
                                                          root := ~, 
                                                          start := 447255, 
                                                          stop := 447616 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 11, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 11, 3 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 447634, root := ~, 
                                                  start := 446452, 
                                                  stop := 447633 ) ], 
                                          count := [ 9, 2, 11, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 447648, root := ~, 
                                          start := 446365, stop := 447647 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 11, 7 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "digraph", 
                                                      Name := "PlainTextString\
" ), content := 0, count := [ 9, 2, 12, 2 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 447713, root := ~, 
                                                  start := 447669, 
                                                  stop := 447712 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "s", 
                                                      Name := "DigraphFromPlai\
nTextString" ), content := 0, count := [ 9, 2, 12, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 447765, root := ~, 
                                                  start := 447716, 
                                                  stop := 447764 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "A string.\
", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ) ], 
                                                  count := [ 9, 2, 12, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Returns", 
                                                  next := 447796, root := ~, 
                                                  start := 447768, 
                                                  stop := 447795 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( content := "\n    ",
                                                          count := 
                                                            [ 9, 2, 12, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "P\
lainTextString", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "A", 
                                                          next := 447839, 
                                                          root := ~, 
                                                          start := 447817, 
                                                          stop := 447838 ), 
                                                      rec( 
                                                          content := " takes a\
 single digraph, and returns a string\n    describing the edges of that digrap\
h.  ", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphFromPlainTextString", count := [ 9, 2, 12, 5 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 12, 5 ], mathmode := "Text", 
                                                          name := "A", 
                                                          next := 447961, 
                                                          root := ~, 
                                                          start := 447928, 
                                                          stop := 447960 ), 
                                                      rec( 
                                                          content := "\n    ta\
kes such a string and returns the digraph which it describes.  Each edge\n    \
is written as a pair of integers separated by a single space.  The edges\n    \
themselves are separated by a double space.  Vertex numbers are reduced by\n  \
  1 when they are encoded, so that vertices in the string are labelled\n    st\
arting at 0.", count := [ 9, 2, 12, 5 ], mathmode := "Text", name := "PCDATA",
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 12, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 448292, 
                                                          root := ~, 
                                                          start := 448288, 
                                                          stop := 448291 ), 
                                                      rec( 
                                                          content := "\n\n    \
Note that the number of vertices of a digraph is not stored, and so vertices\n\
    which are not connected to any edge may be lost.", count := 
                                                            [ 9, 2, 12, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 448431, 
                                                          root := ~, 
                                                          start := 448427, 
                                                          stop := 448430 ), 
                                                      rec( 
                                                          content := "\n\n    \
\n    The operation ", count := [ 9, 2, 12, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphFromPlainTextString", count := [ 9, 2, 12, 7 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 12, 7 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 448489, 
                                                          root := ~, 
                                                          start := 448456, 
                                                          stop := 448488 ), 
                                                      rec( 
                                                          content := "\n    ta\
kes an optional first argument ", count := [ 9, 2, 12, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsMutab\
leDigraph" ), content := 0, count := [ 9, 2, 12, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 448557, 
                                                          root := ~, 
                                                          start := 448527, 
                                                          stop := 448556 ), 
                                                      rec( 
                                                          content := "\n    or\
 ", count := [ 9, 2, 12, 7 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                         ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsImmut\
ableDigraph" ), content := 0, count := [ 9, 2, 12, 7 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 448597, 
                                                          root := ~, 
                                                          start := 448565, 
                                                          stop := 448596 ), 
                                                      rec( 
                                                          content := ", which \
specifies whether the output digraph shall\n    be mutable or immutable. If no\
 first argument is provided, then an immutable\n    digraph is returned by def\
ault.\n\n    ", count := [ 9, 2, 12, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[2, 3], [1], [1]]);\n<immutable digraph with 3 vertices, \
4 edges>\ngap> PlainTextString(gr);\n\"0 1  0 2  1 0  2 0\"\ngap> DigraphFromP\
lainTextString(last);\n<immutable digraph with 3 vertices, 4 edges>\n", 
                                                                  count := 
                                                                    [ 9, 2, 
                                                                      12, 8 ],
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 12, 8 ], mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 449018, 
                                                          root := ~, 
                                                          start := 448770, 
                                                          stop := 449017 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 12, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 12, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 449035, root := ~, 
                                                  start := 447799, 
                                                  stop := 449034 ) ], 
                                          count := [ 9, 2, 12, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 449049, root := ~, 
                                          start := 447654, stop := 449048 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 12, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filename, digrap\
h, delimiter, offset", Name := "WritePlainTextDigraph" ), content := 0, 
                                                  count := [ 9, 2, 13, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Func", 
                                                  next := 449149, root := ~, 
                                                  start := 449070, 
                                                  stop := 449148 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filename, delimi\
ter, offset, ignore", Name := "ReadPlainTextDigraph" ), content := 0, 
                                                  count := [ 9, 2, 13, 4 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 449229, root := ~, 
                                                  start := 449152, 
                                                  stop := 449228 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
se functions write and read a single digraph in a human-readable plain\n    te\
xt format as follows: each line contains a single edge, and each edge is\n    \
written as a pair of integers separated by the string ", count := 
                                                            [ 9, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
elimiter", count := [ 9, 2, 13, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 449477, 
                                                          root := ~, 
                                                          start := 449461, 
                                                          stop := 449476 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 2, 13, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 449482, 
                                                          root := ~, 
                                                          start := 449478, 
                                                          stop := 449481 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 449503, 
                                                          root := ~, 
                                                          start := 449488, 
                                                          stop := 449502 ), 
                                                      rec( 
                                                          content := " should \
be the name of a file which will be written to or\n    read from, and ", 
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ffset", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 449593, 
                                                          root := ~, 
                                                          start := 449580, 
                                                          stop := 449592 ), 
                                                      rec( 
                                                          content := " should \
be an integer which is added to each\n    vertex number as it is written or re\
ad.  For example, if\n    ", count := [ 9, 2, 13, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "W\
ritePlainTextDigraph", count := [ 9, 2, 13, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 449731, 
                                                          root := ~, 
                                                          start := 449703, 
                                                          stop := 449730 ), 
                                                      rec( 
                                                          content := " is call\
ed with ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ffset", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 449760, 
                                                          root := ~, 
                                                          start := 449747, 
                                                          stop := 449759 ), 
                                                      rec( content := " ", 
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "-\
1", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 449770, 
                                                          root := ~, 
                                                          start := 449761, 
                                                          stop := 449769 ), 
                                                      rec( 
                                                          content := ", then\n\
    the vertices will be numbered in the file starting from 0 instead of 1 -\n\
    ", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
eadPlainTextDigraph", count := [ 9, 2, 13, 6 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 13, 6 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 449885, 
                                                          root := ~, 
                                                          start := 449858, 
                                                          stop := 449884 ), 
                                                      rec( 
                                                          content := " would t\
hen need to be called with ", count := [ 9, 2, 13, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "o\
ffset", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 449933, 
                                                          root := ~, 
                                                          start := 449920, 
                                                          stop := 449932 ), 
                                                      rec( 
                                                          content := "\n    ",
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "1\
", count := [ 9, 2, 13, 6 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 449946, 
                                                          root := ~, 
                                                          start := 449938, 
                                                          stop := 449945 ), 
                                                      rec( 
                                                          content := " to conv\
ert back to the original graph.", count := [ 9, 2, 13, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 13, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 449989, 
                                                          root := ~, 
                                                          start := 449985, 
                                                          stop := 449988 ), 
                                                      rec( 
                                                          content := "\n\n    \
", count := [ 9, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", root := ~ )
                                                        , 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "i\
gnore", count := [ 9, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 13, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 450008, 
                                                          root := ~, 
                                                          start := 449995, 
                                                          stop := 450007 ), 
                                                      rec( 
                                                          content := " should \
be a list of characters which will be ignored when\n    reading the graph.\n  \
  ", count := [ 9, 2, 13, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[1, 2, 3], [1, 1], [2]]);\n<immutable multidigraph with 3\
 vertices, 6 edges>\ngap> filename := Concatenation(DIGRAPHS_Dir(), \"/tst/out\
/plain.txt\");;\ngap> WritePlainTextDigraph(filename, gr, \",\", -1);\ngap> Re\
adPlainTextDigraph(filename, \",\", 1, ['/', '%']);\n<immutable multidigraph w\
ith 3 vertices, 6 edges>\n", count := [ 9, 2, 13, 8 ], name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 13, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 450451, 
                                                          root := ~, 
                                                          start := 450094, 
                                                          stop := 450450 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 13, 9 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 13, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 450468, root := ~, 
                                                  start := 449232, 
                                                  stop := 450467 ) ], 
                                          count := [ 9, 2, 13, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 450482, root := ~, 
                                          start := 449055, stop := 450481 ), 
                                      rec( content := "\n\n    ", 
                                          count := [ 9, 2, 13, 9 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  attributes := 
                                                    rec( 
                                                      Arg := "filename, digrap\
h", Name := "WriteDIMACSDigraph" ), content := 0, count := [ 9, 2, 14, 2 ], 
                                                  mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 450560, root := ~, 
                                                  start := 450503, 
                                                  stop := 450559 ), 
                                              rec( 
                                                  attributes := 
                                                    rec( Arg := "filename", 
                                                      Name := "ReadDIMACSDigra\
ph" ), content := 0, count := [ 9, 2, 14, 4 ], mathmode := "Text", 
                                                  name := "Oper", 
                                                  next := 450610, root := ~, 
                                                  start := 450563, 
                                                  stop := 450609 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n    The\
se operations write or read the single symmetric digraph ", 
                                                          count := 
                                                            [ 9, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 450705, 
                                                          root := ~, 
                                                          start := 450691, 
                                                          stop := 450704 ), 
                                                      rec( 
                                                          content := "\n    to\
 or from a file in DIMACS format, as appropriate. The operation\n    ", 
                                                          count := 
                                                            [ 9, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "W\
riteDIMACSDigraph", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ 9, 2, 14, 5 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 450805, 
                                                          root := ~, 
                                                          start := 450780, 
                                                          stop := 450804 ), 
                                                      rec( 
                                                          content := " records\
 the vertices and edges of ", count := [ 9, 2, 14, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 450854, 
                                                          root := ~, 
                                                          start := 450840, 
                                                          stop := 450853 ), 
                                                      rec( 
                                                          content := ".\n    T\
he vertex labels of ", count := [ 9, 2, 14, 5 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "d\
igraph", count := [ 9, 2, 14, 5 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 450895, 
                                                          root := ~, 
                                                          start := 450881, 
                                                          stop := 450894 ), 
                                                      rec( 
                                                          content := " will be\
 recorded only if they are\n    integers. See ", count := [ 9, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsSymme\
tricDigraph" ), content := 0, count := [ 9, 2, 14, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 450980, 
                                                          root := ~, 
                                                          start := 450948, 
                                                          stop := 450979 ), 
                                                      rec( content := " and ",
                                                          count := 
                                                            [ 9, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ 9, 2, 14, 5 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 451024, 
                                                          root := ~, 
                                                          start := 450985, 
                                                          stop := 451023 ), 
                                                      rec( content := ".", 
                                                          count := 
                                                            [ 9, 2, 14, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 451029, 
                                                          root := ~, 
                                                          start := 451025, 
                                                          stop := 451028 ), 
                                                      rec( 
                                                          content := "\n\n    \
The first argument ", count := [ 9, 2, 14, 6 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 451069, 
                                                          root := ~, 
                                                          start := 451054, 
                                                          stop := 451068 ), 
                                                      rec( 
                                                          content := " should \
be the name of the file which will\n    be written to or read from.  A file ca\
n contain one symmetric digraph in\n    DIMACS format. If ", 
                                                          count := 
                                                            [ 9, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "f\
ilename", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "A", 
                                                          next := 451226, 
                                                          root := ~, 
                                                          start := 451211, 
                                                          stop := 451225 ), 
                                                      rec( 
                                                          content := " ends in\
 one of ", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
gz", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 451252, 
                                                          root := ~, 
                                                          start := 451242, 
                                                          stop := 451251 ), 
                                                      rec( content := ", ", 
                                                          count := 
                                                            [ 9, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
bz2", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 451265, 
                                                          root := ~, 
                                                          start := 451254, 
                                                          stop := 451264 ), 
                                                      rec( 
                                                          content := ",\n    o\
r ", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := ".\
xz", count := [ 9, 2, 14, 6 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ 9, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 451284, 
                                                          root := ~, 
                                                          start := 451274, 
                                                          stop := 451283 ), 
                                                      rec( 
                                                          content := ", then t\
he file is compressed, or decompressed, appropriately.\n    ", 
                                                          count := 
                                                            [ 9, 2, 14, 6 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 14, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 451355, 
                                                          root := ~, 
                                                          start := 451351, 
                                                          stop := 451354 ), 
                                                      rec( 
                                                          content := "\n\n    \
The DIMACS format is described as follows.  Each line in the DIMACS file has\n\
    one of four types:\n    ", count := [ 9, 2, 14, 7 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "\n        A line beginning with ", 
                                                                          coun\
t := [ 9, 2, 14, 9 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "c", count := [ 9, 2, 14, 9 ],\
 mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 9 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "C", next := 451523, root := ~, start := 451515, stop \
:= 451522 ), rec( content := " and followed by any number of characters\n     \
   is a comment line, and is ignored.\n      ", count := [ 9, 2, 14, 9 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 9 ], 
                                                                  name := "Ite\
m", next := 451621, root := ~, start := 451478, stop := 451620 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        A line beginning with ", 
                                                                          coun\
t := [ 9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "p", count := [ 9, 2, 14, 11 ]\
, mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 11\
 ], mathmode := "Text", name := "C", next := 451673, root := ~, start := 45166\
5, stop := 451672 ), rec( content := " defines the numbers of vertices and edg\
es\n        the digraph.  This line has the format ", count := [ 9, 2, 14, 11 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "p edge <nr_vertices>\n          <nr_edges>", count :\
= [ 9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count\
 := [ 9, 2, 14, 11 ], mathmode := "Text", name := "C", next := 451823, root :=\
 ~, start := 451763, stop := 451822 ), rec( content := ", where ", count := [ \
9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\
utes := rec(  ), content := [ rec( content := "<nr_vertices>", count := [ 9, 2\
, 14, 11 ], mathmode := "Text", name := "PCDATA", next := 6, root := ~ ) ], 
                                                                          coun\
t := [ 9, 2, 14, 11 ], mathmode := "Text", name := "C", next := 451857, root :\
= ~, start := 451831, stop := 451856 ), rec( content := " and\n        ", coun\
t := [ 9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "<nr_edges>", count := [ 9, 2,\
 14, 11 ], mathmode := "Text", name := "PCDATA", next := 6, root := ~ ) ], 
                                                                          coun\
t := [ 9, 2, 14, 11 ], mathmode := "Text", name := "C", next := 451893, root :\
= ~, start := 451870, stop := 451892 ), rec( content := " are replaced by the \
relevant integers. There\n        must be exactly one such line in the file, a\
nd it must occur before any\n        of the following kinds of line.", count :\
= [ 9, 2, 14, 11 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := 0, count := [ 9, 2, 14, 12 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "P", next := 452062, root := ~, start := 452058, stop := 452061 ), 
                                                                      rec( 
                                                                          cont\
ent := "\n\n        Although it is required to be present, the value of\n     \
   ", count := [ 9, 2, 14, 12 ], mathmode := "Text", name := "PCDATA", root :=\
 ~ ), rec( attributes := rec(  ), content := [ rec( content := "<nr_edges>", c\
ount := [ 9, 2, 14, 12 ], mathmode := "Text", name := "PCDATA", next := 6, roo\
t := ~ ) ], count := [ 9, 2, 14, 12 ], mathmode := "Text", name := "C", next :\
= 452155, root := ~, start := 452132, stop := 452154 ), rec( content := " will\
 be ignored. The correct number of edges\n        will be deduced from the res\
t of the information in the file.\n      ", count := [ 9, 2, 14, 12 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 11 ], 
                                                                  name := "Ite\
m", next := 452284, root := ~, start := 451628, stop := 452283 ), 
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "\n        A line of the form ", count\
 := [ 9, 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "e <v> <w>", count := [ 9, 2, \
14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2\
, 14, 14 ], mathmode := "Text", name := "C", next := 452353, root := ~, start \
:= 452325, stop := 452352 ), rec( content := ", where ", count := [ 9, 2, 14, \
14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := re\
c(  ), content := [ rec( content := "<v>", count := [ 9, 2, 14, 14 ], mathmode\
 := "Text", name := "PCDATA", next := 6, root := ~ ) ], count := [ 9, 2, 14, 1\
4 ], mathmode := "Text", name := "C", next := 452377, root := ~, start := 4523\
61, stop := 452376 ), rec( content := "\n        and ", count := [ 9, 2, 14, 1\
4 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec\
(  ), content := [ rec( content := "<w>", count := [ 9, 2, 14, 14 ], mathmode \
:= "Text", name := "PCDATA", next := 6, root := ~ ) ], count := [ 9, 2, 14, 14\
 ], mathmode := "Text", name := "C", next := 452406, root := ~, start := 45239\
0, stop := 452405 ), rec( content := " are integers in the range ", count := 
                                                                            [ \
9, 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attrib\
utes := rec(  ), content := [ rec( content := "[1 ..\n          <nr_vertices>]\
", count := [ 9, 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ \
) ], count := [ 9, 2, 14, 14 ], mathmode := "Text", name := "C", next := 45247\
6, root := ~, start := 452433, stop := 452475 ), rec( content := ", specifies \
that there is a (symmetric) edge\n        in the digraph between the vertices \
", count := [ 9, 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ 
                                                                         ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "<v>", count := [ 9, 2, 14, 14\
 ], mathmode := "Text", name := "PCDATA", next := 6, root := ~ ) ], count := 
                                                                            [ \
9, 2, 14, 14 ], mathmode := "Text", name := "C", next := 452581, root := ~, 
                                                                          star\
t := 452565, stop := 452580 ), rec( content := " and\n        ", count := [ 9,\
 2, 14, 14 ], mathmode := "Text", name := "PCDATA", root := ~ ), rec( attribut\
es := rec(  ), content := [ rec( content := "<w>", count := [ 9, 2, 14, 14 ], \
mathmode := "Text", name := "PCDATA", next := 6, root := ~ ) ], count := [ 9, \
2, 14, 14 ], mathmode := "Text", name := "C", next := 452610, root := ~, start\
 := 452594, stop := 452609 ), rec( content := ". A symmetric edge only needs t\
o be defined once; an\n        additional line ", count := [ 9, 2, 14, 14 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "e <v> <w>", count := [ 9, 2, 14, 14 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 14 ], mathmode :=\
 "Text", name := "C", next := 452715, root := ~, start := 452687, stop := 4527\
14 ), rec( content := ", or ", count := [ 9, 2, 14, 14 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( conte\
nt := "e <w>\n          <v>", count := [ 9, 2, 14, 14 ], mathmode := "Text", n\
ame := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 14 ], mathmode := "Text",
                                                                          name\
 := "C", next := 452758, root := ~, start := 452720, stop := 452757 ), 
                                                                      rec( 
                                                                          cont\
ent := ", will be interpreted as an additional, multiple, edge.\n        Loops\
 are permitted.\n      ", count := [ 9, 2, 14, 14 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 14 ], name := "Item", 
                                                                  next := 4528\
56, root := ~, start := 452291, stop := 452855 ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "\n        A line of the form ", count := [ 9, 2, 14, 16 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :=\
 [ rec( content := "n <v> <label>", count := [ 9, 2, 14, 16 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 16 ], mathmode := "\
Text", name := "C", next := 452929, root := ~, start := 452897, stop := 452928\
 ), rec( content := ", where\n        ", count := [ 9, 2, 14, 16 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content :\
= [ rec( content := "<v>", count := [ 9, 2, 14, 16 ], mathmode := "Text", name\
 := "PCDATA", next := 6, root := ~ ) ], count := [ 9, 2, 14, 16 ], mathmode :=\
 "Text", name := "C", next := 452961, root := ~, start := 452945, stop := 4529\
60 ), rec( content := " is an integer in the range ", count := [ 9, 2, 14, 16 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "[1 ..\n          <nr_vertices>]", count := [ 9, 2, 1\
4, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2,\
 14, 16 ], mathmode := "Text", name := "C", next := 453032, root := ~, start :\
= 452989, stop := 453031 ), rec( content := " and ", count := [ 9, 2, 14, 16 ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( content := "<label>", count := [ 9, 2, 14, 16 ], mathmode := "Te\
xt", name := "PCDATA", next := 6, root := ~ ) ], count := [ 9, 2, 14, 16 ], 
                                                                          math\
mode := "Text", name := "C", next := 453057, root := ~, start := 453037, stop \
:= 453056 ), rec( content := " is an integer,\n        signifies that the vert\
ex ", count := [ 9, 2, 14, 16 ], mathmode := "Text", name := "PCDATA", root :=\
 ~ ), rec( attributes := rec(  ), content := [ rec( content := "<v>", count :=\
 [ 9, 2, 14, 16 ], mathmode := "Text", name := "PCDATA", next := 6, root := ~ \
) ], count := [ 9, 2, 14, 16 ], mathmode := "Text", name := "C", next := 45312\
3, root := ~, start := 453107, stop := 453122 ), rec( content := " has the lab\
el\n        ", count := [ 9, 2, 14, 16 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ), rec( attributes := rec(  ), content := [ rec( content := "<label>", c\
ount := [ 9, 2, 14, 16 ], mathmode := "Text", name := "PCDATA", next := 6, roo\
t := ~ ) ], count := [ 9, 2, 14, 16 ], mathmode := "Text", name := "C", next :\
= 453166, root := ~, start := 453146, stop := 453165 ), rec( content := " in t\
he digraph. If a label is not specified for a\n        vertex, then ", count :\
= [ 9, 2, 14, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ), 
                                                                      rec( 
                                                                          attr\
ibutes := rec(  ), content := [ rec( content := "ReadDIMACSDigraph", count := \
[ 9, 2, 14, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count :\
= [ 9, 2, 14, 16 ], mathmode := "Text", name := "C", next := 453262, root := ~
                                                                            , 
                                                                          star\
t := 453238, stop := 453261 ), rec( content := " will assign the label\n      \
  ", count := [ 9, 2, 14, 16 ], mathmode := "Text", name := "PCDATA", root := \
~ ), rec( attributes := rec(  ), content := [ rec( content := "1", count := [ \
9, 2, 14, 16 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], count := 
                                                                            [ \
9, 2, 14, 16 ], mathmode := "Text", name := "C", next := 453301, root := ~, 
                                                                          star\
t := 453293, stop := 453300 ), rec( content := ", according to the DIMACS spec\
ification.\n      ", count := [ 9, 2, 14, 16 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ 9, 2, 14, 16 ], name := "Item", next := 4533\
55, root := ~, start := 452863, stop := 453354 ) ], count := [ 9, 2, 14, 8 ], 
                                                          mathmode := "Text", 
                                                          name := "List", 
                                                          next := 453367, 
                                                          root := ~, 
                                                          start := 451465, 
                                                          stop := 453366 ), 
                                                      rec( 
                                                          content := "\n\n    \
A detailed definition of the DIMACS format can be found at\n    ", 
                                                          count := 
                                                            [ 9, 2, 14, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "h\
ttp://mat.gsia.cmu.edu/COLOR/general/ccformat.ps", count := [ 9, 2, 14, 18 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ 9, 2, 14, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "URL", 
                                                          next := 453496, 
                                                          root := ~, 
                                                          start := 453436, 
                                                          stop := 453495 ), 
                                                      rec( 
                                                          content := ", in Sec\
tion\n    2.1. Note that optional descriptor lines, as described in Section 2.\
1, will\n    be ignored.\n    ", count := [ 9, 2, 14, 18 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 0, 
                                                          count := 
                                                            [ 9, 2, 14, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "P", 
                                                          next := 453613, 
                                                          root := ~, 
                                                          start := 453609, 
                                                          stop := 453612 ), 
                                                      rec( 
                                                          content := "\n\n\n  \
  ", count := [ 9, 2, 14, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
ngap> gr := Digraph([[2], [1, 3, 4], [2, 4], [2, 3]]);\n<immutable digraph wit\
h 4 vertices, 8 edges>\ngap> filename := Concatenation(DIGRAPHS_Dir(),\n>     \
                         \"/tst/out/dimacs.dimacs\");;\ngap> WriteDIMACSDigrap\
h(filename, gr);;\ngap> ReadDIMACSDigraph(filename);\n<immutable digraph with \
4 vertices, 8 edges>", count := [ 9, 2, 14, 20 ], name := "PCDATA", root := ~ 
                                                                 ) ], 
                                                          count := 
                                                            [ 9, 2, 14, 20 ], 
                                                          mathmode := "Text", 
                                                          name := "Example", 
                                                          next := 453975, 
                                                          root := ~, 
                                                          start := 453620, 
                                                          stop := 453974 ), 
                                                      rec( content := "\n  ", 
                                                          count := 
                                                            [ 9, 2, 14, 21 ], 
                                                          mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ 9, 2, 14, 5 ], 
                                                  mathmode := "Text", 
                                                  name := "Description", 
                                                  next := 453992, root := ~, 
                                                  start := 450613, 
                                                  stop := 453991 ) ], 
                                          count := [ 9, 2, 14, 1 ], 
                                          mathmode := "Text", 
                                          name := "ManSection", 
                                          next := 454006, root := ~, 
                                          start := 450488, stop := 454005 ), 
                                      rec( content := "\n\n  ", 
                                          count := [ 9, 2, 14, 21 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ 9, 2, 0, 1 ], mathmode := "Text",
                                  name := "Section", next := 454020, 
                                  root := ~, start := 421151, stop := 454019 )
                                , 
                              rec( content := "\n", count := [ 9, 2, 14, 21 ],
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ 9, 0, 0, 1 ], 
                          mathmode := "Text", name := "Chapter", 
                          next := 454031, root := ~, start := 399111, 
                          stop := 454030 ), 
                      rec( content := "\n ", count := [ 9, 2, 14, 21 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( content := " visualising, io ", 
                          count := [ 9, 2, 14, 21 ], mathmode := "Text", 
                          name := "XMLCOMMENT", root := ~ ), 
                      rec( content := "\n", count := [ 9, 2, 14, 21 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ) ],
                  count := [ 0, 0, 4, 1 ], mathmode := "Text", 
                  name := "Body", next := 454065, root := ~, start := 3969, 
                  stop := 454064 ), 
              rec( attributes := rec(  ), 
                  content := 
                    [ 
                      rec( content := "\n  ", count := [ "A", 0, 0, 1 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( 
                                  content := "\n    Grape to Digraphs Command M\
ap\n  ", count := [ "A", 0, 0, 2 ], mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 0, 0, 2 ], 
                          mathmode := "Text", name := "Heading", 
                          next := 454136, root := ~, start := 454080, 
                          stop := 454135 ), 
                      rec( content := "\n  Below is a table of ", 
                          count := [ "A", 0, 0, 3 ], mathmode := "Text", 
                          name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Not := "Text" ), 
                          content := 
                            [ 
                              rec( attributes := rec( Text := "Grape" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://www.maths.qmul.ac.\
uk/~leonard/grape/", count := [ "A", 0, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 0, 0, 3 ], 
                                  mathmode := "Text", name := "URL", 
                                  next := 87, root := ~, start := 17, 
                                  stop := 86 ) ], count := [ "A", 0, 0, 3 ], 
                          name := "Alt", next := 93, root := ~, start := 1, 
                          stop := 92 ), 
                      rec( attributes := rec( Only := "Text" ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Grape", 
                                          count := [ "A", 0, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 0, 0, 3 ], 
                                  name := "Package", next := 137, root := ~, 
                                  start := 113, stop := 136 ) ], 
                          count := [ "A", 0, 0, 3 ], mathmode := "Text", 
                          name := "Alt", next := 143, root := ~, start := 93, 
                          stop := 142 ), 
                      rec( content := " commands with the ", 
                          count := [ "A", 0, 0, 3 ], mathmode := "Text", 
                          name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "Digraphs", 
                                  count := [ "A", 0, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 0, 0, 3 ], 
                          mathmode := "Text", name := "Package", next := 28, 
                          root := ~, start := 1, stop := 27 ), 
                      rec( 
                          content := " counterparts.\n  The sections in this c\
hapter correspond to the chapters in the ", count := [ "A", 0, 0, 3 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec( Not := "Text" ), 
                          content := 
                            [ 
                              rec( attributes := rec( Text := "Grape" ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "http://www.maths.qmul.ac.\
uk/~leonard/grape/", count := [ "A", 0, 0, 3 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 0, 0, 3 ], 
                                  mathmode := "Text", name := "URL", 
                                  next := 87, root := ~, start := 17, 
                                  stop := 86 ) ], count := [ "A", 0, 0, 3 ], 
                          name := "Alt", next := 93, root := ~, start := 1, 
                          stop := 92 ), 
                      rec( attributes := rec( Only := "Text" ), 
                          content := 
                            [ 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( content := "Grape", 
                                          count := [ "A", 0, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 0, 0, 3 ], 
                                  name := "Package", next := 137, root := ~, 
                                  start := 113, stop := 136 ) ], 
                          count := [ "A", 0, 0, 3 ], mathmode := "Text", 
                          name := "Alt", next := 143, root := ~, start := 93, 
                          stop := 142 ), 
                      rec( content := "\n  manual.\n\n  ", 
                          count := [ "A", 0, 0, 3 ], mathmode := "Text", 
                          name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n    ", 
                                  count := [ "A", 1, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n      Functions to cons\
truct and modify graphs\n    ", count := [ "A", 1, 0, 2 ], mathmode := "Text",
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 454381, root := ~, start := 454310, 
                                  stop := 454380 ), 
                              rec( content := "\n    ", 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Not := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( content := "\n      ", 
                                          count := [ "A", 1, 0, 3 ], 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n        The tab\
le in this section contains more information when viewed in\n        html form\
at.\n      ", count := [ "A", 1, 0, 3 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ "A", 1, 0, 3 ], 
                                          name := "E", next := 454519, 
                                          root := ~, start := 454409, 
                                          stop := 454518 ), 
                                      rec( content := "\n    ", 
                                          count := [ "A", 1, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "Alt", 
                                  next := 454530, root := ~, start := 454386, 
                                  stop := 454529 ), 
                              rec( content := "\n\n    ", 
                                  count := [ "A", 1, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Align := "|l|l|l|" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 4 ], 
                                          name := "HorLine", next := 454576, 
                                          root := ~, start := 454566, 
                                          stop := 454575 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ "A", 1, 0, 5 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 1, 0, 5 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ "A", 1, 0, 5 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ "A", 1, 0, 5 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 5 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ "A", 1, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 1, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 454645, root := ~, 
                                                  start := 454597, 
                                                  stop := 454644 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ "A", 1, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 1, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 1, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 454705, root := ~, 
                                                  start := 454654, 
                                                  stop := 454704 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Comments\n          ", count := [ "A", 1, 0, 9 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 9 ], 
                                                          name := "Alt", 
                                                          next := 454786, 
                                                          root := ~, 
                                                          start := 454731, 
                                                          stop := 454785 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 454802, root := ~, 
                                                  start := 454714, 
                                                  stop := 454801 ) ], 
                                          count := [ "A", 1, 0, 4 ], 
                                          name := "Row", next := 454815, 
                                          root := ~, start := 454583, 
                                          stop := 454814 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 10 ], 
                                          name := "HorLine", next := 454832, 
                                          root := ~, start := 454822, 
                                          stop := 454831 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
raph", count := [ "A", 1, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 1, 0, 11 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 454883, 
                                                          root := ~, 
                                                          start := 454871, 
                                                          stop := 454882 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 454899, root := ~, 
                                                  start := 454854, 
                                                  stop := 454898 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
" ), content := 0, count := [ "A", 1, 0, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 454946, 
                                                          root := ~, 
                                                          start := 454925, 
                                                          stop := 454945 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 13 ], 
                                                  name := "Item", 
                                                  next := 454962, root := ~, 
                                                  start := 454908, 
                                                  stop := 454961 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n          Used with the arguments of ", count := [ "A", 1, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Graph", count := [ "A", 1, 0, 15 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 15 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4550\
55, root := ~, start := 455043, stop := 455054 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 1, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 1, 0, 15 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 1, 0, 15 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 1, 0, 15 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 1, 0, 15 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 1, 0, 15 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 1, 0, 15 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
, ", count := [ "A", 1, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Oper := "Digraph" ), content := 0, count := [ "A", 1, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "Ref", next := 455101, root := ~, start := 455068, 
                                                                  stop := 4551\
00 ), rec( HTML := true, content := " will return an equivalent digraph. ", 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 15 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 16 ],
                                                                  mathmode := \
"Text", name := "P", next := 455141, root := ~, start := 455137, stop := 45514\
0 ), rec( HTML := true, content := "\n          ", count := [ "A", 1, 0, 16 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 15 ], 
                                                          name := "Alt", 
                                                          next := 455158, 
                                                          root := ~, 
                                                          start := 454988, 
                                                          stop := 455157 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 16 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 15 ], 
                                                  name := "Item", 
                                                  next := 455174, root := ~, 
                                                  start := 454971, 
                                                  stop := 455173 ) ], 
                                          count := [ "A", 1, 0, 10 ], 
                                          name := "Row", next := 455187, 
                                          root := ~, start := 454840, 
                                          stop := 455186 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 17 ], 
                                          name := "HorLine", next := 455204, 
                                          root := ~, start := 455194, 
                                          stop := 455203 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 18 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "E\
dgeOrbitsGraph", count := [ "A", 1, 0, 18 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 1, 0, 18 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 455265, 
                                                          root := ~, 
                                                          start := 455243, 
                                                          stop := 455264 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 18 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 18 ], 
                                                  name := "Item", 
                                                  next := 455281, root := ~, 
                                                  start := 455226, 
                                                  stop := 455280 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 20 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "EdgeOrb\
itsDigraph" ), content := 0, count := [ "A", 1, 0, 20 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 455338, 
                                                          root := ~, 
                                                          start := 455307, 
                                                          stop := 455337 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 20 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 20 ], 
                                                  name := "Item", 
                                                  next := 455354, root := ~, 
                                                  start := 455290, 
                                                  stop := 455353 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 22 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n          The operation ", count := [ "A", 1, 0, 22 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "EdgeOrbitsDigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 22 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 455453, root := ~, start := 455422, 
                                                                  stop := 4554\
52 ), rec( HTML := true, content := " behaves the same as\n          ", 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 22 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "EdgeOrbitsDigraph", count := [ "A", 1, 0, 22 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 22 ], 
                                                                  mathmode := \
"Text", name := "C", next := 455508, root := ~, start := 455484, stop := 45550\
7 ), rec( HTML := true, content := " in ", count := [ "A", 1, 0, 22 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 1, 0, 22 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 22 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 22 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 1, 0, 22 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 1, 0, 22 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 1, 0, 22 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 1, 0, 22 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 1, 0, 22 ], name := "Alt", next := 455537, 
                                                          root := ~, 
                                                          start := 455380, 
                                                          stop := 455536 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 22 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 22 ], 
                                                  name := "Item", 
                                                  next := 455553, root := ~, 
                                                  start := 455363, 
                                                  stop := 455552 ) ], 
                                          count := [ "A", 1, 0, 17 ], 
                                          name := "Row", next := 455566, 
                                          root := ~, start := 455212, 
                                          stop := 455565 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 23 ], 
                                          name := "HorLine", next := 455583, 
                                          root := ~, start := 455573, 
                                          stop := 455582 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 24 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "N\
ullGraph", count := [ "A", 1, 0, 24 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 1, 0, 24 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 455638, 
                                                          root := ~, 
                                                          start := 455622, 
                                                          stop := 455637 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 24 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 24 ], 
                                                  name := "Item", 
                                                  next := 455654, root := ~, 
                                                  start := 455605, 
                                                  stop := 455653 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 26 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "NullDig\
raph" ), content := 0, count := [ "A", 1, 0, 26 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 455705, 
                                                          root := ~, 
                                                          start := 455680, 
                                                          stop := 455704 ), 
                                                      rec( 
                                                          content := "\n      \
    ", count := [ "A", 1, 0, 26 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            or\n            ", count := [ "A", 1, 0, 26 ], mathmode := "Text\
", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "EmptyDigrap\
h" ), content := 0, count := [ "A", 1, 0, 26 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 455787, root := ~, start := 455761, stop := 455786 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
\n          ", count := [ "A", 1, 0, 26 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 1, 0, 26 ], name := "Alt", next := 455804, 
                                                          root := ~, 
                                                          start := 455716, 
                                                          stop := 455803 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 26 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 26 ], 
                                                  name := "Item", 
                                                  next := 455820, root := ~, 
                                                  start := 455663, 
                                                  stop := 455819 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 28 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Note that, unlike in ", count := [ "A", 1, 0, 28 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 1, 0, 28 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 28 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 28 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 1, 0, 28 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 1, 0, 28 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 1, 0, 28 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
, the arguments of  ", count := [ "A", 1, 0, 28 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "NullDigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 28 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 455963, root := ~, start := 455924, 
                                                                  stop := 4559\
62 ), rec( HTML := true, content := " and ", count := [ "A", 1, 0, 28 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "EmptyD\
igraph" ), content := 0, count := [ "A", 1, 0, 28 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 455994, root := ~, start := 455968, stop := 455993 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 are just\n            non-negative integers. Since digraphs in ", 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 28 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 1, 0, 28 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 28 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 are immutable,\n            there is no reason (although it is possible) to c\
reate a null digraph\n            and then add edges, as you might be used to \
doing in ", count := [ "A", 1, 0, 28 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 1, 0, 28 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 1, 0, 28 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 1, 0, 28 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 1, 0, 28 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 1, 0, 28 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 1, 0, 28 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 1, 0, 28 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 1, 0, 28 ], name := "Alt", next := 456255, 
                                                          root := ~, 
                                                          start := 455846, 
                                                          stop := 456254 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 28 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 28 ], 
                                                  name := "Item", 
                                                  next := 456271, root := ~, 
                                                  start := 455829, 
                                                  stop := 456270 ) ], 
                                          count := [ "A", 1, 0, 23 ], 
                                          name := "Row", next := 456284, 
                                          root := ~, start := 455591, 
                                          stop := 456283 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 29 ], 
                                          name := "HorLine", next := 456301, 
                                          root := ~, start := 456291, 
                                          stop := 456300 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 30 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
ompleteGraph", count := [ "A", 1, 0, 30 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 1, 0, 30 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 456360, 
                                                          root := ~, 
                                                          start := 456340, 
                                                          stop := 456359 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 30 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 30 ], 
                                                  name := "Item", 
                                                  next := 456376, root := ~, 
                                                  start := 456323, 
                                                  stop := 456375 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 32 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Complet\
eDigraph" ), content := 0, count := [ "A", 1, 0, 32 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 456431, 
                                                          root := ~, 
                                                          start := 456402, 
                                                          stop := 456430 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 32 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 32 ], 
                                                  name := "Item", 
                                                  next := 456447, root := ~, 
                                                  start := 456385, 
                                                  stop := 456446 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 34 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Note that, unlike in ", count := [ "A", 1, 0, 34 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 1, 0, 34 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 34 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 34 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 1, 0, 34 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 1, 0, 34 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 1, 0, 34 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
, the argument to ", count := [ "A", 1, 0, 34 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "CompleteDigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 34 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 456592, root := ~, start := 456549, 
                                                                  stop := 4565\
91 ), rec( HTML := true, content := " is simply a non-negative integer\n      \
      indicating the number of vertices. By default a complete digraph in\n   \
         ", count := [ "A", 1, 0, 34 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 1, 0, 34 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 34 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 does not have any loops. If you want a complete digraph\n            with loo\
ps at every vertex, then use ", count := [ "A", 1, 0, 34 ], mathmode := "Text"
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "DigraphAddAllLoops" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 34 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 456880, root := ~, start := 456834, 
                                                                  stop := 4568\
79 ), rec( HTML := true, content := ".\n          ", count := [ "A", 1, 0, 34 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 34 ], 
                                                          name := "Alt", 
                                                          next := 456898, 
                                                          root := ~, 
                                                          start := 456473, 
                                                          stop := 456897 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 34 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 34 ], 
                                                  name := "Item", 
                                                  next := 456914, root := ~, 
                                                  start := 456456, 
                                                  stop := 456913 ) ], 
                                          count := [ "A", 1, 0, 29 ], 
                                          name := "Row", next := 456927, 
                                          root := ~, start := 456309, 
                                          stop := 456926 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 35 ], 
                                          name := "HorLine", next := 456944, 
                                          root := ~, start := 456934, 
                                          stop := 456943 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 36 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "J\
ohnsonGraph", count := [ "A", 1, 0, 36 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 1, 0, 36 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 457002, 
                                                          root := ~, 
                                                          start := 456983, 
                                                          stop := 457001 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 36 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 36 ], 
                                                  name := "Item", 
                                                  next := 457018, root := ~, 
                                                  start := 456966, 
                                                  stop := 457017 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 38 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Johnson\
Digraph" ), content := 0, count := [ "A", 1, 0, 38 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 457072, 
                                                          root := ~, 
                                                          start := 457044, 
                                                          stop := 457071 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 38 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 38 ], 
                                                  name := "Item", 
                                                  next := 457088, root := ~, 
                                                  start := 457027, 
                                                  stop := 457087 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 40 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 1, 0, 40 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 1, 0, 40 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 40 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 40 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 1, 0, 40 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 1, 0, 40 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 1, 0, 40 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 function ", count := [ "A", 1, 0, 40 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "JohnsonGraph", count :=\
 [ "A", 1, 0, 40 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 40 ],
                                                                  mathmode := \
"Text", name := "C", next := 457184, root := ~, start := 457165, stop := 45718\
3 ), rec( HTML := true, content := " is equivalent to\n            ", 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 40 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Johnso\
nDigraph" ), content := 0, count := [ "A", 1, 0, 40 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 457242, root := ~, start := 457214, stop := 457241 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 1, 0, 40 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 1, 0, 40 ], name := "Alt", next := 457260, 
                                                          root := ~, 
                                                          start := 457114, 
                                                          stop := 457259 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 40 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 40 ], 
                                                  name := "Item", 
                                                  next := 457276, root := ~, 
                                                  start := 457097, 
                                                  stop := 457275 ) ], 
                                          count := [ "A", 1, 0, 35 ], 
                                          name := "Row", next := 457289, 
                                          root := ~, start := 456952, 
                                          stop := 457288 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 41 ], 
                                          name := "HorLine", next := 457306, 
                                          root := ~, start := 457296, 
                                          stop := 457305 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 42 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
ayleyGraph", count := [ "A", 1, 0, 42 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 1, 0, 42 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 457363, 
                                                          root := ~, 
                                                          start := 457345, 
                                                          stop := 457362 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 42 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 42 ], 
                                                  name := "Item", 
                                                  next := 457379, root := ~, 
                                                  start := 457328, 
                                                  stop := 457378 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 44 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "CayleyD\
igraph" ), content := 0, count := [ "A", 1, 0, 44 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 457432, 
                                                          root := ~, 
                                                          start := 457405, 
                                                          stop := 457431 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 44 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 44 ], 
                                                  name := "Item", 
                                                  next := 457448, root := ~, 
                                                  start := 457388, 
                                                  stop := 457447 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 46 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The operation ", count := [ "A", 1, 0, 46 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "CayleyDigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 46 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 457545, root := ~, start := 457518, 
                                                                  stop := 4575\
44 ), rec( HTML := true, content := " behaves the same as\n            ", 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 46 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "CayleyGraph", count := [ "A", 1, 0, 46 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 46 ], 
                                                                  mathmode := \
"Text", name := "C", next := 457596, root := ~, start := 457578, stop := 45759\
5 ), rec( HTML := true, content := " in ", count := [ "A", 1, 0, 46 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 1, 0, 46 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 46 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 46 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 1, 0, 46 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 1, 0, 46 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 1, 0, 46 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 1, 0, 46 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 1, 0, 46 ], name := "Alt", next := 457625, 
                                                          root := ~, 
                                                          start := 457474, 
                                                          stop := 457624 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 46 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 46 ], 
                                                  name := "Item", 
                                                  next := 457641, root := ~, 
                                                  start := 457457, 
                                                  stop := 457640 ) ], 
                                          count := [ "A", 1, 0, 41 ], 
                                          name := "Row", next := 457654, 
                                          root := ~, start := 457314, 
                                          stop := 457653 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 47 ], 
                                          name := "HorLine", next := 457671, 
                                          root := ~, start := 457661, 
                                          stop := 457670 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 48 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
ddEdgeOrbit", count := [ "A", 1, 0, 48 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 1, 0, 48 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 457729, 
                                                          root := ~, 
                                                          start := 457710, 
                                                          stop := 457728 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 48 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 48 ], 
                                                  name := "Item", 
                                                  next := 457745, root := ~, 
                                                  start := 457693, 
                                                  stop := 457744 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 50 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
AddEdgeOrbit" ), content := 0, count := [ "A", 1, 0, 50 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 457804, 
                                                          root := ~, 
                                                          start := 457771, 
                                                          stop := 457803 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 50 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 50 ], 
                                                  name := "Item", 
                                                  next := 457820, root := ~, 
                                                  start := 457754, 
                                                  stop := 457819 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 52 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Note that, unlike in ", count := [ "A", 1, 0, 52 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 1, 0, 52 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 52 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 52 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 1, 0, 52 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 1, 0, 52 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 1, 0, 52 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
, digraphs in ", count := [ "A", 1, 0, 52 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "Digraphs", count := [ "A", 1, 0, 52 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ "A", 1, 0, 52 ], mathmode := "Text", 
                                                                  name := "Pac\
kage", next := 28, root := ~, start := 1, stop := 27 ), rec( HTML := true, 
                                                                  content := "\
 are immutable,\n            and this operation returns a new digraph, i.e. it\
 does not modify the\n            digraph given as an argument.\n          ", 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 52 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 52 ], 
                                                          name := "Alt", 
                                                          next := 458084, 
                                                          root := ~, 
                                                          start := 457846, 
                                                          stop := 458083 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 52 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 52 ], 
                                                  name := "Item", 
                                                  next := 458100, root := ~, 
                                                  start := 457829, 
                                                  stop := 458099 ) ], 
                                          count := [ "A", 1, 0, 47 ], 
                                          name := "Row", next := 458113, 
                                          root := ~, start := 457679, 
                                          stop := 458112 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 53 ], 
                                          name := "HorLine", next := 458130, 
                                          root := ~, start := 458120, 
                                          stop := 458129 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 54 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "R\
emoveEdgeOrbit", count := [ "A", 1, 0, 54 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 1, 0, 54 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 458191, 
                                                          root := ~, 
                                                          start := 458169, 
                                                          stop := 458190 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 54 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 54 ], 
                                                  name := "Item", 
                                                  next := 458207, root := ~, 
                                                  start := 458152, 
                                                  stop := 458206 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 56 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
RemoveEdgeOrbit" ), content := 0, count := [ "A", 1, 0, 56 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 458269, 
                                                          root := ~, 
                                                          start := 458233, 
                                                          stop := 458268 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 56 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 56 ], 
                                                  name := "Item", 
                                                  next := 458285, root := ~, 
                                                  start := 458216, 
                                                  stop := 458284 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 58 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Note that, unlike in ", count := [ "A", 1, 0, 58 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 1, 0, 58 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 58 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 58 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 1, 0, 58 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 1, 0, 58 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 1, 0, 58 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
, digraphs in ", count := [ "A", 1, 0, 58 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "Digraphs", count := [ "A", 1, 0, 58 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ "A", 1, 0, 58 ], mathmode := "Text", 
                                                                  name := "Pac\
kage", next := 28, root := ~, start := 1, stop := 27 ), rec( HTML := true, 
                                                                  content := "\
 are immutable,\n            and this operation returns a new digraph, i.e. it\
 does not modify the\n            digraph given as an argument.\n          ", 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 58 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 1, 0, 58 ], 
                                                          name := "Alt", 
                                                          next := 458549, 
                                                          root := ~, 
                                                          start := 458311, 
                                                          stop := 458548 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 58 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 58 ], 
                                                  name := "Item", 
                                                  next := 458565, root := ~, 
                                                  start := 458294, 
                                                  stop := 458564 ) ], 
                                          count := [ "A", 1, 0, 53 ], 
                                          name := "Row", next := 458578, 
                                          root := ~, start := 458138, 
                                          stop := 458577 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 59 ], 
                                          name := "HorLine", next := 458595, 
                                          root := ~, start := 458585, 
                                          stop := 458594 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 60 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
ssignVertexNames", count := [ "A", 1, 0, 60 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 1, 0, 60 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 458658, 
                                                          root := ~, 
                                                          start := 458634, 
                                                          stop := 458657 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 60 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 60 ], 
                                                  name := "Item", 
                                                  next := 458674, root := ~, 
                                                  start := 458617, 
                                                  stop := 458673 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 62 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "SetDigr\
aphVertexLabels" ), content := 0, count := [ "A", 1, 0, 62 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 458736, 
                                                          root := ~, 
                                                          start := 458700, 
                                                          stop := 458735 ), 
                                                      rec( 
                                                          content := "\n      \
    ", count := [ "A", 1, 0, 62 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            and\n            ", count := [ "A", 1, 0, 62 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "SetDigraph\
VertexLabel" ), content := 0, count := [ "A", 1, 0, 62 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 458828, root := ~, start := 458793, stop := 458827 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
\n          ", count := [ "A", 1, 0, 62 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 1, 0, 62 ], name := "Alt", next := 458845, 
                                                          root := ~, 
                                                          start := 458747, 
                                                          stop := 458844 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 62 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 62 ], 
                                                  name := "Item", 
                                                  next := 458861, root := ~, 
                                                  start := 458683, 
                                                  stop := 458860 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 1, 0, 64 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Use  ", count := [ "A", 1, 0, 64 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "SetDigraphVertexLabel" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 1, 
                                                                      0, 64 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 458957, root := ~, start := 458922, 
                                                                  stop := 4589\
56 ), rec( HTML := true, content := " to set an individual\n            vertex\
 label and ", count := [ "A", 1, 0, 64 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Oper := "SetDigraphVertexLabels" ), content := 0, count := [ "A", 1, 
                                                                      0, 64 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 459044, root := ~, start := 459008, 
                                                                  stop := 4590\
43 ), rec( HTML := true, content := " to set all of\n            the vertex la\
bels.\n          ", count := [ "A", 1, 0, 64 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 1, 0, 64 ], name := "Alt", 
                                                          next := 459106, 
                                                          root := ~, 
                                                          start := 458887, 
                                                          stop := 459105 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 1, 0, 64 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 1, 0, 64 ], 
                                                  name := "Item", 
                                                  next := 459122, root := ~, 
                                                  start := 458870, 
                                                  stop := 459121 ) ], 
                                          count := [ "A", 1, 0, 59 ], 
                                          name := "Row", next := 459135, 
                                          root := ~, start := 458603, 
                                          stop := 459134 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 1, 0, 65 ], 
                                          name := "HorLine", next := 459152, 
                                          root := ~, start := 459142, 
                                          stop := 459151 ) ], 
                                  count := [ "A", 1, 0, 4 ], 
                                  mathmode := "Text", name := "Table", 
                                  next := 459165, root := ~, start := 454536, 
                                  stop := 459164 ), 
                              rec( content := "\n  ", 
                                  count := [ "A", 1, 0, 66 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 1, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 459178, root := ~, start := 454296, 
                          stop := 459177 ), 
                      rec( content := "\n\n  ", count := [ "A", 1, 0, 66 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n    ", 
                                  count := [ "A", 2, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n      Functions to insp\
ect graphs, vertices and edges\n    ", count := [ "A", 2, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 2, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 459274, root := ~, start := 459196, 
                                  stop := 459273 ), 
                              rec( content := "\n    ", 
                                  count := [ "A", 2, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Not := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( content := "\n      ", 
                                          count := [ "A", 2, 0, 3 ], 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n        The tab\
le in this section contains more information when viewed in\n        html form\
at.\n      ", count := [ "A", 2, 0, 3 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ "A", 2, 0, 3 ], 
                                          name := "E", next := 459412, 
                                          root := ~, start := 459302, 
                                          stop := 459411 ), 
                                      rec( content := "\n    ", 
                                          count := [ "A", 2, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 2, 0, 3 ], 
                                  mathmode := "Text", name := "Alt", 
                                  next := 459423, root := ~, start := 459279, 
                                  stop := 459422 ), 
                              rec( content := "\n\n    ", 
                                  count := [ "A", 2, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Align := "|l|l|l|" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 4 ], 
                                          name := "HorLine", next := 459469, 
                                          root := ~, start := 459459, 
                                          stop := 459468 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ "A", 2, 0, 5 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 2, 0, 5 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ "A", 2, 0, 5 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ "A", 2, 0, 5 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 5 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ "A", 2, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 2, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 459539, root := ~, 
                                                  start := 459491, 
                                                  stop := 459538 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ "A", 2, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 2, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 459599, root := ~, 
                                                  start := 459548, 
                                                  stop := 459598 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Comments\n          ", count := [ "A", 2, 0, 9 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 9 ], 
                                                          name := "Alt", 
                                                          next := 459680, 
                                                          root := ~, 
                                                          start := 459625, 
                                                          stop := 459679 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 459696, root := ~, 
                                                  start := 459608, 
                                                  stop := 459695 ) ], 
                                          count := [ "A", 2, 0, 4 ], 
                                          name := "Row", next := 459709, 
                                          root := ~, start := 459477, 
                                          stop := 459708 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 10 ], 
                                          name := "HorLine", next := 459726, 
                                          root := ~, start := 459716, 
                                          stop := 459725 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sGraph", count := [ "A", 2, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 11 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 459779, 
                                                          root := ~, 
                                                          start := 459765, 
                                                          stop := 459778 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 459795, root := ~, 
                                                  start := 459748, 
                                                  stop := 459794 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Filt := "IsDigra\
ph" ), content := 0, count := [ "A", 2, 0, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 459844, 
                                                          root := ~, 
                                                          start := 459821, 
                                                          stop := 459843 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 13 ], 
                                                  name := "Item", 
                                                  next := 459860, root := ~, 
                                                  start := 459804, 
                                                  stop := 459859 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 2, 0, 15 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec( Filt := "IsDigraph" ), content := 0,
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 15 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 459939, root := ~, start := 459916, 
                                                                  stop := 4599\
38 ), rec( HTML := true, content := " is a category and not a function like\n \
           ", count := [ "A", 2, 0, 15 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "IsGraph", count := [ "A\
", 2, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 15 ],
                                                                  mathmode := \
"Text", name := "C", next := 460004, root := ~, start := 459990, stop := 46000\
3 ), rec( HTML := true, content := ".\n          ", count := [ "A", 2, 0, 15 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 15 ], 
                                                          name := "Alt", 
                                                          next := 460022, 
                                                          root := ~, 
                                                          start := 459886, 
                                                          stop := 460021 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 15 ], 
                                                  name := "Item", 
                                                  next := 460038, root := ~, 
                                                  start := 459869, 
                                                  stop := 460037 ) ], 
                                          count := [ "A", 2, 0, 10 ], 
                                          name := "Row", next := 460051, 
                                          root := ~, start := 459734, 
                                          stop := 460050 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 16 ], 
                                          name := "HorLine", next := 460068, 
                                          root := ~, start := 460058, 
                                          stop := 460067 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
rderGraph", count := [ "A", 2, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 17 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 460124, 
                                                          root := ~, 
                                                          start := 460107, 
                                                          stop := 460123 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 17 ], 
                                                  name := "Item", 
                                                  next := 460140, root := ~, 
                                                  start := 460090, 
                                                  stop := 460139 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
NrVertices" ), content := 0, count := [ "A", 2, 0, 19 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 460197, 
                                                          root := ~, 
                                                          start := 460166, 
                                                          stop := 460196 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 19 ], 
                                                  name := "Item", 
                                                  next := 460213, root := ~, 
                                                  start := 460149, 
                                                  stop := 460212 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The operation ", count := [ "A", 2, 0, 21 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphNrVertices" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 21 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 460314, root := ~, start := 460283, 
                                                                  stop := 4603\
13 ), rec( HTML := true, content := " behaves the same as\n            ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 21 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "OrderGraph", count := [ "A", 2, 0, 21 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 21 ], mathmode := \
"Text", name := "C", next := 460364, root := ~, start := 460347, stop := 46036\
3 ), rec( HTML := true, content := " in ", count := [ "A", 2, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 21 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 21 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 21 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 21 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 21 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 21 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 21 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 21 ], name := "Alt", next := 460393, 
                                                          root := ~, 
                                                          start := 460239, 
                                                          stop := 460392 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 21 ], 
                                                  name := "Item", 
                                                  next := 460409, root := ~, 
                                                  start := 460222, 
                                                  stop := 460408 ) ], 
                                          count := [ "A", 2, 0, 16 ], 
                                          name := "Row", next := 460422, 
                                          root := ~, start := 460076, 
                                          stop := 460421 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 22 ], 
                                          name := "HorLine", next := 460439, 
                                          root := ~, start := 460429, 
                                          stop := 460438 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sVertex(", count := [ "A", 2, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( content := "graph", count := [ "A", 2, 0, 23 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 23 ], 
                                                                  mathmode := \
"Text", name := "A", next := 460502, root := ~, start := 460490, stop := 46050\
1 ), rec( content := ", ", count := [ "A", 2, 0, 23 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( content := "v\
", count := [ "A", 2, 0, 23 ], mathmode := "Text", name := "PCDATA", root := ~\
 ) ], count := [ "A", 2, 0, 23 ], mathmode := "Text", name := "A", 
                                                                  next := 4605\
12, root := ~, start := 460504, stop := 460511 ), rec( content := ")", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 23 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 23 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 460517, 
                                                          root := ~, 
                                                          start := 460478, 
                                                          stop := 460516 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 23 ], 
                                                  name := "Item", 
                                                  next := 460533, root := ~, 
                                                  start := 460461, 
                                                  stop := 460532 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "v", count := [ "A", 2, 0, 25 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 25 ], 
                                                                  mathmode := \
"Text", name := "A", next := 460570, root := ~, start := 460562, stop := 46056\
9 ), rec( content := " in DigraphVertices(", count := [ "A", 2, 0, 25 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          cont\
ent := "digraph", count := [ "A", 2, 0, 25 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ "A", 2, 0, 25 ], mathmode := "Text", 
                                                                  name := "A",
                                                                  next := 4606\
04, root := ~, start := 460590, stop := 460603 ), rec( content := ")", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 25 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 25 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 460609, 
                                                          root := ~, 
                                                          start := 460559, 
                                                          stop := 460608 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 25 ], 
                                                  name := "Item", 
                                                  next := 460625, root := ~, 
                                                  start := 460542, 
                                                  stop := 460624 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The attribute ", count := [ "A", 2, 0, 27 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphVertices" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 460724, root := ~, start := 460695, 
                                                                  stop := 4607\
23 ), rec( HTML := true, content := " can be used to return\n            the l\
ist of vertices of a digraph, or if ", count := [ "A", 2, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "v", count := [ "A", 2, 0, 27 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 27 ], mathmode := "Text", 
                                                                  name := "A",
                                                                  next := 4608\
08, root := ~, start := 460800, stop := 460807 ), rec( HTML := true, 
                                                                  content := "\
 is known to be\n            a positive integer, then you can simply do\n     \
       ", count := [ "A", 2, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := \
true, content := "v", count := [ "A", 2, 0, 27 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 2, 0, 27 ], mathmode := "Text", name \
:= "A", next := 460902, root := ~, start := 460894, stop := 460901 ), rec( 
                                                                          HTML\
 := true, content := " <= DigraphNrVertices(", count := [ "A", 2, 0, 27 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                          cont\
ent := [ rec( HTML := true, content := "digraph", count := [ "A", 2, 0, 27 ], \
mathmode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 27 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "A", next := 460941, root := ~, start := 460927, stop \
:= 460940 ), rec( HTML := true, content := ")", count := [ "A", 2, 0, 27 ], 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "C", next := 460946, root := ~, start := 460891, stop := 46094\
5 ), rec( HTML := true, content := "\n          ", count := [ "A", 2, 0, 27 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 27 ], 
                                                          name := "Alt", 
                                                          next := 460963, 
                                                          root := ~, 
                                                          start := 460651, 
                                                          stop := 460962 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 27 ], 
                                                  name := "Item", 
                                                  next := 460979, root := ~, 
                                                  start := 460634, 
                                                  stop := 460978 ) ], 
                                          count := [ "A", 2, 0, 22 ], 
                                          name := "Row", next := 460992, 
                                          root := ~, start := 460447, 
                                          stop := 460991 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 28 ], 
                                          name := "HorLine", next := 461009, 
                                          root := ~, start := 460999, 
                                          stop := 461008 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
ertexName", count := [ "A", 2, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 29 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 461065, 
                                                          root := ~, 
                                                          start := 461048, 
                                                          stop := 461064 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 29 ], 
                                                  name := "Item", 
                                                  next := 461081, root := ~, 
                                                  start := 461031, 
                                                  stop := 461080 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 31 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabel" ), content := 0, count := [ "A", 2, 0, 31 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 461139, 
                                                          root := ~, 
                                                          start := 461107, 
                                                          stop := 461138 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 31 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 31 ], 
                                                  name := "Item", 
                                                  next := 461155, root := ~, 
                                                  start := 461090, 
                                                  stop := 461154 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Unlike ", count := [ "A", 2, 0, 33 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true,
                                                                          cont\
ent := "VertexName", count := [ "A", 2, 0, 33 ], mathmode := "Text", name := "\
PCDATA", root := ~ ) ], count := [ "A", 2, 0, 33 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4612\
35, root := ~, start := 461218, stop := 461234 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 2, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 2, 0, 33 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 2, 0, 33 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 2, 0, 33 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 33 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 33 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 33 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
, the return value of\n            ", count := [ "A", 2, 0, 33 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digrap\
hVertexLabel" ), content := 0, count := [ "A", 2, 0, 33 ], mathmode := "Text",
                                                                  name := "Ref\
", next := 461312, root := ~, start := 461280, stop := 461311 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 is mutable.\n          ", count := [ "A", 2, 0, 33 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 2, 0, 33 ], name := "Alt", 
                                                          next := 461341, 
                                                          root := ~, 
                                                          start := 461181, 
                                                          stop := 461340 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 33 ], 
                                                  name := "Item", 
                                                  next := 461357, root := ~, 
                                                  start := 461164, 
                                                  stop := 461356 ) ], 
                                          count := [ "A", 2, 0, 28 ], 
                                          name := "Row", next := 461370, 
                                          root := ~, start := 461017, 
                                          stop := 461369 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 34 ], 
                                          name := "HorLine", next := 461387, 
                                          root := ~, start := 461377, 
                                          stop := 461386 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
ertexNames", count := [ "A", 2, 0, 35 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 35 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 461444, 
                                                          root := ~, 
                                                          start := 461426, 
                                                          stop := 461443 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 35 ], 
                                                  name := "Item", 
                                                  next := 461460, root := ~, 
                                                  start := 461409, 
                                                  stop := 461459 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 37 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
VertexLabels" ), content := 0, count := [ "A", 2, 0, 37 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 461519, 
                                                          root := ~, 
                                                          start := 461486, 
                                                          stop := 461518 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 37 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 37 ], 
                                                  name := "Item", 
                                                  next := 461535, root := ~, 
                                                  start := 461469, 
                                                  stop := 461534 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Unlike ", count := [ "A", 2, 0, 39 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true,
                                                                          cont\
ent := "VertexNames", count := [ "A", 2, 0, 39 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 2, 0, 39 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4616\
16, root := ~, start := 461598, stop := 461615 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 2, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 2, 0, 39 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 2, 0, 39 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 2, 0, 39 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 39 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 39 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 39 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
, the return value of\n            ", count := [ "A", 2, 0, 39 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digrap\
hVertexLabels" ), content := 0, count := [ "A", 2, 0, 39 ], mathmode := "Text"
                                                                    , 
                                                                  name := "Ref\
", next := 461694, root := ~, start := 461661, stop := 461693 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 is mutable.\n          ", count := [ "A", 2, 0, 39 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 2, 0, 39 ], name := "Alt", 
                                                          next := 461723, 
                                                          root := ~, 
                                                          start := 461561, 
                                                          stop := 461722 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 39 ], 
                                                  name := "Item", 
                                                  next := 461739, root := ~, 
                                                  start := 461544, 
                                                  stop := 461738 ) ], 
                                          count := [ "A", 2, 0, 34 ], 
                                          name := "Row", next := 461752, 
                                          root := ~, start := 461395, 
                                          stop := 461751 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 40 ], 
                                          name := "HorLine", next := 461769, 
                                          root := ~, start := 461759, 
                                          stop := 461768 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
ertices", count := [ "A", 2, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 41 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 461823, 
                                                          root := ~, 
                                                          start := 461808, 
                                                          stop := 461822 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 41 ], 
                                                  name := "Item", 
                                                  next := 461839, root := ~, 
                                                  start := 461791, 
                                                  stop := 461838 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 43 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Vertices" ), content := 0, count := [ "A", 2, 0, 43 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 461894, 
                                                          root := ~, 
                                                          start := 461865, 
                                                          stop := 461893 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 43 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 43 ], 
                                                  name := "Item", 
                                                  next := 461910, root := ~, 
                                                  start := 461848, 
                                                  stop := 461909 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The vertices of a digraph in ", count := [ "A", 2, 0, 45 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 2, 0, 45 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 45 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 is always the range ", count := [ "A", 2, 0, 45 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true,
                                                                          cont\
ent := "[1\n              .. n]", count := [ "A", 2, 0, 45 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 45 ], mathmode := "\
Text", name := "C", next := 462055, root := ~, start := 462026, stop := 462054\
 ), rec( HTML := true, content := " where ", count := [ "A", 2, 0, 45 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "n", count := [ "A", 2, 0, 45 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 45 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4620\
70, root := ~, start := 462062, stop := 462069 ), rec( HTML := true, 
                                                                  content := "\
 is the number of vertices of the\n            digraph.  The operation ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 45 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digrap\
hVertices" ), content := 0, count := [ "A", 2, 0, 45 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 462169, root := ~, start := 462140, stop := 462168 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 behaves the\n            same as ", count := [ "A", 2, 0, 45 ], mathmode := "\
Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Vertices", count := [ "A", 2, 0, 45 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 45 ], mathmode := "T\
ext", name := "C", next := 462217, root := ~, start := 462202, stop := 462216 
                                                                 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 in ", count := [ "A", 2, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 2, 0, 45 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 2, 0, 45 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 2, 0, 45 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 45 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 45 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 45 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 45 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 45 ], name := "Alt", next := 462246, 
                                                          root := ~, 
                                                          start := 461936, 
                                                          stop := 462245 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 45 ], 
                                                  name := "Item", 
                                                  next := 462262, root := ~, 
                                                  start := 461919, 
                                                  stop := 462261 ) ], 
                                          count := [ "A", 2, 0, 40 ], 
                                          name := "Row", next := 462275, 
                                          root := ~, start := 461777, 
                                          stop := 462274 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 46 ], 
                                          name := "HorLine", next := 462292, 
                                          root := ~, start := 462282, 
                                          stop := 462291 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 47 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
ertexDegree", count := [ "A", 2, 0, 47 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 47 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 462350, 
                                                          root := ~, 
                                                          start := 462331, 
                                                          stop := 462349 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 47 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 47 ], 
                                                  name := "Item", 
                                                  next := 462366, root := ~, 
                                                  start := 462314, 
                                                  stop := 462365 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 49 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "OutDegr\
eeOfVertex" ), content := 0, count := [ "A", 2, 0, 49 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 462423, 
                                                          root := ~, 
                                                          start := 462392, 
                                                          stop := 462422 ), 
                                                      rec( 
                                                          content := "\n      \
    ", count := [ "A", 2, 0, 49 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            (see also: ", count := [ "A", 2, 0, 49 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "InDegreeOfVertex" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 49 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 462505, root := ~, start := 462475, 
                                                                  stop := 4625\
04 ), rec( HTML := true, content := ")\n          ", count := [ "A", 2, 0, 49 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 49 ], 
                                                          name := "Alt", 
                                                          next := 462523, 
                                                          root := ~, 
                                                          start := 462434, 
                                                          stop := 462522 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 49 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 49 ], 
                                                  name := "Item", 
                                                  next := 462539, root := ~, 
                                                  start := 462375, 
                                                  stop := 462538 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 51 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The operation ", count := [ "A", 2, 0, 51 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "OutDegreeOfVertex" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 51 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 462640, root := ~, start := 462609, 
                                                                  stop := 4626\
39 ), rec( HTML := true, content := " behaves the same as\n            ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 51 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "VertexDegree", count := [ "A", 2, 0, 51 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 51 ], 
                                                                  mathmode := \
"Text", name := "C", next := 462692, root := ~, start := 462673, stop := 46269\
1 ), rec( HTML := true, content := " in ", count := [ "A", 2, 0, 51 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 51 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 51 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 51 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 51 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 51 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 51 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 51 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 51 ], name := "Alt", next := 462721, 
                                                          root := ~, 
                                                          start := 462565, 
                                                          stop := 462720 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 51 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 51 ], 
                                                  name := "Item", 
                                                  next := 462737, root := ~, 
                                                  start := 462548, 
                                                  stop := 462736 ) ], 
                                          count := [ "A", 2, 0, 46 ], 
                                          name := "Row", next := 462750, 
                                          root := ~, start := 462300, 
                                          stop := 462749 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 52 ], 
                                          name := "HorLine", next := 462767, 
                                          root := ~, start := 462757, 
                                          stop := 462766 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 53 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
ertexDegrees", count := [ "A", 2, 0, 53 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 2, 0, 53 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 462826, 
                                                          root := ~, 
                                                          start := 462806, 
                                                          stop := 462825 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 53 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 53 ], 
                                                  name := "Item", 
                                                  next := 462842, root := ~, 
                                                  start := 462789, 
                                                  stop := 462841 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 55 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "OutDegr\
eeSet" ), content := 0, count := [ "A", 2, 0, 55 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 462894, 
                                                          root := ~, 
                                                          start := 462868, 
                                                          stop := 462893 ), 
                                                      rec( 
                                                          content := "\n      \
    ", count := [ "A", 2, 0, 55 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            (see also:\n            ", count := [ "A", 2, 0, 55 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "OutDeg\
reeSequence" ), content := 0, count := [ "A", 2, 0, 55 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 462989, root := ~, start := 462958, stop := 462988 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
,\n            ", count := [ "A", 2, 0, 55 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "OutDegrees" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 55 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 463027, root := ~, start := 463003, 
                                                                  stop := 4630\
26 ), rec( HTML := true, content := ",\n            ", count := [ "A", 2, 0, 
                                                                      55 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "InDegr\
ees" ), content := 0, count := [ "A", 2, 0, 55 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 463064, root := ~, start := 463041, stop := 463063 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
,\n            ", count := [ "A", 2, 0, 55 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "InDegreeSequence" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 55 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 463108, root := ~, start := 463078, 
                                                                  stop := 4631\
07 ), rec( HTML := true, content := ",\n            ", count := [ "A", 2, 0, 
                                                                      55 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "InDegr\
eeSet" ), content := 0, count := [ "A", 2, 0, 55 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 463147, root := ~, start := 463122, stop := 463146 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
)\n          ", count := [ "A", 2, 0, 55 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 55 ], name := "Alt", next := 463165, 
                                                          root := ~, 
                                                          start := 462905, 
                                                          stop := 463164 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 55 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 55 ], 
                                                  name := "Item", 
                                                  next := 463181, root := ~, 
                                                  start := 462851, 
                                                  stop := 463180 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 57 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The operation ", count := [ "A", 2, 0, 57 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "OutDegreeSet" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 57 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 463277, root := ~, start := 463251, 
                                                                  stop := 4632\
76 ), rec( HTML := true, content := " behaves the same as\n            ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 57 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "VertexDegrees", count := [ "A", 2, 0, 57 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 57 ], 
                                                                  mathmode := \
"Text", name := "C", next := 463330, root := ~, start := 463310, stop := 46332\
9 ), rec( HTML := true, content := " in ", count := [ "A", 2, 0, 57 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 57 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 57 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 57 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 57 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 57 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 57 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 57 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 57 ], name := "Alt", next := 463359, 
                                                          root := ~, 
                                                          start := 463207, 
                                                          stop := 463358 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 57 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 57 ], 
                                                  name := "Item", 
                                                  next := 463375, root := ~, 
                                                  start := 463190, 
                                                  stop := 463374 ) ], 
                                          count := [ "A", 2, 0, 52 ], 
                                          name := "Row", next := 463388, 
                                          root := ~, start := 462775, 
                                          stop := 463387 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 58 ], 
                                          name := "HorLine", next := 463405, 
                                          root := ~, start := 463395, 
                                          stop := 463404 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 59 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sLoopy", count := [ "A", 2, 0, 59 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 59 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 463458, 
                                                          root := ~, 
                                                          start := 463444, 
                                                          stop := 463457 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 59 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 59 ], 
                                                  name := "Item", 
                                                  next := 463474, root := ~, 
                                                  start := 463427, 
                                                  stop := 463473 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 61 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "Digraph\
HasLoops" ), content := 0, count := [ "A", 2, 0, 61 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 463529, 
                                                          root := ~, 
                                                          start := 463500, 
                                                          stop := 463528 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 61 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 61 ], 
                                                  name := "Item", 
                                                  next := 463545, root := ~, 
                                                  start := 463483, 
                                                  stop := 463544 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 63 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The operation ", count := [ "A", 2, 0, 63 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Prop := "DigraphHasLoops" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 63 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 463644, root := ~, start := 463615, 
                                                                  stop := 4636\
43 ), rec( HTML := true, content := " behaves the same as\n            ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 63 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "IsLoopy", count := [ "A", 2, 0, 63 ], mathmode := "Text"
                                                                            , 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 63 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4636\
91, root := ~, start := 463677, stop := 463690 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 2, 0, 63 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 2, 0, 63 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 2, 0, 63 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 2, 0, 63 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 63 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 63 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 63 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 63 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 63 ], name := "Alt", next := 463720, 
                                                          root := ~, 
                                                          start := 463571, 
                                                          stop := 463719 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 63 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 63 ], 
                                                  name := "Item", 
                                                  next := 463736, root := ~, 
                                                  start := 463554, 
                                                  stop := 463735 ) ], 
                                          count := [ "A", 2, 0, 58 ], 
                                          name := "Row", next := 463749, 
                                          root := ~, start := 463413, 
                                          stop := 463748 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 64 ], 
                                          name := "HorLine", next := 463766, 
                                          root := ~, start := 463756, 
                                          stop := 463765 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 65 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sSimpleGraph", count := [ "A", 2, 0, 65 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 2, 0, 65 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 463825, 
                                                          root := ~, 
                                                          start := 463805, 
                                                          stop := 463824 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 65 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 65 ], 
                                                  name := "Item", 
                                                  next := 463841, root := ~, 
                                                  start := 463788, 
                                                  stop := 463840 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 67 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 2, 0, 67 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec( Prop := "IsSymmetricDigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 67 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 463929, root := ~, start := 463897, 
                                                                  stop := 4639\
28 ), rec( HTML := true, content := "\n            and not  ", count := 
                                                                    [ "A", 2, 
                                                                      0, 67 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "Digrap\
hHasLoops" ), content := 0, count := [ "A", 2, 0, 67 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 463980, root := ~, start := 463951, stop := 463979 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
\n          ", count := [ "A", 2, 0, 67 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 2, 0, 67 ], name := "Alt", next := 463997, 
                                                          root := ~, 
                                                          start := 463867, 
                                                          stop := 463996 ), 
                                                      rec( 
                                                          content := "\n      \
    ", count := [ "A", 2, 0, 67 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "HTML" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "\\
n            ", count := [ "A", 2, 0, 67 ], name := "PCDATA", root := ~ ), 
                                                              rec( 
                                                                  attributes :\
= rec( Prop := "IsSymmetricDigraph" ), content := 0, count := [ "A", 2, 0, 67 
                                                                     ], 
                                                                  name := "Ref\
", next := 464069, root := ~, start := 464037, stop := 464068 ), 
                                                              rec( 
                                                                  content := "\
\n          ", count := [ "A", 2, 0, 67 ], name := "PCDATA", root := ~ ) ], 
                                                          count := 
                                                            [ "A", 2, 0, 67 ],
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 464086, 
                                                          root := ~, 
                                                          start := 464008, 
                                                          stop := 464085 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 67 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 67 ], 
                                                  name := "Item", 
                                                  next := 464102, root := ~, 
                                                  start := 463850, 
                                                  stop := 464101 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 69 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 2, 0, 69 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 69 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 69 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 69 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 69 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 69 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 69 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 function ", count := [ "A", 2, 0, 69 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "IsSimpleGraph", count :\
= [ "A", 2, 0, 69 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 69 ],
                                                                  mathmode := \
"Text", name := "C", next := 464199, root := ~, start := 464179, stop := 46419\
8 ), rec( HTML := true, content := " is equivalent to\n            ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 69 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsSymm\
etricDigraph" ), content := 0, count := [ "A", 2, 0, 69 ], mathmode := "Text",
                                                                  name := "Ref\
", next := 464261, root := ~, start := 464229, stop := 464260 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
\n            and not  ", count := [ "A", 2, 0, 69 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Prop := "DigraphHasLoops" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 69 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 464312, root := ~, start := 464283, 
                                                                  stop := 4643\
11 ), rec( HTML := true, content := ".\n          ", count := [ "A", 2, 0, 69 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 69 ], 
                                                          name := "Alt", 
                                                          next := 464330, 
                                                          root := ~, 
                                                          start := 464128, 
                                                          stop := 464329 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 69 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 69 ], 
                                                  name := "Item", 
                                                  next := 464346, root := ~, 
                                                  start := 464111, 
                                                  stop := 464345 ) ], 
                                          count := [ "A", 2, 0, 64 ], 
                                          name := "Row", next := 464359, 
                                          root := ~, start := 463774, 
                                          stop := 464358 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 70 ], 
                                          name := "HorLine", next := 464376, 
                                          root := ~, start := 464366, 
                                          stop := 464375 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 71 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
djacency", count := [ "A", 2, 0, 71 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 71 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 464431, 
                                                          root := ~, 
                                                          start := 464415, 
                                                          stop := 464430 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 71 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 71 ], 
                                                  name := "Item", 
                                                  next := 464447, root := ~, 
                                                  start := 464398, 
                                                  stop := 464446 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 73 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "OutNeig\
hboursOfVertex" ), content := 0, count := [ "A", 2, 0, 73 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 464508, 
                                                          root := ~, 
                                                          start := 464473, 
                                                          stop := 464507 ), 
                                                      rec( 
                                                          content := "\n      \
    ", count := [ "A", 2, 0, 73 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            (see also ", count := [ "A", 2, 0, 73 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "InNeighboursOfVertex" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 73 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 464593, root := ~, start := 464559, 
                                                                  stop := 4645\
92 ), rec( HTML := true, content := ")\n          ", count := [ "A", 2, 0, 73 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 73 ], 
                                                          name := "Alt", 
                                                          next := 464611, 
                                                          root := ~, 
                                                          start := 464519, 
                                                          stop := 464610 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 73 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 73 ], 
                                                  name := "Item", 
                                                  next := 464627, root := ~, 
                                                  start := 464456, 
                                                  stop := 464626 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 75 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The operation ", count := [ "A", 2, 0, 75 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "OutNeighboursOfVertex" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 75 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 464732, root := ~, start := 464697, 
                                                                  stop := 4647\
31 ), rec( HTML := true, content := " behaves the same\n            as ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 75 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Adjacency", count := [ "A", 2, 0, 75 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 75 ], mathmode := "\
Text", name := "C", next := 464781, root := ~, start := 464765, stop := 464780\
 ), rec( HTML := true, content := " in ", count := [ "A", 2, 0, 75 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 75 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 75 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 75 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 75 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 75 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 75 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 75 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 75 ], name := "Alt", next := 464810, 
                                                          root := ~, 
                                                          start := 464653, 
                                                          stop := 464809 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 75 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 75 ], 
                                                  name := "Item", 
                                                  next := 464826, root := ~, 
                                                  start := 464636, 
                                                  stop := 464825 ) ], 
                                          count := [ "A", 2, 0, 70 ], 
                                          name := "Row", next := 464839, 
                                          root := ~, start := 464384, 
                                          stop := 464838 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 76 ], 
                                          name := "HorLine", next := 464856, 
                                          root := ~, start := 464846, 
                                          stop := 464855 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 77 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sEdge", count := [ "A", 2, 0, 77 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 77 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 464908, 
                                                          root := ~, 
                                                          start := 464895, 
                                                          stop := 464907 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 77 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 77 ], 
                                                  name := "Item", 
                                                  next := 464924, root := ~, 
                                                  start := 464878, 
                                                  stop := 464923 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 79 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graph and list", Oper := "IsDigraphEdge" ), content := 0, count := 
                                                            [ "A", 2, 0, 79 ],
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 465006, 
                                                          root := ~, 
                                                          start := 464950, 
                                                          stop := 465005 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 79 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 79 ], 
                                                  name := "Item", 
                                                  next := 465022, root := ~, 
                                                  start := 464933, 
                                                  stop := 465021 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 81 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The arguments of\n            ", count := [ "A", 2, 0, 81 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for d\
igraph and list", Oper := "IsDigraphEdge" ), content := 0, count := [ "A", 2, 
                                                                      0, 81 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 465163, root := ~, start := 465107, 
                                                                  stop := 4651\
62 ), rec( HTML := true, content := "\n            can be a digraph and an edg\
e, or a digraph and two vertices. In the\n            first form the operation\
\n            ", count := [ "A", 2, 0, 81 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec( Label := "for digraph and list", 
                                                                      Oper := \
"IsDigraphEdge" ), content := 0, count := [ "A", 2, 0, 81 ], mathmode := "Text\
", name := "Ref", next := 465349, root := ~, start := 465293, stop := 465348 )
                                                                , 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
\n            behaves the same as ", count := [ "A", 2, 0, 81 ], mathmode := "\
Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "IsEdge", count := [ "A", 2, 0, 81 ], mathmode := "Text",
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 81 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4653\
95, root := ~, start := 465382, stop := 465394 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 2, 0, 81 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 2, 0, 81 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 2, 0, 81 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 2, 0, 81 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 81 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 81 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 81 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 81 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 81 ], name := "Alt", next := 465424, 
                                                          root := ~, 
                                                          start := 465048, 
                                                          stop := 465423 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 81 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 81 ], 
                                                  name := "Item", 
                                                  next := 465440, root := ~, 
                                                  start := 465031, 
                                                  stop := 465439 ) ], 
                                          count := [ "A", 2, 0, 76 ], 
                                          name := "Row", next := 465453, 
                                          root := ~, start := 464864, 
                                          stop := 465452 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 82 ], 
                                          name := "HorLine", next := 465470, 
                                          root := ~, start := 465460, 
                                          stop := 465469 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 83 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
irectedEdges", count := [ "A", 2, 0, 83 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 2, 0, 83 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 465529, 
                                                          root := ~, 
                                                          start := 465509, 
                                                          stop := 465528 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 83 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 83 ], 
                                                  name := "Item", 
                                                  next := 465545, root := ~, 
                                                  start := 465492, 
                                                  stop := 465544 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 85 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Edges" ), content := 0, count := [ "A", 2, 0, 85 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 465597, 
                                                          root := ~, 
                                                          start := 465571, 
                                                          stop := 465596 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 85 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 85 ], 
                                                  name := "Item", 
                                                  next := 465613, root := ~, 
                                                  start := 465554, 
                                                  stop := 465612 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 87 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The attribute ", count := [ "A", 2, 0, 87 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphEdges" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 87 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 465709, root := ~, start := 465683, 
                                                                  stop := 4657\
08 ), rec( HTML := true, content := " behaves the same\n            as ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 87 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "DirectedEdges", count := [ "A", 2, 0, 87 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 87 ], 
                                                                  mathmode := \
"Text", name := "C", next := 465762, root := ~, start := 465742, stop := 46576\
1 ), rec( HTML := true, content := " in ", count := [ "A", 2, 0, 87 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 87 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 87 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 87 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 87 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 87 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 87 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 87 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 87 ], name := "Alt", next := 465791, 
                                                          root := ~, 
                                                          start := 465639, 
                                                          stop := 465790 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 87 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 87 ], 
                                                  name := "Item", 
                                                  next := 465807, root := ~, 
                                                  start := 465622, 
                                                  stop := 465806 ) ], 
                                          count := [ "A", 2, 0, 82 ], 
                                          name := "Row", next := 465820, 
                                          root := ~, start := 465478, 
                                          stop := 465819 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 88 ], 
                                          name := "HorLine", next := 465837, 
                                          root := ~, start := 465827, 
                                          stop := 465836 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 89 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "U\
ndirectedEdges", count := [ "A", 2, 0, 89 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 2, 0, 89 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 465898, 
                                                          root := ~, 
                                                          start := 465876, 
                                                          stop := 465897 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 89 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 89 ], 
                                                  name := "Item", 
                                                  next := 465914, root := ~, 
                                                  start := 465859, 
                                                  stop := 465913 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 2, 0, 91 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 91 ], 
                                                  name := "Item", 
                                                  next := 465960, root := ~, 
                                                  start := 465923, 
                                                  stop := 465959 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 93 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            There is no analogous function in ", count := [ "A", 2, 0, 93 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 2, 0, 93 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 93 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, and no plans to\n            include one.\n          ", count := [ "A", 2, 
                                                                      0, 93 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 93 ], 
                                                          name := "Alt", 
                                                          next := 466119, 
                                                          root := ~, 
                                                          start := 465986, 
                                                          stop := 466118 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 93 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 93 ], 
                                                  name := "Item", 
                                                  next := 466135, root := ~, 
                                                  start := 465969, 
                                                  stop := 466134 ) ], 
                                          count := [ "A", 2, 0, 88 ], 
                                          name := "Row", next := 466148, 
                                          root := ~, start := 465845, 
                                          stop := 466147 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 94 ], 
                                          name := "HorLine", next := 466165, 
                                          root := ~, start := 466155, 
                                          stop := 466164 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 95 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
istance", count := [ "A", 2, 0, 95 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 95 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 466219, 
                                                          root := ~, 
                                                          start := 466204, 
                                                          stop := 466218 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 95 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 95 ], 
                                                  name := "Item", 
                                                  next := 466235, root := ~, 
                                                  start := 466187, 
                                                  stop := 466234 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 97 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph and two vertices", Oper := "DigraphShortestDistance" ), content := 0, 
                                                          count := 
                                                            [ "A", 2, 0, 97 ],
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 466352, 
                                                          root := ~, 
                                                          start := 466261, 
                                                          stop := 466351 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 97 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 97 ], 
                                                  name := "Item", 
                                                  next := 466368, root := ~, 
                                                  start := 466244, 
                                                  stop := 466367 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 99 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The operation ", count := [ "A", 2, 0, 99 ], mathmode := "Text",
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Label := "for a digraph and two ver\
tices", Oper := "DigraphShortestDistance" ), content := 0, count := [ "A", 2, 
                                                                      0, 99 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 466526, root := ~, start := 466438, 
                                                                  stop := 4665\
25 ), rec( HTML := true, content := " behaves the same as\n            ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 99 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Distance", count := [ "A", 2, 0, 99 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 99 ], mathmode := "T\
ext", name := "C", next := 466574, root := ~, start := 466559, stop := 466573 
                                                                 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 in ", count := [ "A", 2, 0, 99 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 2, 0, 99 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 2, 0, 99 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 2, 0, 99 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 99 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 2, 0, 99 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 2, 0, 99 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 99 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 2, 0, 99 ], name := "Alt", next := 466603, 
                                                          root := ~, 
                                                          start := 466394, 
                                                          stop := 466602 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 99 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 99 ], 
                                                  name := "Item", 
                                                  next := 466619, root := ~, 
                                                  start := 466377, 
                                                  stop := 466618 ) ], 
                                          count := [ "A", 2, 0, 94 ], 
                                          name := "Row", next := 466632, 
                                          root := ~, start := 466173, 
                                          stop := 466631 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 100 ], 
                                          name := "HorLine", next := 466649, 
                                          root := ~, start := 466639, 
                                          stop := 466648 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 101 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
iameter", count := [ "A", 2, 0, 101 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 101 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 466703, 
                                                          root := ~, 
                                                          start := 466688, 
                                                          stop := 466702 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 101 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 101 ],
                                                  name := "Item", 
                                                  next := 466719, root := ~, 
                                                  start := 466671, 
                                                  stop := 466718 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 103 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Diameter" ), content := 0, count := [ "A", 2, 0, 103 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 466774, 
                                                          root := ~, 
                                                          start := 466745, 
                                                          stop := 466773 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 103 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 103 ],
                                                  name := "Item", 
                                                  next := 466790, root := ~, 
                                                  start := 466728, 
                                                  stop := 466789 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 105 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The attribute ", count := [ "A", 2, 0, 105 ], mathmode := "Text"
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphDiameter" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 105 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "Ref", next := 466889, root := ~, start := 466860, 
                                                                  stop := 4668\
88 ), rec( HTML := true, content := " behaves the same\n            as ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 105 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Diameter", count := [ "A", 2, 0, 105 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 105 ], mathmode := \
"Text", name := "C", next := 466937, root := ~, start := 466922, stop := 46693\
6 ), rec( HTML := true, content := " in ", count := [ "A", 2, 0, 105 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 105 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 105 ],
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 105 ]
                                                                    , 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 105 ], name := "PCDATA", root :\
= ~ ) ], count := [ "A", 2, 0, 105 ], name := "Package", next := 137, root := \
~, start := 113, stop := 136 ) ], count := [ "A", 2, 0, 105 ], mathmode := "Te\
xt", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 105 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 2, 0, 105 ], name := "Alt", 
                                                          next := 466966, 
                                                          root := ~, 
                                                          start := 466816, 
                                                          stop := 466965 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 105 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 105 ],
                                                  name := "Item", 
                                                  next := 466982, root := ~, 
                                                  start := 466799, 
                                                  stop := 466981 ) ], 
                                          count := [ "A", 2, 0, 100 ], 
                                          name := "Row", next := 466995, 
                                          root := ~, start := 466657, 
                                          stop := 466994 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 106 ], 
                                          name := "HorLine", next := 467012, 
                                          root := ~, start := 467002, 
                                          stop := 467011 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 107 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
irth", count := [ "A", 2, 0, 107 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 107 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 467063, 
                                                          root := ~, 
                                                          start := 467051, 
                                                          stop := 467062 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 107 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 107 ],
                                                  name := "Item", 
                                                  next := 467079, root := ~, 
                                                  start := 467034, 
                                                  stop := 467078 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 109 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
UndirectedGirth" ), content := 0, count := [ "A", 2, 0, 109 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 467141, 
                                                          root := ~, 
                                                          start := 467105, 
                                                          stop := 467140 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 109 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 109 ],
                                                  name := "Item", 
                                                  next := 467157, root := ~, 
                                                  start := 467088, 
                                                  stop := 467156 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 111 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The attribute ", count := [ "A", 2, 0, 111 ], mathmode := "Text"
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphUndirectedGirth" ),
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 111 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "Ref", next := 467263, root := ~, start := 467227, 
                                                                  stop := 4672\
62 ), rec( HTML := true, content := " behaves the same\n            as ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 111 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Girth", count := [ "A", 2, 0, 111 ], mathmode := "Text",
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 111 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4673\
08, root := ~, start := 467296, stop := 467307 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 2, 0, 111 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 2, 0, 111 ], mathmode := "Text", name := "PCDATA", roo\
t := ~ ) ], count := [ "A", 2, 0, 111 ], mathmode := "Text", name := "URL", 
                                                                          next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 2, 0, 111 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 111 ], name := "PCDATA", root :\
= ~ ) ], count := [ "A", 2, 0, 111 ], name := "Package", next := 137, root := \
~, start := 113, stop := 136 ) ], count := [ "A", 2, 0, 111 ], mathmode := "Te\
xt", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 except that in the case that the\n            argument is a forest, ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 111 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "infinity", count := [ "A", 2, 0, 111 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 111 ], mathmode := \
"Text", name := "K", next := 467402, root := ~, start := 467387, stop := 46740\
1 ), rec( HTML := true, content := " is returned by ", count := [ "A", 2, 0, 
                                                                      111 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 2, 0, 111 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 111 ], mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
\n            whereas ", count := [ "A", 2, 0, 111 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true,
                                                                          cont\
ent := "-1", count := [ "A", 2, 0, 111 ], mathmode := "Text", name := "PCDATA"
                                                                            , 
                                                                          root\
 := ~ ) ], count := [ "A", 2, 0, 111 ], mathmode := "Text", name := "C", 
                                                                  next := 4674\
58, root := ~, start := 467449, stop := 467457 ), rec( HTML := true, 
                                                                  content := "\
 is returned by ", count := [ "A", 2, 0, 111 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 111 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 111 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 111 ]
                                                                    , 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 111 ], name := "PCDATA", root :\
= ~ ) ], count := [ "A", 2, 0, 111 ], name := "Package", next := 137, root := \
~, start := 113, stop := 136 ) ], count := [ "A", 2, 0, 111 ], mathmode := "Te\
xt", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 111 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 2, 0, 111 ], name := "Alt", 
                                                          next := 467499, 
                                                          root := ~, 
                                                          start := 467183, 
                                                          stop := 467498 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 111 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 111 ],
                                                  name := "Item", 
                                                  next := 467515, root := ~, 
                                                  start := 467166, 
                                                  stop := 467514 ) ], 
                                          count := [ "A", 2, 0, 106 ], 
                                          name := "Row", next := 467528, 
                                          root := ~, start := 467020, 
                                          stop := 467527 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 112 ], 
                                          name := "HorLine", next := 467545, 
                                          root := ~, start := 467535, 
                                          stop := 467544 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 113 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sConnectedGraph", count := [ "A", 2, 0, 113 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 2, 0, 113 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 467607, 
                                                          root := ~, 
                                                          start := 467584, 
                                                          stop := 467606 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 113 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 113 ],
                                                  name := "Item", 
                                                  next := 467623, root := ~, 
                                                  start := 467567, 
                                                  stop := 467622 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 115 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsStron\
glyConnectedDigraph" ), content := 0, count := [ "A", 2, 0, 115 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 467689, 
                                                          root := ~, 
                                                          start := 467649, 
                                                          stop := 467688 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 115 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 115 ],
                                                  name := "Item", 
                                                  next := 467705, root := ~, 
                                                  start := 467632, 
                                                  stop := 467704 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 117 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The attribute ", count := [ "A", 2, 0, 117 ], mathmode := "Text"
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Prop := "IsStronglyConnectedDigraph\
" ), content := 0, count := [ "A", 2, 0, 117 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 467815, root := ~, start := 467775, stop := 467814 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 behaves the\n            same as ", count := [ "A", 2, 0, 117 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "IsConnectedGraph", count := [ "A", 2, 0, 117 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 117 ], 
                                                                  mathmode := \
"Text", name := "C", next := 467871, root := ~, start := 467848, stop := 46787\
0 ), rec( HTML := true, content := " in ", count := [ "A", 2, 0, 117 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 117 ], mat\
hmode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 117 ],
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 117 ]
                                                                    , 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 117 ], name := "PCDATA", root :\
= ~ ) ], count := [ "A", 2, 0, 117 ], name := "Package", next := 137, root := \
~, start := 113, stop := 136 ) ], count := [ "A", 2, 0, 117 ], mathmode := "Te\
xt", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 2, 0, 117 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 2, 0, 117 ], name := "Alt", 
                                                          next := 467900, 
                                                          root := ~, 
                                                          start := 467731, 
                                                          stop := 467899 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 117 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 117 ],
                                                  name := "Item", 
                                                  next := 467916, root := ~, 
                                                  start := 467714, 
                                                  stop := 467915 ) ], 
                                          count := [ "A", 2, 0, 112 ], 
                                          name := "Row", next := 467929, 
                                          root := ~, start := 467553, 
                                          stop := 467928 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 118 ], 
                                          name := "HorLine", next := 467946, 
                                          root := ~, start := 467936, 
                                          stop := 467945 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 119 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sBipartite", count := [ "A", 2, 0, 119 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 119 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 468003, 
                                                          root := ~, 
                                                          start := 467985, 
                                                          stop := 468002 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 119 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 119 ],
                                                  name := "Item", 
                                                  next := 468019, root := ~, 
                                                  start := 467968, 
                                                  stop := 468018 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 121 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsBipar\
titeDigraph" ), content := 0, count := [ "A", 2, 0, 121 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 468077, 
                                                          root := ~, 
                                                          start := 468045, 
                                                          stop := 468076 ), 
                                                      rec( 
                                                          content := "\n      \
    ", count := [ "A", 2, 0, 121 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            and ", count := [ "A", 2, 0, 121 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Prop := "IsSymmetricDigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 121 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "Ref", next := 468154, root := ~, start := 468122, 
                                                                  stop := 4681\
53 ), rec( HTML := true, content := "\n          ", count := [ "A", 2, 0, 121 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 121 ], 
                                                          name := "Alt", 
                                                          next := 468171, 
                                                          root := ~, 
                                                          start := 468088, 
                                                          stop := 468170 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 121 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 121 ],
                                                  name := "Item", 
                                                  next := 468187, root := ~, 
                                                  start := 468028, 
                                                  stop := 468186 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 123 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 2, 0, 123 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 123 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 123 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 123 ]
                                                                    , 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 123 ], name := "PCDATA", root :\
= ~ ) ], count := [ "A", 2, 0, 123 ], name := "Package", next := 137, root := \
~, start := 113, stop := 136 ) ], count := [ "A", 2, 0, 123 ], mathmode := "Te\
xt", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 function ", count := [ "A", 2, 0, 123 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "IsBipartite", count := 
                                                                            [ \
"A", 2, 0, 123 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 123 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "C", next := 468282, root := ~, start := 468264, stop := 46828\
1 ), rec( HTML := true, content := " is equivalent to\n            ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 123 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsBipa\
rtiteDigraph" ), content := 0, count := [ "A", 2, 0, 123 ], mathmode := "Text"
                                                                    , 
                                                                  name := "Ref\
", next := 468344, root := ~, start := 468312, stop := 468343 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 and ", count := [ "A", 2, 0, 123 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Prop := "IsSymmetricDigraph" ), content := 0, count := [ "A", 2, 0, 
                                                                      123 ], 
                                                                  mathmode := \
"Text", name := "Ref", next := 468395, root := ~, start := 468349, 
                                                                  stop := 4683\
94 ), rec( HTML := true, content := ".\n          ", count := [ "A", 2, 0, 
                                                                      123 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 123 ], 
                                                          name := "Alt", 
                                                          next := 468413, 
                                                          root := ~, 
                                                          start := 468213, 
                                                          stop := 468412 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 123 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 123 ],
                                                  name := "Item", 
                                                  next := 468429, root := ~, 
                                                  start := 468196, 
                                                  stop := 468428 ) ], 
                                          count := [ "A", 2, 0, 118 ], 
                                          name := "Row", next := 468442, 
                                          root := ~, start := 467954, 
                                          stop := 468441 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 124 ], 
                                          name := "HorLine", next := 468459, 
                                          root := ~, start := 468449, 
                                          stop := 468458 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 125 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sNullGraph", count := [ "A", 2, 0, 125 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 2, 0, 125 ]
                                                            , 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 468516, 
                                                          root := ~, 
                                                          start := 468498, 
                                                          stop := 468515 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 125 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 125 ],
                                                  name := "Item", 
                                                  next := 468532, root := ~, 
                                                  start := 468481, 
                                                  stop := 468531 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 127 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsNullD\
igraph" ), content := 0, count := [ "A", 2, 0, 127 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 468585, 
                                                          root := ~, 
                                                          start := 468558, 
                                                          stop := 468584 ), 
                                                      rec( 
                                                          content := "\n      \
    ", count := [ "A", 2, 0, 127 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            or ", count := [ "A", 2, 0, 127 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Prop := "IsEmptyDigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 127 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "Ref", next := 468657, root := ~, start := 468629, 
                                                                  stop := 4686\
56 ), rec( HTML := true, content := "\n          ", count := [ "A", 2, 0, 127 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 127 ], 
                                                          name := "Alt", 
                                                          next := 468674, 
                                                          root := ~, 
                                                          start := 468596, 
                                                          stop := 468673 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 127 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 127 ],
                                                  name := "Item", 
                                                  next := 468690, root := ~, 
                                                  start := 468541, 
                                                  stop := 468689 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 129 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 2, 0, 129 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 129 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 129 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 129 ]
                                                                    , 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 129 ], name := "PCDATA", root :\
= ~ ) ], count := [ "A", 2, 0, 129 ], name := "Package", next := 137, root := \
~, start := 113, stop := 136 ) ], count := [ "A", 2, 0, 129 ], mathmode := "Te\
xt", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 function ", count := [ "A", 2, 0, 129 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "IsNullGraph", count := 
                                                                            [ \
"A", 2, 0, 129 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 129 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "C", next := 468785, root := ~, start := 468767, stop := 46878\
4 ), rec( HTML := true, content := " is equivalent to\n            ", 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 129 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsEmpt\
yDigraph" ), content := 0, count := [ "A", 2, 0, 129 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 468843, root := ~, start := 468815, stop := 468842 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 and its synonym ", count := [ "A", 2, 0, 129 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Prop := "IsNullDigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 129 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "Ref", next := 468901, root := ~, start := 468860, 
                                                                  stop := 4689\
00 ), rec( HTML := true, content := ".\n          ", count := [ "A", 2, 0, 
                                                                      129 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 129 ], 
                                                          name := "Alt", 
                                                          next := 468919, 
                                                          root := ~, 
                                                          start := 468716, 
                                                          stop := 468918 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 129 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 129 ],
                                                  name := "Item", 
                                                  next := 468935, root := ~, 
                                                  start := 468699, 
                                                  stop := 468934 ) ], 
                                          count := [ "A", 2, 0, 124 ], 
                                          name := "Row", next := 468948, 
                                          root := ~, start := 468467, 
                                          stop := 468947 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 130 ], 
                                          name := "HorLine", next := 468965, 
                                          root := ~, start := 468955, 
                                          stop := 468964 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 131 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sCompleteGraph", count := [ "A", 2, 0, 131 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ "A", 2, 0, 131 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 469026, 
                                                          root := ~, 
                                                          start := 469004, 
                                                          stop := 469025 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 131 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 131 ],
                                                  name := "Item", 
                                                  next := 469042, root := ~, 
                                                  start := 468987, 
                                                  stop := 469041 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 133 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsCompl\
eteDigraph" ), content := 0, count := [ "A", 2, 0, 133 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 469099, 
                                                          root := ~, 
                                                          start := 469068, 
                                                          stop := 469098 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 133 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 133 ],
                                                  name := "Item", 
                                                  next := 469115, root := ~, 
                                                  start := 469051, 
                                                  stop := 469114 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 2, 0, 135 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 2, 0, 135 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 2, 0, 135 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 135 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 135 ]
                                                                    , 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 2, 0, 135 ], name := "PCDATA", root :\
= ~ ) ], count := [ "A", 2, 0, 135 ], name := "Package", next := 137, root := \
~, start := 113, stop := 136 ) ], count := [ "A", 2, 0, 135 ], mathmode := "Te\
xt", name := "Alt", next := 143, root := ~, start := 93, stop := 142 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 function ", count := [ "A", 2, 0, 135 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "IsCompleteGraph", count\
 := [ "A", 2, 0, 135 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 2, 
                                                                      0, 135 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "C", next := 469214, root := ~, start := 469192, stop := 46921\
3 ), rec( HTML := true, content := " is roughly\n            equivalent to\n  \
          ", count := [ "A", 2, 0, 135 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Prop := "IsCompleteDigraph" ), content := 0, count := [ "A", 2, 0, 135 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "Ref", next := 469295, root := ~, start := 469264, 
                                                                  stop := 4692\
94 ), rec( HTML := true, content := " except that in ", count := [ "A", 2, 0, 
                                                                      135 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 2, 0, 135 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 135 ], mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
\n            a complete digraph has ", count := [ "A", 2, 0, 135 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "no loops", count := [ "A", 2, 0, 135 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 135 ], mathmode := \
"Text", name := "E", next := 469372, root := ~, start := 469357, stop := 46937\
1 ), rec( HTML := true, content := ".\n          ", count := [ "A", 2, 0, 135 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 2, 0, 135 ], 
                                                          name := "Alt", 
                                                          next := 469390, 
                                                          root := ~, 
                                                          start := 469141, 
                                                          stop := 469389 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 2, 0, 135 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 2, 0, 135 ],
                                                  name := "Item", 
                                                  next := 469406, root := ~, 
                                                  start := 469124, 
                                                  stop := 469405 ) ], 
                                          count := [ "A", 2, 0, 130 ], 
                                          name := "Row", next := 469419, 
                                          root := ~, start := 468973, 
                                          stop := 469418 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 2, 0, 136 ], 
                                          name := "HorLine", next := 469436, 
                                          root := ~, start := 469426, 
                                          stop := 469435 ) ], 
                                  count := [ "A", 2, 0, 4 ], 
                                  mathmode := "Text", name := "Table", 
                                  next := 469449, root := ~, start := 459429, 
                                  stop := 469448 ), 
                              rec( content := "\n  ", 
                                  count := [ "A", 2, 0, 137 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 2, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 469462, root := ~, start := 459182, 
                          stop := 469461 ), 
                      rec( content := "\n\n  ", count := [ "A", 2, 0, 137 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n    ", 
                                  count := [ "A", 3, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n      Functions to dete\
rmine regularity properties of graphs\n    ", count := [ "A", 3, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 3, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 469565, root := ~, start := 469480, 
                                  stop := 469564 ), 
                              rec( content := "\n    ", 
                                  count := [ "A", 3, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Not := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( content := "\n      ", 
                                          count := [ "A", 3, 0, 3 ], 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n        The tab\
le in this section contains more information when viewed in\n        html form\
at.\n      ", count := [ "A", 3, 0, 3 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ "A", 3, 0, 3 ], 
                                          name := "E", next := 469703, 
                                          root := ~, start := 469593, 
                                          stop := 469702 ), 
                                      rec( content := "\n    ", 
                                          count := [ "A", 3, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 3, 0, 3 ], 
                                  mathmode := "Text", name := "Alt", 
                                  next := 469714, root := ~, start := 469570, 
                                  stop := 469713 ), 
                              rec( content := "\n\n    ", 
                                  count := [ "A", 3, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Align := "|l|l|l|" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 3, 0, 4 ], 
                                          name := "HorLine", next := 469760, 
                                          root := ~, start := 469750, 
                                          stop := 469759 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ "A", 3, 0, 5 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 3, 0, 5 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ "A", 3, 0, 5 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ "A", 3, 0, 5 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 5 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ "A", 3, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 3, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 469830, root := ~, 
                                                  start := 469782, 
                                                  stop := 469829 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ "A", 3, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 3, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 3, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 469890, root := ~, 
                                                  start := 469839, 
                                                  stop := 469889 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Comments\n          ", count := [ "A", 3, 0, 9 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 9 ], 
                                                          name := "Alt", 
                                                          next := 469971, 
                                                          root := ~, 
                                                          start := 469916, 
                                                          stop := 469970 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 469987, root := ~, 
                                                  start := 469899, 
                                                  stop := 469986 ) ], 
                                          count := [ "A", 3, 0, 4 ], 
                                          name := "Row", next := 470000, 
                                          root := ~, start := 469768, 
                                          stop := 469999 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 3, 0, 10 ], 
                                          name := "HorLine", next := 470017, 
                                          root := ~, start := 470007, 
                                          stop := 470016 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sRegularGraph", count := [ "A", 3, 0, 11 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 3, 0, 11 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 470077, 
                                                          root := ~, 
                                                          start := 470056, 
                                                          stop := 470076 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 470093, root := ~, 
                                                  start := 470039, 
                                                  stop := 470092 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsOutRe\
gularDigraph" ), content := 0, count := [ "A", 3, 0, 13 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 470152, 
                                                          root := ~, 
                                                          start := 470119, 
                                                          stop := 470151 ), 
                                                      rec( 
                                                          content := "\n      \
    ", count := [ "A", 3, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            (see also\n            ", count := [ "A", 3, 0, 13 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsInRe\
gularDigraph" ), content := 0, count := [ "A", 3, 0, 13 ], mathmode := "Text",
                                                                  name := "Ref\
", next := 470247, root := ~, start := 470215, stop := 470246 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
\n            and\n            ", count := [ "A", 3, 0, 13 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsRegularD\
igraph" ), content := 0, count := [ "A", 3, 0, 13 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 470306, root := ~, start := 470276, stop := 470305 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
)\n          ", count := [ "A", 3, 0, 13 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 3, 0, 13 ], name := "Alt", next := 470324, 
                                                          root := ~, 
                                                          start := 470163, 
                                                          stop := 470323 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 13 ], 
                                                  name := "Item", 
                                                  next := 470340, root := ~, 
                                                  start := 470102, 
                                                  stop := 470339 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 3, 0, 15 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 3, 0, 15 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 15 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 15 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 3, 0, 15 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 3, 0, 15 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 3, 0, 15 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 function ", count := [ "A", 3, 0, 15 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "IsRegularGraph", count \
:= [ "A", 3, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 15 ],
                                                                  mathmode := \
"Text", name := "C", next := 470438, root := ~, start := 470417, stop := 47043\
7 ), rec( HTML := true, content := " is\n            equivalent to ", 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 15 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsOutR\
egularDigraph" ), content := 0, count := [ "A", 3, 0, 15 ], mathmode := "Text"
                                                                    , 
                                                                  name := "Ref\
", next := 470501, root := ~, start := 470468, stop := 470500 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 3, 0, 15 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 3, 0, 15 ], name := "Alt", next := 470519, 
                                                          root := ~, 
                                                          start := 470366, 
                                                          stop := 470518 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 15 ], 
                                                  name := "Item", 
                                                  next := 470535, root := ~, 
                                                  start := 470349, 
                                                  stop := 470534 ) ], 
                                          count := [ "A", 3, 0, 10 ], 
                                          name := "Row", next := 470548, 
                                          root := ~, start := 470025, 
                                          stop := 470547 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 3, 0, 16 ], 
                                          name := "HorLine", next := 470565, 
                                          root := ~, start := 470555, 
                                          stop := 470564 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
ocalParameters", count := [ "A", 3, 0, 17 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 3, 0, 17 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 470626, 
                                                          root := ~, 
                                                          start := 470604, 
                                                          stop := 470625 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 17 ], 
                                                  name := "Item", 
                                                  next := 470642, root := ~, 
                                                  start := 470587, 
                                                  stop := 470641 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 3, 0, 19 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 19 ], 
                                                  name := "Item", 
                                                  next := 470688, root := ~, 
                                                  start := 470651, 
                                                  stop := 470687 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
  ", count := [ "A", 3, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 3, 0, 21 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 3, 0, 21 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 21 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 21 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 3, 0, 21 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 3, 0, 21 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 3, 0, 21 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 function ", count := [ "A", 3, 0, 21 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "LocalParameters", count\
 := [ "A", 3, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 21 ],
                                                                  mathmode := \
"Text", name := "C", next := 470786, root := ~, start := 470764, stop := 47078\
5 ), rec( HTML := true, content := " has no equivalent\n            function i\
n ", count := [ "A", 3, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 3, 0, 21 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 21 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, although this might change in the future.\n          ", count := [ "A", 3, 
                                                                      0, 21 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 21 ], 
                                                          name := "Alt", 
                                                          next := 470899, 
                                                          root := ~, 
                                                          start := 470713, 
                                                          stop := 470898 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 21 ], 
                                                  name := "Item", 
                                                  next := 470915, root := ~, 
                                                  start := 470697, 
                                                  stop := 470914 ) ], 
                                          count := [ "A", 3, 0, 16 ], 
                                          name := "Row", next := 470928, 
                                          root := ~, start := 470573, 
                                          stop := 470927 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 3, 0, 22 ], 
                                          name := "HorLine", next := 470945, 
                                          root := ~, start := 470935, 
                                          stop := 470944 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
lobalParameters", count := [ "A", 3, 0, 23 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ "A", 3, 0, 23 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 471007, 
                                                          root := ~, 
                                                          start := 470984, 
                                                          stop := 471006 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 23 ], 
                                                  name := "Item", 
                                                  next := 471023, root := ~, 
                                                  start := 470967, 
                                                  stop := 471022 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 3, 0, 25 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 25 ], 
                                                  name := "Item", 
                                                  next := 471069, root := ~, 
                                                  start := 471032, 
                                                  stop := 471068 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
  ", count := [ "A", 3, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 3, 0, 27 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 3, 0, 27 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 27 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 27 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 3, 0, 27 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 3, 0, 27 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 3, 0, 27 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 function ", count := [ "A", 3, 0, 27 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "GlobalParameters", coun\
t := [ "A", 3, 0, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "C", next := 471168, root := ~, start := 471145, stop := 47116\
7 ), rec( HTML := true, content := " has no equivalent\n            function i\
n ", count := [ "A", 3, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 3, 0, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, although this might change in the future.\n          ", count := [ "A", 3, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 27 ], 
                                                          name := "Alt", 
                                                          next := 471281, 
                                                          root := ~, 
                                                          start := 471094, 
                                                          stop := 471280 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 27 ], 
                                                  name := "Item", 
                                                  next := 471297, root := ~, 
                                                  start := 471078, 
                                                  stop := 471296 ) ], 
                                          count := [ "A", 3, 0, 22 ], 
                                          name := "Row", next := 471310, 
                                          root := ~, start := 470953, 
                                          stop := 471309 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 3, 0, 28 ], 
                                          name := "HorLine", next := 471327, 
                                          root := ~, start := 471317, 
                                          stop := 471326 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sDistanceRegular", count := [ "A", 3, 0, 29 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 3, 0, 29 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 471390, 
                                                          root := ~, 
                                                          start := 471366, 
                                                          stop := 471389 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 29 ], 
                                                  name := "Item", 
                                                  next := 471406, root := ~, 
                                                  start := 471349, 
                                                  stop := 471405 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 31 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Prop := "IsDista\
nceRegularDigraph" ), content := 0, count := [ "A", 3, 0, 31 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 471470, 
                                                          root := ~, 
                                                          start := 471432, 
                                                          stop := 471469 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 31 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 31 ], 
                                                  name := "Item", 
                                                  next := 471486, root := ~, 
                                                  start := 471415, 
                                                  stop := 471485 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 3, 0, 33 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 3, 0, 33 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 33 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 33 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 3, 0, 33 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 3, 0, 33 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 3, 0, 33 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 function ", count := [ "A", 3, 0, 33 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "IsDistanceRegular", 
                                                                          coun\
t := [ "A", 3, 0, 33 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 33 ],
                                                                  mathmode := \
"Text", name := "C", next := 471587, root := ~, start := 471563, stop := 47158\
6 ), rec( HTML := true, content := " is\n            equivalent to ", 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 33 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsDist\
anceRegularDigraph" ), content := 0, count := [ "A", 3, 0, 33 ], mathmode := "\
Text", name := "Ref", next := 471655, root := ~, start := 471617, stop := 4716\
54 ), rec( HTML := true, content := ".\n          ", count := [ "A", 3, 0, 33 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 33 ], 
                                                          name := "Alt", 
                                                          next := 471673, 
                                                          root := ~, 
                                                          start := 471512, 
                                                          stop := 471672 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 33 ], 
                                                  name := "Item", 
                                                  next := 471689, root := ~, 
                                                  start := 471495, 
                                                  stop := 471688 ) ], 
                                          count := [ "A", 3, 0, 28 ], 
                                          name := "Row", next := 471702, 
                                          root := ~, start := 471335, 
                                          stop := 471701 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 3, 0, 34 ], 
                                          name := "HorLine", next := 471719, 
                                          root := ~, start := 471709, 
                                          stop := 471718 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
ollapsedAdjacencyMat", count := [ "A", 3, 0, 35 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 3, 0, 35 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 471786, 
                                                          root := ~, 
                                                          start := 471758, 
                                                          stop := 471785 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 35 ], 
                                                  name := "Item", 
                                                  next := 471802, root := ~, 
                                                  start := 471741, 
                                                  stop := 471801 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 3, 0, 37 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 37 ], 
                                                  name := "Item", 
                                                  next := 471848, root := ~, 
                                                  start := 471811, 
                                                  stop := 471847 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
  ", count := [ "A", 3, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 3, 0, 39 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 3, 0, 39 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 39 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 39 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 3, 0, 39 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 3, 0, 39 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 3, 0, 39 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 function ", count := [ "A", 3, 0, 39 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "CollapsedAdjacencyMat",
                                                                          coun\
t := [ "A", 3, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 39 ],
                                                                  mathmode := \
"Text", name := "C", next := 471952, root := ~, start := 471924, stop := 47195\
1 ), rec( HTML := true, content := " has no equivalent\n            function i\
n ", count := [ "A", 3, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 3, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 39 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, although this might change in the future.\n          ", count := [ "A", 3, 
                                                                      0, 39 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 39 ], 
                                                          name := "Alt", 
                                                          next := 472065, 
                                                          root := ~, 
                                                          start := 471873, 
                                                          stop := 472064 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 39 ], 
                                                  name := "Item", 
                                                  next := 472081, root := ~, 
                                                  start := 471857, 
                                                  stop := 472080 ) ], 
                                          count := [ "A", 3, 0, 34 ], 
                                          name := "Row", next := 472094, 
                                          root := ~, start := 471727, 
                                          stop := 472093 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 3, 0, 40 ], 
                                          name := "HorLine", next := 472111, 
                                          root := ~, start := 472101, 
                                          stop := 472110 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "O\
rbitalGraphColadjMats", count := [ "A", 3, 0, 41 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 3, 0, 41 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 472179, 
                                                          root := ~, 
                                                          start := 472150, 
                                                          stop := 472178 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 41 ], 
                                                  name := "Item", 
                                                  next := 472195, root := ~, 
                                                  start := 472133, 
                                                  stop := 472194 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 3, 0, 43 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 43 ], 
                                                  name := "Item", 
                                                  next := 472241, root := ~, 
                                                  start := 472204, 
                                                  stop := 472240 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
  ", count := [ "A", 3, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 3, 0, 45 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 3, 0, 45 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 45 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 45 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 3, 0, 45 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 3, 0, 45 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 3, 0, 45 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 function ", count := [ "A", 3, 0, 45 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "OrbitalGraphColadjMats"
                                                                            , 
                                                                          coun\
t := [ "A", 3, 0, 45 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 45 ],
                                                                  mathmode := \
"Text", name := "C", next := 472346, root := ~, start := 472317, stop := 47234\
5 ), rec( HTML := true, content := " has no equivalent\n            function i\
n ", count := [ "A", 3, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 3, 0, 45 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 45 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, although this might change in the future.\n          ", count := [ "A", 3, 
                                                                      0, 45 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 45 ], 
                                                          name := "Alt", 
                                                          next := 472459, 
                                                          root := ~, 
                                                          start := 472266, 
                                                          stop := 472458 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 45 ], 
                                                  name := "Item", 
                                                  next := 472475, root := ~, 
                                                  start := 472250, 
                                                  stop := 472474 ) ], 
                                          count := [ "A", 3, 0, 40 ], 
                                          name := "Row", next := 472488, 
                                          root := ~, start := 472119, 
                                          stop := 472487 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 3, 0, 46 ], 
                                          name := "HorLine", next := 472505, 
                                          root := ~, start := 472495, 
                                          stop := 472504 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 3, 0, 47 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
ertexTransitiveDRGs", count := [ "A", 3, 0, 47 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 3, 0, 47 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 472571, 
                                                          root := ~, 
                                                          start := 472544, 
                                                          stop := 472570 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 47 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 47 ], 
                                                  name := "Item", 
                                                  next := 472587, root := ~, 
                                                  start := 472527, 
                                                  stop := 472586 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 3, 0, 49 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 49 ], 
                                                  name := "Item", 
                                                  next := 472633, root := ~, 
                                                  start := 472596, 
                                                  stop := 472632 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
  ", count := [ "A", 3, 0, 51 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The ", count := [ "A", 3, 0, 51 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Not := "Text" ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          attri\
butes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "h\
ttp://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 3, 0, 51 ], mathm\
ode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 51 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 51 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 3, 0, 51 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 3, 0, 51 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 3, 0, 51 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 function ", count := [ "A", 3, 0, 51 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "VertexTransitiveDRGs", 
                                                                          coun\
t := [ "A", 3, 0, 51 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 51 ],
                                                                  mathmode := \
"Text", name := "C", next := 472736, root := ~, start := 472709, stop := 47273\
5 ), rec( HTML := true, content := " has no equivalent\n            function i\
n ", count := [ "A", 3, 0, 51 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 3, 0, 51 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 3, 
                                                                      0, 51 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, although this might change in the future.\n          ", count := [ "A", 3, 
                                                                      0, 51 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 3, 0, 51 ], 
                                                          name := "Alt", 
                                                          next := 472849, 
                                                          root := ~, 
                                                          start := 472658, 
                                                          stop := 472848 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 3, 0, 51 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 3, 0, 51 ], 
                                                  name := "Item", 
                                                  next := 472865, root := ~, 
                                                  start := 472642, 
                                                  stop := 472864 ) ], 
                                          count := [ "A", 3, 0, 46 ], 
                                          name := "Row", next := 472878, 
                                          root := ~, start := 472513, 
                                          stop := 472877 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 3, 0, 52 ], 
                                          name := "HorLine", next := 472895, 
                                          root := ~, start := 472885, 
                                          stop := 472894 ) ], 
                                  count := [ "A", 3, 0, 4 ], 
                                  mathmode := "Text", name := "Table", 
                                  next := 472909, root := ~, start := 469720, 
                                  stop := 472908 ), 
                              rec( content := "\n\n  ", 
                                  count := [ "A", 3, 0, 53 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 3, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 472923, root := ~, start := 469466, 
                          stop := 472922 ), 
                      rec( content := "\n\n  ", count := [ "A", 3, 0, 53 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n    ", 
                                  count := [ "A", 4, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n      Some special vert\
ex subsets of a graph\n    ", count := [ "A", 4, 0, 2 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 4, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 473010, root := ~, start := 472941, 
                                  stop := 473009 ), 
                              rec( content := "\n    ", 
                                  count := [ "A", 4, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Not := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( content := "\n      ", 
                                          count := [ "A", 4, 0, 3 ], 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n        The tab\
le in this section contains more information when viewed in\n        html form\
at.\n      ", count := [ "A", 4, 0, 3 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ "A", 4, 0, 3 ], 
                                          name := "E", next := 473148, 
                                          root := ~, start := 473038, 
                                          stop := 473147 ), 
                                      rec( content := "\n    ", 
                                          count := [ "A", 4, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 4, 0, 3 ], 
                                  mathmode := "Text", name := "Alt", 
                                  next := 473159, root := ~, start := 473015, 
                                  stop := 473158 ), 
                              rec( content := "\n\n    ", 
                                  count := [ "A", 4, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Align := "|l|l|l|" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 4, 0, 4 ], 
                                          name := "HorLine", next := 473205, 
                                          root := ~, start := 473195, 
                                          stop := 473204 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ "A", 4, 0, 5 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 4, 0, 5 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ "A", 4, 0, 5 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ "A", 4, 0, 5 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 5 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ "A", 4, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 4, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 473275, root := ~, 
                                                  start := 473227, 
                                                  stop := 473274 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ "A", 4, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 4, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 4, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 473335, root := ~, 
                                                  start := 473284, 
                                                  stop := 473334 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Comments\n          ", count := [ "A", 4, 0, 9 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 9 ], 
                                                          name := "Alt", 
                                                          next := 473416, 
                                                          root := ~, 
                                                          start := 473361, 
                                                          stop := 473415 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 473432, root := ~, 
                                                  start := 473344, 
                                                  stop := 473431 ) ], 
                                          count := [ "A", 4, 0, 4 ], 
                                          name := "Row", next := 473445, 
                                          root := ~, start := 473213, 
                                          stop := 473444 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 4, 0, 10 ], 
                                          name := "HorLine", next := 473462, 
                                          root := ~, start := 473452, 
                                          stop := 473461 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
onnectedComponent", count := [ "A", 4, 0, 11 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 4, 0, 11 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 473526, 
                                                          root := ~, 
                                                          start := 473501, 
                                                          stop := 473525 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 473542, root := ~, 
                                                  start := 473484, 
                                                  stop := 473541 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
ConnectedComponent" ), content := 0, count := [ "A", 4, 0, 13 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 473607, 
                                                          root := ~, 
                                                          start := 473568, 
                                                          stop := 473606 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 13 ], 
                                                  name := "Item", 
                                                  next := 473623, root := ~, 
                                                  start := 473551, 
                                                  stop := 473622 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            When applied to a simple di/graph and a vertex,\n            ", 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 15 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "ConnectedComponent", count := [ "A", 4, 0, 15 ], mathmod\
e := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "C", next := 473764, root := ~, start := 473739, stop := 47376\
3 ), rec( HTML := true, content := " in ", count := [ "A", 4, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 4, 0, 15 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 15 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 15 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 15 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 15 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 15 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 4, 0, 15 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "DigraphCon\
nectedComponent" ), content := 0, count := [ "A", 4, 0, 15 ], mathmode := "Tex\
t", name := "Ref", next := 473844, root := ~, start := 473805, stop := 473843 
                                                                 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n            ", count := [ "A", 4, 0, 15 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Oper := "DigraphConnectedComponent"\
 ), content := 0, count := [ "A", 4, 0, 15 ], mathmode := "Text", name := "Ref\
", next := 473897, root := ~, start := 473858, stop := 473896 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 can also be applied to\n            non-simple graphs (in the language of ", 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 15 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 4, 0, 15 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 15 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 15 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 15 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 15 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 15 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
).\n          ", count := [ "A", 4, 0, 15 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 4, 0, 15 ], name := "Alt", 
                                                          next := 473997, 
                                                          root := ~, 
                                                          start := 473649, 
                                                          stop := 473996 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 15 ], 
                                                  name := "Item", 
                                                  next := 474013, root := ~, 
                                                  start := 473632, 
                                                  stop := 474012 ) ], 
                                          count := [ "A", 4, 0, 10 ], 
                                          name := "Row", next := 474026, 
                                          root := ~, start := 473470, 
                                          stop := 474025 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 4, 0, 16 ], 
                                          name := "HorLine", next := 474043, 
                                          root := ~, start := 474033, 
                                          stop := 474042 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
onnectedComponents", count := [ "A", 4, 0, 17 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 4, 0, 17 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 474108, 
                                                          root := ~, 
                                                          start := 474082, 
                                                          stop := 474107 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 17 ], 
                                                  name := "Item", 
                                                  next := 474124, root := ~, 
                                                  start := 474065, 
                                                  stop := 474123 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
ConnectedComponents" ), content := 0, count := [ "A", 4, 0, 19 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 474190, 
                                                          root := ~, 
                                                          start := 474150, 
                                                          stop := 474189 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 19 ], 
                                                  name := "Item", 
                                                  next := 474206, root := ~, 
                                                  start := 474133, 
                                                  stop := 474205 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            When applied to a simple di/graph,\n            ", count := 
                                                                    [ "A", 4, 
                                                                      0, 21 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "ConnectedComponents", count := [ "A", 4, 0, 21 ], mathmo\
de := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "C", next := 474335, root := ~, start := 474309, stop := 47433\
4 ), rec( HTML := true, content := " in ", count := [ "A", 4, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 4, 0, 21 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 21 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 21 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 21 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 21 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 21 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 4, 0, 21 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "DigraphCon\
nectedComponents" ), content := 0, count := [ "A", 4, 0, 21 ], mathmode := "Te\
xt", name := "Ref", next := 474416, root := ~, start := 474376, stop := 474415\
 ), rec( HTML := true, content := ".\n            ", count := [ "A", 4, 0, 21 
                                                                     ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Digrap\
hConnectedComponents" ), content := 0, count := [ "A", 4, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "Ref", next := 474470, root := ~, start := 474430, 
                                                                  stop := 4744\
69 ), rec( HTML := true, content := " can also be applied to\n            non-\
simple graphs (in the language of ", count := [ "A", 4, 0, 21 ], mathmode := "\
Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" ),
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 4, 0, 21 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 21 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 21 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 21 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 21 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 21 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
).\n          ", count := [ "A", 4, 0, 21 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 4, 0, 21 ], name := "Alt", 
                                                          next := 474570, 
                                                          root := ~, 
                                                          start := 474232, 
                                                          stop := 474569 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 21 ], 
                                                  name := "Item", 
                                                  next := 474586, root := ~, 
                                                  start := 474215, 
                                                  stop := 474585 ) ], 
                                          count := [ "A", 4, 0, 16 ], 
                                          name := "Row", next := 474599, 
                                          root := ~, start := 474051, 
                                          stop := 474598 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 4, 0, 22 ], 
                                          name := "HorLine", next := 474616, 
                                          root := ~, start := 474606, 
                                          stop := 474615 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
icomponents", count := [ "A", 4, 0, 23 ], mathmode := "Text", name := "PCDATA"
                                                                    , 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 4, 0, 23 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 474674, 
                                                          root := ~, 
                                                          start := 474655, 
                                                          stop := 474673 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 23 ], 
                                                  name := "Item", 
                                                  next := 474690, root := ~, 
                                                  start := 474638, 
                                                  stop := 474689 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
Bicomponents" ), content := 0, count := [ "A", 4, 0, 25 ], mathmode := "Text",
                                                          name := "Ref", 
                                                          next := 474749, 
                                                          root := ~, 
                                                          start := 474716, 
                                                          stop := 474748 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 25 ], 
                                                  name := "Item", 
                                                  next := 474765, root := ~, 
                                                  start := 474699, 
                                                  stop := 474764 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            When applied to a simple bipartite di/graph,\n            ", 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Bicomponents", count := [ "A", 4, 0, 27 ], mathmode := "\
Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "C", next := 474897, root := ~, start := 474878, stop := 47489\
6 ), rec( HTML := true, content := " in ", count := [ "A", 4, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 4, 0, 27 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 27 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 27 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 27 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 27 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 27 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 4, 0, 27 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "DigraphBic\
omponents" ), content := 0, count := [ "A", 4, 0, 27 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 474971, root := ~, start := 474938, stop := 474970 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n            The definition of ", count := [ "A", 4, 0, 27 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ), rec( attributes := rec( Prop := "IsBipart\
iteDigraph" ), content := 0, count := [ "A", 4, 0, 27 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 475035, root := ~, start := 475003, stop := 475034 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 does not require\n            its argument to be simple (in the language of "
                                                                    , 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 4, 0, 27 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 27 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 27 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 27 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 27 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 27 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
), i.e. the\n            bipartite graphs in ", count := [ "A", 4, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 4, 0, 27 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 27 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 27 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 27 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 27 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 27 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 are a proper subset of the bipartite\n            digraphs in ", count := 
                                                                    [ "A", 4, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 4, 0, 27 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 27 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 4, 0, 27 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 4, 0, 27 ], name := "Alt", next := 475259, 
                                                          root := ~, 
                                                          start := 474791, 
                                                          stop := 475258 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 27 ], 
                                                  name := "Item", 
                                                  next := 475275, root := ~, 
                                                  start := 474774, 
                                                  stop := 475274 ) ], 
                                          count := [ "A", 4, 0, 22 ], 
                                          name := "Row", next := 475288, 
                                          root := ~, start := 474624, 
                                          stop := 475287 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 4, 0, 28 ], 
                                          name := "HorLine", next := 475305, 
                                          root := ~, start := 475295, 
                                          stop := 475304 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
istanceSet", count := [ "A", 4, 0, 29 ], mathmode := "Text", name := "PCDATA",
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 4, 0, 29 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 475362, 
                                                          root := ~, 
                                                          start := 475344, 
                                                          stop := 475361 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 29 ], 
                                                  name := "Item", 
                                                  next := 475378, root := ~, 
                                                  start := 475327, 
                                                  stop := 475377 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
     ", count := [ "A", 4, 0, 31 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for a \
digraph, a pos int, and an int", Oper := "DigraphDistanceSet" ), 
                                                          content := 0, 
                                                          count := 
                                                            [ "A", 4, 0, 31 ],
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 475497, 
                                                          root := ~, 
                                                          start := 475406, 
                                                          stop := 475496 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 31 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 31 ], 
                                                  name := "Item", 
                                                  next := 475513, root := ~, 
                                                  start := 475387, 
                                                  stop := 475512 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 4, 0, 33 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "DistanceSet", count := [ "A", 4, 0, 33 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 4, 0, 33 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4755\
87, root := ~, start := 475569, stop := 475586 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 4, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 4, 0, 33 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 4, 0, 33 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 4, 0, 33 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 33 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 33 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 33 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 4, 0, 33 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for a dig\
raph, a pos int, and an int", Oper := "DigraphDistanceSet" ), content := 0, 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 33 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 475719, root := ~, start := 475628, 
                                                                  stop := 4757\
18 ), rec( HTML := true, content := " in ", count := [ "A", 4, 0, 33 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 4, 0, 33 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 33 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 4, 0, 33 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 4, 0, 33 ], name := "Alt", next := 475751, 
                                                          root := ~, 
                                                          start := 475539, 
                                                          stop := 475750 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 33 ], 
                                                  name := "Item", 
                                                  next := 475767, root := ~, 
                                                  start := 475522, 
                                                  stop := 475766 ) ], 
                                          count := [ "A", 4, 0, 28 ], 
                                          name := "Row", next := 475780, 
                                          root := ~, start := 475313, 
                                          stop := 475779 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 4, 0, 34 ], 
                                          name := "HorLine", next := 475797, 
                                          root := ~, start := 475787, 
                                          stop := 475796 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "L\
ayers", count := [ "A", 4, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 4, 0, 35 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 475849, 
                                                          root := ~, 
                                                          start := 475836, 
                                                          stop := 475848 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 35 ], 
                                                  name := "Item", 
                                                  next := 475865, root := ~, 
                                                  start := 475819, 
                                                  stop := 475864 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 37 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Layers" ), content := 0, count := [ "A", 4, 0, 37 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 475918, 
                                                          root := ~, 
                                                          start := 475891, 
                                                          stop := 475917 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 37 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 37 ], 
                                                  name := "Item", 
                                                  next := 475934, root := ~, 
                                                  start := 475874, 
                                                  stop := 475933 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 4, 0, 39 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "Layers", count := [ "A", 4, 0, 39 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 4, 0, 39 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4760\
03, root := ~, start := 475990, stop := 476002 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 4, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 4, 0, 39 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 4, 0, 39 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 4, 0, 39 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 39 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 39 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 39 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 4, 0, 39 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "DigraphLay\
ers" ), content := 0, count := [ "A", 4, 0, 39 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 476071, root := ~, start := 476044, stop := 476070 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 in ", count := [ "A", 4, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 4, 0, 39 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 39 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 4, 0, 39 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 4, 0, 39 ], name := "Alt", next := 476103, 
                                                          root := ~, 
                                                          start := 475960, 
                                                          stop := 476102 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 39 ], 
                                                  name := "Item", 
                                                  next := 476119, root := ~, 
                                                  start := 475943, 
                                                  stop := 476118 ) ], 
                                          count := [ "A", 4, 0, 34 ], 
                                          name := "Row", next := 476132, 
                                          root := ~, start := 475805, 
                                          stop := 476131 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 4, 0, 40 ], 
                                          name := "HorLine", next := 476149, 
                                          root := ~, start := 476139, 
                                          stop := 476148 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
ndependentSet", count := [ "A", 4, 0, 41 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 4, 0, 41 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 476209, 
                                                          root := ~, 
                                                          start := 476188, 
                                                          stop := 476208 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 41 ], 
                                                  name := "Item", 
                                                  next := 476225, root := ~, 
                                                  start := 476171, 
                                                  stop := 476224 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 43 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
IndependentSet" ), content := 0, count := [ "A", 4, 0, 43 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 476286, 
                                                          root := ~, 
                                                          start := 476251, 
                                                          stop := 476285 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 43 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 43 ], 
                                                  name := "Item", 
                                                  next := 476302, root := ~, 
                                                  start := 476234, 
                                                  stop := 476301 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 4, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 4, 0, 45 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "IndependentSet", count := [ "A", 4, 0, 45 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ "A", 4, 0, 45 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4763\
79, root := ~, start := 476358, stop := 476378 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 4, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 4, 0, 45 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 4, 0, 45 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 4, 0, 45 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 4, 0, 45 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 4, 0, 45 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 4, 0, 45 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 4, 0, 45 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "DigraphInd\
ependentSet" ), content := 0, count := [ "A", 4, 0, 45 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 476455, root := ~, start := 476420, stop := 476454 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 in ", count := [ "A", 4, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 4, 0, 45 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 4, 
                                                                      0, 45 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 4, 0, 45 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 4, 0, 45 ], name := "Alt", next := 476487, 
                                                          root := ~, 
                                                          start := 476328, 
                                                          stop := 476486 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 4, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 4, 0, 45 ], 
                                                  name := "Item", 
                                                  next := 476503, root := ~, 
                                                  start := 476311, 
                                                  stop := 476502 ) ], 
                                          count := [ "A", 4, 0, 40 ], 
                                          name := "Row", next := 476516, 
                                          root := ~, start := 476157, 
                                          stop := 476515 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 4, 0, 46 ], 
                                          name := "HorLine", next := 476533, 
                                          root := ~, start := 476523, 
                                          stop := 476532 ) ], 
                                  count := [ "A", 4, 0, 4 ], 
                                  mathmode := "Text", name := "Table", 
                                  next := 476547, root := ~, start := 473165, 
                                  stop := 476546 ), 
                              rec( content := "\n\n  ", 
                                  count := [ "A", 4, 0, 47 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 4, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 476561, root := ~, start := 472927, 
                          stop := 476560 ), 
                      rec( content := "\n\n  ", count := [ "A", 4, 0, 47 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n    ", 
                                  count := [ "A", 5, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n      Functions to cons\
truct new graphs from old\n    ", count := [ "A", 5, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 5, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 476652, root := ~, start := 476579, 
                                  stop := 476651 ), 
                              rec( content := "\n    ", 
                                  count := [ "A", 5, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Not := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( content := "\n      ", 
                                          count := [ "A", 5, 0, 3 ], 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n        The tab\
le in this section contains more information when viewed in\n        html form\
at.\n      ", count := [ "A", 5, 0, 3 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ "A", 5, 0, 3 ], 
                                          name := "E", next := 476790, 
                                          root := ~, start := 476680, 
                                          stop := 476789 ), 
                                      rec( content := "\n    ", 
                                          count := [ "A", 5, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 5, 0, 3 ], 
                                  mathmode := "Text", name := "Alt", 
                                  next := 476801, root := ~, start := 476657, 
                                  stop := 476800 ), 
                              rec( content := "\n\n    ", 
                                  count := [ "A", 5, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Align := "|l|l|l|" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 4 ], 
                                          name := "HorLine", next := 476847, 
                                          root := ~, start := 476837, 
                                          stop := 476846 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ "A", 5, 0, 5 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 5, 0, 5 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ "A", 5, 0, 5 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ "A", 5, 0, 5 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 5 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ "A", 5, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 5, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 476917, root := ~, 
                                                  start := 476869, 
                                                  stop := 476916 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ "A", 5, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 5, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 5, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 476977, root := ~, 
                                                  start := 476926, 
                                                  stop := 476976 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Comments\n          ", count := [ "A", 5, 0, 9 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 9 ], 
                                                          name := "Alt", 
                                                          next := 477058, 
                                                          root := ~, 
                                                          start := 477003, 
                                                          stop := 477057 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 477074, root := ~, 
                                                  start := 476986, 
                                                  stop := 477073 ) ], 
                                          count := [ "A", 5, 0, 4 ], 
                                          name := "Row", next := 477087, 
                                          root := ~, start := 476855, 
                                          stop := 477086 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 10 ], 
                                          name := "HorLine", next := 477104, 
                                          root := ~, start := 477094, 
                                          stop := 477103 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
nducedSubgraph", count := [ "A", 5, 0, 11 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 5, 0, 11 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 477165, 
                                                          root := ~, 
                                                          start := 477143, 
                                                          stop := 477164 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 477181, root := ~, 
                                                  start := 477126, 
                                                  stop := 477180 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Induced\
Subdigraph" ), content := 0, count := [ "A", 5, 0, 13 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 477238, 
                                                          root := ~, 
                                                          start := 477207, 
                                                          stop := 477237 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 13 ], 
                                                  name := "Item", 
                                                  next := 477254, root := ~, 
                                                  start := 477190, 
                                                  stop := 477253 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 5, 0, 15 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec( Oper := "InducedSubdigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 15 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 477341, root := ~, start := 477310, 
                                                                  stop := 4773\
40 ), rec( HTML := true, content := " in ", count := [ "A", 5, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 15 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 15 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 does not allow a third\n            argument ", count := [ "A", 5, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "G", count := [ "A", 5, 0, 15 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 15 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4774\
08, root := ~, start := 477400, stop := 477407 ), rec( HTML := true, 
                                                                  content := "\
 specifying a group of automorphisms on the\n            resultant graph. This\
 may be included in a future release.\n          ", count := [ "A", 5, 0, 15 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 15 ], 
                                                          name := "Alt", 
                                                          next := 477539, 
                                                          root := ~, 
                                                          start := 477280, 
                                                          stop := 477538 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 15 ], 
                                                  name := "Item", 
                                                  next := 477555, root := ~, 
                                                  start := 477263, 
                                                  stop := 477554 ) ], 
                                          count := [ "A", 5, 0, 10 ], 
                                          name := "Row", next := 477568, 
                                          root := ~, start := 477112, 
                                          stop := 477567 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 16 ], 
                                          name := "HorLine", next := 477585, 
                                          root := ~, start := 477575, 
                                          stop := 477584 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
istanceSetInduced", count := [ "A", 5, 0, 17 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 5, 0, 17 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 477649, 
                                                          root := ~, 
                                                          start := 477624, 
                                                          stop := 477648 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 17 ], 
                                                  name := "Item", 
                                                  next := 477665, root := ~, 
                                                  start := 477607, 
                                                  stop := 477664 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 5, 0, 19 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 19 ], 
                                                  name := "Item", 
                                                  next := 477711, root := ~, 
                                                  start := 477674, 
                                                  stop := 477710 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            There is no analogous function in ", count := [ "A", 5, 0, 21 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 21 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 21 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, and no plans to\n            include one.\n          ", count := [ "A", 5, 
                                                                      0, 21 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 21 ], 
                                                          name := "Alt", 
                                                          next := 477870, 
                                                          root := ~, 
                                                          start := 477737, 
                                                          stop := 477869 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 21 ], 
                                                  name := "Item", 
                                                  next := 477886, root := ~, 
                                                  start := 477720, 
                                                  stop := 477885 ) ], 
                                          count := [ "A", 5, 0, 16 ], 
                                          name := "Row", next := 477899, 
                                          root := ~, start := 477593, 
                                          stop := 477898 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 22 ], 
                                          name := "HorLine", next := 477916, 
                                          root := ~, start := 477906, 
                                          stop := 477915 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
istanceGraph", count := [ "A", 5, 0, 23 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 5, 0, 23 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 477975, 
                                                          root := ~, 
                                                          start := 477955, 
                                                          stop := 477974 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 23 ], 
                                                  name := "Item", 
                                                  next := 477991, root := ~, 
                                                  start := 477938, 
                                                  stop := 477990 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graph and list", Oper := "DistanceDigraph" ), content := 0, 
                                                          count := 
                                                            [ "A", 5, 0, 25 ],
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 478075, 
                                                          root := ~, 
                                                          start := 478017, 
                                                          stop := 478074 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 25 ], 
                                                  name := "Item", 
                                                  next := 478091, root := ~, 
                                                  start := 478000, 
                                                  stop := 478090 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 5, 0, 27 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "DistanceGraph", count := [ "A", 5, 0, 27 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 27 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4781\
67, root := ~, start := 478147, stop := 478166 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 5, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 5, 0, 27 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 5, 0, 27 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 5, 0, 27 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 5, 0, 27 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 5, 0, 27 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 5, 0, 27 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 5, 0, 27 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Label := "for digra\
ph and list", Oper := "DistanceDigraph" ), content := 0, count := [ "A", 5, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 478266, root := ~, start := 478208, 
                                                                  stop := 4782\
65 ), rec( HTML := true, content := " in\n            ", count := [ "A", 5, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 27 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 27 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 5, 0, 27 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 5, 0, 27 ], name := "Alt", next := 478310, 
                                                          root := ~, 
                                                          start := 478117, 
                                                          stop := 478309 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 27 ], 
                                                  name := "Item", 
                                                  next := 478326, root := ~, 
                                                  start := 478100, 
                                                  stop := 478325 ) ], 
                                          count := [ "A", 5, 0, 22 ], 
                                          name := "Row", next := 478339, 
                                          root := ~, start := 477924, 
                                          stop := 478338 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 28 ], 
                                          name := "HorLine", next := 478356, 
                                          root := ~, start := 478346, 
                                          stop := 478355 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
omplementGraph", count := [ "A", 5, 0, 29 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 5, 0, 29 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 478417, 
                                                          root := ~, 
                                                          start := 478395, 
                                                          stop := 478416 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 29 ], 
                                                  name := "Item", 
                                                  next := 478433, root := ~, 
                                                  start := 478378, 
                                                  stop := 478432 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 31 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
Dual" ), content := 0, count := [ "A", 5, 0, 31 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 478484, 
                                                          root := ~, 
                                                          start := 478459, 
                                                          stop := 478483 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 31 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 31 ], 
                                                  name := "Item", 
                                                  next := 478500, root := ~, 
                                                  start := 478442, 
                                                  stop := 478499 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 5, 0, 33 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec( Oper := "DigraphDual" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 33 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 478581, root := ~, start := 478556, 
                                                                  stop := 4785\
80 ), rec( HTML := true, content := " in ", count := [ "A", 5, 0, 33 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 33 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 33 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 5, 0, 33 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          HTML \
:= true, content := "ComplementGraph", count := [ "A", 5, 0, 33 ], mathmode :=\
 "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 33 ], 
                                                                  mathmode := \
"Text", name := "C", next := 478647, root := ~, start := 478625, stop := 47864\
6 ), rec( HTML := true, content := " in ", count := [ "A", 5, 0, 33 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 5, 0, 33 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 33 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 33 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 5, 0, 33 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 5, 0, 33 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 5, 0, 33 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 with the optional argument\n            ", count := [ "A", 5, 0, 33 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "comploops", count := [ "A", 5, 0, 33 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 33 ], mathmode := "\
Text", name := "A", next := 478714, root := ~, start := 478698, stop := 478713\
 ), rec( HTML := true, content := " set to ", count := [ "A", 5, 0, 33 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "true", count := [ "A", 5, 0, 33 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 33 ], mathmode := "Text", 
                                                                  name := "K",
                                                                  next := 4787\
33, root := ~, start := 478722, stop := 478732 ), rec( HTML := true, 
                                                                  content := "\
 (loops/nonloops are\n            complemented).\n          ", count := 
                                                                    [ "A", 5, 
                                                                      0, 33 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 33 ], 
                                                          name := "Alt", 
                                                          next := 478797, 
                                                          root := ~, 
                                                          start := 478526, 
                                                          stop := 478796 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 33 ], 
                                                  name := "Item", 
                                                  next := 478813, root := ~, 
                                                  start := 478509, 
                                                  stop := 478812 ) ], 
                                          count := [ "A", 5, 0, 28 ], 
                                          name := "Row", next := 478826, 
                                          root := ~, start := 478364, 
                                          stop := 478825 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 34 ], 
                                          name := "HorLine", next := 478843, 
                                          root := ~, start := 478833, 
                                          stop := 478842 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "P\
ointGraph", count := [ "A", 5, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 5, 0, 35 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 478899, 
                                                          root := ~, 
                                                          start := 478882, 
                                                          stop := 478898 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 35 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 35 ], 
                                                  name := "Item", 
                                                  next := 478915, root := ~, 
                                                  start := 478865, 
                                                  stop := 478914 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 5, 0, 37 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 37 ], 
                                                  name := "Item", 
                                                  next := 478961, root := ~, 
                                                  start := 478924, 
                                                  stop := 478960 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            There is no analogous function in ", count := [ "A", 5, 0, 39 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 39 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 39 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, and no plans to\n            include one.\n          ", count := [ "A", 5, 
                                                                      0, 39 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 39 ], 
                                                          name := "Alt", 
                                                          next := 479120, 
                                                          root := ~, 
                                                          start := 478987, 
                                                          stop := 479119 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 39 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 39 ], 
                                                  name := "Item", 
                                                  next := 479136, root := ~, 
                                                  start := 478970, 
                                                  stop := 479135 ) ], 
                                          count := [ "A", 5, 0, 34 ], 
                                          name := "Row", next := 479149, 
                                          root := ~, start := 478851, 
                                          stop := 479148 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 40 ], 
                                          name := "HorLine", next := 479166, 
                                          root := ~, start := 479156, 
                                          stop := 479165 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "E\
dgeGraph", count := [ "A", 5, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 5, 0, 41 ],
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 479221, 
                                                          root := ~, 
                                                          start := 479205, 
                                                          stop := 479220 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 41 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 41 ], 
                                                  name := "Item", 
                                                  next := 479237, root := ~, 
                                                  start := 479188, 
                                                  stop := 479236 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 43 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "EdgeUnd\
irectedDigraph" ), content := 0, count := [ "A", 5, 0, 43 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 479298, 
                                                          root := ~, 
                                                          start := 479263, 
                                                          stop := 479297 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 43 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 43 ], 
                                                  name := "Item", 
                                                  next := 479314, root := ~, 
                                                  start := 479246, 
                                                  stop := 479313 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 5, 0, 45 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "EdgeGraph", count := [ "A", 5, 0, 45 ], mathmode := "Text", name := "P\
CDATA", root := ~ ) ], count := [ "A", 5, 0, 45 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4793\
86, root := ~, start := 479370, stop := 479385 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 5, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 5, 0, 45 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 5, 0, 45 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 5, 0, 45 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 5, 0, 45 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 5, 0, 45 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 5, 0, 45 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 5, 0, 45 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "EdgeUndire\
ctedDigraph" ), content := 0, count := [ "A", 5, 0, 45 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 479462, root := ~, start := 479427, stop := 479461 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 in ", count := [ "A", 5, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 5, 0, 45 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 45 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 5, 0, 45 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 5, 0, 45 ], name := "Alt", next := 479494, 
                                                          root := ~, 
                                                          start := 479340, 
                                                          stop := 479493 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 45 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 45 ], 
                                                  name := "Item", 
                                                  next := 479510, root := ~, 
                                                  start := 479323, 
                                                  stop := 479509 ) ], 
                                          count := [ "A", 5, 0, 40 ], 
                                          name := "Row", next := 479523, 
                                          root := ~, start := 479174, 
                                          stop := 479522 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 46 ], 
                                          name := "HorLine", next := 479540, 
                                          root := ~, start := 479530, 
                                          stop := 479539 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 47 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "S\
witchedGraph", count := [ "A", 5, 0, 47 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 5, 0, 47 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 479599, 
                                                          root := ~, 
                                                          start := 479579, 
                                                          stop := 479598 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 47 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 47 ], 
                                                  name := "Item", 
                                                  next := 479615, root := ~, 
                                                  start := 479562, 
                                                  stop := 479614 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 5, 0, 49 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 49 ], 
                                                  name := "Item", 
                                                  next := 479661, root := ~, 
                                                  start := 479624, 
                                                  stop := 479660 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 51 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            There is no analogous function in ", count := [ "A", 5, 0, 51 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 51 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 51 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, and no plans to\n            include one.\n          ", count := [ "A", 5, 
                                                                      0, 51 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 51 ], 
                                                          name := "Alt", 
                                                          next := 479820, 
                                                          root := ~, 
                                                          start := 479687, 
                                                          stop := 479819 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 51 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 51 ], 
                                                  name := "Item", 
                                                  next := 479836, root := ~, 
                                                  start := 479670, 
                                                  stop := 479835 ) ], 
                                          count := [ "A", 5, 0, 46 ], 
                                          name := "Row", next := 479849, 
                                          root := ~, start := 479548, 
                                          stop := 479848 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 52 ], 
                                          name := "HorLine", next := 479866, 
                                          root := ~, start := 479856, 
                                          stop := 479865 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 53 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "U\
nderlyingGraph", count := [ "A", 5, 0, 53 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 5, 0, 53 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 479927, 
                                                          root := ~, 
                                                          start := 479905, 
                                                          stop := 479926 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 53 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 53 ], 
                                                  name := "Item", 
                                                  next := 479943, root := ~, 
                                                  start := 479888, 
                                                  stop := 479942 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 55 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Digraph\
SymmetricClosure" ), content := 0, count := [ "A", 5, 0, 55 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 480006, 
                                                          root := ~, 
                                                          start := 479969, 
                                                          stop := 480005 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 55 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 55 ], 
                                                  name := "Item", 
                                                  next := 480022, root := ~, 
                                                  start := 479952, 
                                                  stop := 480021 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 57 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 5, 0, 57 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "UnderlyingGraph", count := [ "A", 5, 0, 57 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 57 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4801\
00, root := ~, start := 480078, stop := 480099 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 5, 0, 57 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 5, 0, 57 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 5, 0, 57 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 5, 0, 57 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 5, 0, 57 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 5, 0, 57 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 5, 0, 57 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 5, 0, 57 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "DigraphSym\
metricClosure" ), content := 0, count := [ "A", 5, 0, 57 ], mathmode := "Text"
                                                                    , 
                                                                  name := "Ref\
", next := 480178, root := ~, start := 480141, stop := 480177 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 in ", count := [ "A", 5, 0, 57 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 5, 0, 57 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 57 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 5, 0, 57 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 5, 0, 57 ], name := "Alt", next := 480210, 
                                                          root := ~, 
                                                          start := 480048, 
                                                          stop := 480209 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 57 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 57 ], 
                                                  name := "Item", 
                                                  next := 480226, root := ~, 
                                                  start := 480031, 
                                                  stop := 480225 ) ], 
                                          count := [ "A", 5, 0, 52 ], 
                                          name := "Row", next := 480239, 
                                          root := ~, start := 479874, 
                                          stop := 480238 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 58 ], 
                                          name := "HorLine", next := 480256, 
                                          root := ~, start := 480246, 
                                          stop := 480255 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 59 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "Q\
uotientGraph", count := [ "A", 5, 0, 59 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 5, 0, 59 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 480315, 
                                                          root := ~, 
                                                          start := 480295, 
                                                          stop := 480314 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 59 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 59 ], 
                                                  name := "Item", 
                                                  next := 480331, root := ~, 
                                                  start := 480278, 
                                                  stop := 480330 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 61 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Quotien\
tDigraph" ), content := 0, count := [ "A", 5, 0, 61 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 480386, 
                                                          root := ~, 
                                                          start := 480357, 
                                                          stop := 480385 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 61 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 61 ], 
                                                  name := "Item", 
                                                  next := 480402, root := ~, 
                                                  start := 480340, 
                                                  stop := 480401 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 63 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 5, 0, 63 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec( Oper := "QuotientDigraph" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 63 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 480487, root := ~, start := 480458, 
                                                                  stop := 4804\
86 ), rec( HTML := true, content := " in ", count := [ "A", 5, 0, 63 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 63 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 63 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 takes a partition\n            ", count := [ "A", 5, 0, 63 ], mathmode := "Te\
xt", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          HTML \
:= true, content := "p", count := [ "A", 5, 0, 63 ], mathmode := "Text", name \
:= "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 63 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4805\
40, root := ~, start := 480532, stop := 480539 ), rec( HTML := true, 
                                                                  content := "\
 of the vertices of the digraph, rather than a set of\n            generating \
pairs.  Hence, the equivalence might not be\n            group-invariant.  Als\
o note that in ", count := [ "A", 5, 0, 63 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true,
                                                                          cont\
ent := "Digraphs", count := [ "A", 5, 0, 63 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ "A", 5, 0, 63 ], mathmode := "Text", 
                                                                  name := "Pac\
kage", next := 28, root := ~, start := 1, stop := 27 ), rec( HTML := true, 
                                                                  content := "\
 multiple edges may be\n            created, whereas in ", count := [ "A", 5, 
                                                                      0, 63 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 5, 0, 63 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 63 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 63 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 5, 0, 63 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 5, 0, 63 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 5, 0, 63 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 they are effectively combined into a\n            single edge.\n          ", 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 63 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 63 ], 
                                                          name := "Alt", 
                                                          next := 480860, 
                                                          root := ~, 
                                                          start := 480428, 
                                                          stop := 480859 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 63 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 63 ], 
                                                  name := "Item", 
                                                  next := 480876, root := ~, 
                                                  start := 480411, 
                                                  stop := 480875 ) ], 
                                          count := [ "A", 5, 0, 58 ], 
                                          name := "Row", next := 480889, 
                                          root := ~, start := 480264, 
                                          stop := 480888 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 64 ], 
                                          name := "HorLine", next := 480906, 
                                          root := ~, start := 480896, 
                                          stop := 480905 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 65 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "B\
ipartiteDouble", count := [ "A", 5, 0, 65 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 5, 0, 65 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 480967, 
                                                          root := ~, 
                                                          start := 480945, 
                                                          stop := 480966 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 65 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 65 ], 
                                                  name := "Item", 
                                                  next := 480983, root := ~, 
                                                  start := 480928, 
                                                  stop := 480982 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 67 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Oper := "Biparti\
teDoubleDigraph" ), content := 0, count := [ "A", 5, 0, 67 ], 
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 481045, 
                                                          root := ~, 
                                                          start := 481009, 
                                                          stop := 481044 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 67 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 67 ], 
                                                  name := "Item", 
                                                  next := 481061, root := ~, 
                                                  start := 480992, 
                                                  stop := 481060 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 69 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 5, 0, 69 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "BipartiteDouble", count := [ "A", 5, 0, 69 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 69 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4811\
39, root := ~, start := 481117, stop := 481138 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 5, 0, 69 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 5, 0, 69 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 5, 0, 69 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 5, 0, 69 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 5, 0, 69 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 5, 0, 69 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 5, 0, 69 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 5, 0, 69 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "BipartiteD\
oubleDigraph" ), content := 0, count := [ "A", 5, 0, 69 ], mathmode := "Text",
                                                                  name := "Ref\
", next := 481216, root := ~, start := 481180, stop := 481215 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 in ", count := [ "A", 5, 0, 69 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 5, 0, 69 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 69 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 5, 0, 69 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 5, 0, 69 ], name := "Alt", next := 481248, 
                                                          root := ~, 
                                                          start := 481087, 
                                                          stop := 481247 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 69 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 69 ], 
                                                  name := "Item", 
                                                  next := 481264, root := ~, 
                                                  start := 481070, 
                                                  stop := 481263 ) ], 
                                          count := [ "A", 5, 0, 64 ], 
                                          name := "Row", next := 481277, 
                                          root := ~, start := 480914, 
                                          stop := 481276 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 70 ], 
                                          name := "HorLine", next := 481294, 
                                          root := ~, start := 481284, 
                                          stop := 481293 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 71 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
eodesicsGraph", count := [ "A", 5, 0, 71 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 5, 0, 71 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 481354, 
                                                          root := ~, 
                                                          start := 481333, 
                                                          stop := 481353 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 71 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 71 ], 
                                                  name := "Item", 
                                                  next := 481370, root := ~, 
                                                  start := 481316, 
                                                  stop := 481369 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 5, 0, 73 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 73 ], 
                                                  name := "Item", 
                                                  next := 481416, root := ~, 
                                                  start := 481379, 
                                                  stop := 481415 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 75 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            There is no analogous function in ", count := [ "A", 5, 0, 75 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 75 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 75 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, and no plans to\n            include one.\n          ", count := [ "A", 5, 
                                                                      0, 75 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 75 ], 
                                                          name := "Alt", 
                                                          next := 481575, 
                                                          root := ~, 
                                                          start := 481442, 
                                                          stop := 481574 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 75 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 75 ], 
                                                  name := "Item", 
                                                  next := 481591, root := ~, 
                                                  start := 481425, 
                                                  stop := 481590 ) ], 
                                          count := [ "A", 5, 0, 70 ], 
                                          name := "Row", next := 481604, 
                                          root := ~, start := 481302, 
                                          stop := 481603 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 76 ], 
                                          name := "HorLine", next := 481621, 
                                          root := ~, start := 481611, 
                                          stop := 481620 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 77 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
ollapsedIndependentOrbitsGraph", count := [ "A", 5, 0, 77 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 77 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 481698, 
                                                          root := ~, 
                                                          start := 481660, 
                                                          stop := 481697 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 77 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 77 ], 
                                                  name := "Item", 
                                                  next := 481714, root := ~, 
                                                  start := 481643, 
                                                  stop := 481713 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 5, 0, 79 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 79 ], 
                                                  name := "Item", 
                                                  next := 481760, root := ~, 
                                                  start := 481723, 
                                                  stop := 481759 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 81 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            There is no analogous function in ", count := [ "A", 5, 0, 81 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 81 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 81 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, although this feature\n            might be implemented in the future.\n    \
      ", count := [ "A", 5, 0, 81 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 5, 0, 81 ],
                                                          name := "Alt", 
                                                          next := 481948, 
                                                          root := ~, 
                                                          start := 481786, 
                                                          stop := 481947 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 81 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 81 ], 
                                                  name := "Item", 
                                                  next := 481964, root := ~, 
                                                  start := 481769, 
                                                  stop := 481963 ) ], 
                                          count := [ "A", 5, 0, 76 ], 
                                          name := "Row", next := 481977, 
                                          root := ~, start := 481629, 
                                          stop := 481976 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 82 ], 
                                          name := "HorLine", next := 481994, 
                                          root := ~, start := 481984, 
                                          stop := 481993 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 83 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
ollapsedCompleteOrbitsGraph", count := [ "A", 5, 0, 83 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 5, 0, 83 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 482068, 
                                                          root := ~, 
                                                          start := 482033, 
                                                          stop := 482067 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 83 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 83 ], 
                                                  name := "Item", 
                                                  next := 482084, root := ~, 
                                                  start := 482016, 
                                                  stop := 482083 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 5, 0, 85 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 85 ], 
                                                  name := "Item", 
                                                  next := 482130, root := ~, 
                                                  start := 482093, 
                                                  stop := 482129 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 87 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            There is no analogous function in ", count := [ "A", 5, 0, 87 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 87 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 87 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, although this feature\n            might be implemented in the future.\n    \
      ", count := [ "A", 5, 0, 87 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 5, 0, 87 ],
                                                          name := "Alt", 
                                                          next := 482318, 
                                                          root := ~, 
                                                          start := 482156, 
                                                          stop := 482317 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 87 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 87 ], 
                                                  name := "Item", 
                                                  next := 482334, root := ~, 
                                                  start := 482139, 
                                                  stop := 482333 ) ], 
                                          count := [ "A", 5, 0, 82 ], 
                                          name := "Row", next := 482347, 
                                          root := ~, start := 482002, 
                                          stop := 482346 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 88 ], 
                                          name := "HorLine", next := 482364, 
                                          root := ~, start := 482354, 
                                          stop := 482363 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 89 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "N\
ewGroupGraph", count := [ "A", 5, 0, 89 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 5, 0, 89 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 482423, 
                                                          root := ~, 
                                                          start := 482403, 
                                                          stop := 482422 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 89 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 89 ], 
                                                  name := "Item", 
                                                  next := 482439, root := ~, 
                                                  start := 482386, 
                                                  stop := 482438 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 5, 0, 91 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 91 ], 
                                                  name := "Item", 
                                                  next := 482485, root := ~, 
                                                  start := 482448, 
                                                  stop := 482484 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 5, 0, 93 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            There is no analogous function in ", count := [ "A", 5, 0, 93 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 5, 0, 93 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 93 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.  However, the same\n            results would be possible by calling ", 
                                                                  count := 
                                                                    [ "A", 5, 
                                                                      0, 93 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Oper := "Digrap\
hCopy" ), content := 0, count := [ "A", 5, 0, 93 ], mathmode := "Text", 
                                                                  name := "Ref\
", next := 482680, root := ~, start := 482655, stop := 482679 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 on\n            the digraph to produce a copy ", count := [ "A", 5, 0, 93 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "gr", count := [ "A", 5, 0, 93 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 93 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4827\
35, root := ~, start := 482726, stop := 482734 ), rec( HTML := true, 
                                                                  content := "\
, and then applying\n            ", count := [ "A", 5, 0, 93 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          HTML \
:= true, content := "SetDigraphGroup(gr, G)", count := [ "A", 5, 0, 93 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 93 ], 
                                                                  mathmode := \
"Text", name := "C", next := 482796, root := ~, start := 482767, stop := 48279\
5 ), rec( HTML := true, content := ".\n          ", count := [ "A", 5, 0, 93 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 5, 0, 93 ], 
                                                          name := "Alt", 
                                                          next := 482814, 
                                                          root := ~, 
                                                          start := 482511, 
                                                          stop := 482813 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 5, 0, 93 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 5, 0, 93 ], 
                                                  name := "Item", 
                                                  next := 482830, root := ~, 
                                                  start := 482494, 
                                                  stop := 482829 ) ], 
                                          count := [ "A", 5, 0, 88 ], 
                                          name := "Row", next := 482843, 
                                          root := ~, start := 482372, 
                                          stop := 482842 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 5, 0, 94 ], 
                                          name := "HorLine", next := 482860, 
                                          root := ~, start := 482850, 
                                          stop := 482859 ) ], 
                                  count := [ "A", 5, 0, 4 ], 
                                  mathmode := "Text", name := "Table", 
                                  next := 482874, root := ~, start := 476807, 
                                  stop := 482873 ), 
                              rec( content := "\n\n  ", 
                                  count := [ "A", 5, 0, 95 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 5, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 482888, root := ~, start := 476565, 
                          stop := 482887 ), 
                      rec( content := "\n\n  ", count := [ "A", 5, 0, 95 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n    ", 
                                  count := [ "A", 6, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n      Vertex-Colouring \
and Complete Subgraphs\n    ", count := [ "A", 6, 0, 2 ], mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 6, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 482976, root := ~, start := 482906, 
                                  stop := 482975 ), 
                              rec( content := "\n    ", 
                                  count := [ "A", 6, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Not := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( content := "\n      ", 
                                          count := [ "A", 6, 0, 3 ], 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n        The tab\
le in this section contains more information when viewed in\n        html form\
at.\n      ", count := [ "A", 6, 0, 3 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ "A", 6, 0, 3 ], 
                                          name := "E", next := 483114, 
                                          root := ~, start := 483004, 
                                          stop := 483113 ), 
                                      rec( content := "\n    ", 
                                          count := [ "A", 6, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 6, 0, 3 ], 
                                  mathmode := "Text", name := "Alt", 
                                  next := 483125, root := ~, start := 482981, 
                                  stop := 483124 ), 
                              rec( content := "\n\n    ", 
                                  count := [ "A", 6, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Align := "|l|l|l|" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 6, 0, 4 ], 
                                          name := "HorLine", next := 483171, 
                                          root := ~, start := 483161, 
                                          stop := 483170 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ "A", 6, 0, 5 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 6, 0, 5 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ "A", 6, 0, 5 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ "A", 6, 0, 5 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 6, 0, 5 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ "A", 6, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 6, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 483241, root := ~, 
                                                  start := 483193, 
                                                  stop := 483240 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ "A", 6, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 6, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 6, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 483301, root := ~, 
                                                  start := 483250, 
                                                  stop := 483300 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Comments\n          ", count := [ "A", 6, 0, 9 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ "A", 6, 0, 9 ], 
                                                          name := "Alt", 
                                                          next := 483382, 
                                                          root := ~, 
                                                          start := 483327, 
                                                          stop := 483381 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 483398, root := ~, 
                                                  start := 483310, 
                                                  stop := 483397 ) ], 
                                          count := [ "A", 6, 0, 4 ], 
                                          name := "Row", next := 483411, 
                                          root := ~, start := 483179, 
                                          stop := 483410 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 6, 0, 10 ], 
                                          name := "HorLine", next := 483428, 
                                          root := ~, start := 483418, 
                                          stop := 483427 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "V\
ertexColouring", count := [ "A", 6, 0, 11 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ) ], count := [ "A", 6, 0, 11 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 483489, 
                                                          root := ~, 
                                                          start := 483467, 
                                                          stop := 483488 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 483505, root := ~, 
                                                  start := 483450, 
                                                  stop := 483504 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Digraph\
GreedyColouring", Label := "for a digraph" ), content := 0, 
                                                          count := 
                                                            [ "A", 6, 0, 13 ],
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 483589, 
                                                          root := ~, 
                                                          start := 483531, 
                                                          stop := 483588 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 13 ], 
                                                  name := "Item", 
                                                  next := 483605, root := ~, 
                                                  start := 483514, 
                                                  stop := 483604 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 6, 0, 15 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "VertexColouring", count := [ "A", 6, 0, 15 ], mathmode := "Text", name\
 := "PCDATA", root := ~ ) ], count := [ "A", 6, 0, 15 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4836\
83, root := ~, start := 483661, stop := 483682 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 6, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 6, 0, 15 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 6, 0, 15 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 6, 0, 15 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 6, 0, 15 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 6, 0, 15 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 6, 0, 15 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to ", count := [ "A", 6, 0, 15 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Attr := "DigraphGreedyColouring", 
                                                                      Label :=\
 "for a digraph" ), content := 0, count := [ "A", 6, 0, 15 ], mathmode := "Tex\
t", name := "Ref", next := 483782, root := ~, start := 483712, stop := 483781 
                                                                 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 in ", count := [ "A", 6, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 6, 0, 15 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 6, 
                                                                      0, 15 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
,\n            except it returns a transformation rather than a list of vertex\
\n            colors.\n          ", count := [ "A", 6, 0, 15 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ "A", 6, 0, 15 ], 
                                                          name := "Alt", 
                                                          next := 483910, 
                                                          root := ~, 
                                                          start := 483631, 
                                                          stop := 483909 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 15 ], 
                                                  name := "Item", 
                                                  next := 483926, root := ~, 
                                                  start := 483614, 
                                                  stop := 483925 ) ], 
                                          count := [ "A", 6, 0, 10 ], 
                                          name := "Row", next := 483939, 
                                          root := ~, start := 483436, 
                                          stop := 483938 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 6, 0, 16 ], 
                                          name := "HorLine", next := 483956, 
                                          root := ~, start := 483946, 
                                          stop := 483955 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
ompleteSubgraphs", count := [ "A", 6, 0, 17 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 6, 0, 17 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 484019, 
                                                          root := ~, 
                                                          start := 483995, 
                                                          stop := 484018 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 17 ], 
                                                  name := "Item", 
                                                  next := 484035, root := ~, 
                                                  start := 483978, 
                                                  stop := 484034 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
Cliques" ), content := 0, count := [ "A", 6, 0, 19 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 484089, 
                                                          root := ~, 
                                                          start := 484061, 
                                                          stop := 484088 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 19 ], 
                                                  name := "Item", 
                                                  next := 484105, root := ~, 
                                                  start := 484044, 
                                                  stop := 484104 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            The functionality of ", count := [ "A", 6, 0, 21 ], mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "CompleteSubgraphs", count := [ "A", 6, 0, 21 ], mathmode\
 := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 6, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "C", next := 484206, root := ~, start := 484182, stop := 48420\
5 ), rec( HTML := true, content := " in ", count := [ "A", 6, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 6, 0, 21 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 6, 0, 21 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 6, 
                                                                      0, 21 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 6, 0, 21 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 6, 0, 21 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 6, 0, 21 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is provided\n            by ", count := [ "A", 6, 0, 21 ], mathmode := "Text"
                                                                    , 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Func := "DigraphCliques" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 6, 
                                                                      0, 21 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 484273, root := ~, start := 484245, 
                                                                  stop := 4842\
72 ), rec( HTML := true, content := " and ", count := [ "A", 6, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digrap\
hMaximalCliques" ), content := 0, count := [ "A", 6, 0, 21 ], mathmode := "Tex\
t", name := "Ref", next := 484313, root := ~, start := 484278, stop := 484312 
                                                                 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
\n            in ", count := [ "A", 6, 0, 21 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true,
                                                                          cont\
ent := "Digraphs", count := [ "A", 6, 0, 21 ], mathmode := "Text", name := "PC\
DATA", root := ~ ) ], count := [ "A", 6, 0, 21 ], mathmode := "Text", 
                                                                  name := "Pac\
kage", next := 28, root := ~, start := 1, stop := 27 ), rec( HTML := true, 
                                                                  content := "\
.\n          ", count := [ "A", 6, 0, 21 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 6, 0, 21 ], name := "Alt", next := 484357, 
                                                          root := ~, 
                                                          start := 484131, 
                                                          stop := 484356 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 21 ], 
                                                  name := "Item", 
                                                  next := 484373, root := ~, 
                                                  start := 484114, 
                                                  stop := 484372 ) ], 
                                          count := [ "A", 6, 0, 16 ], 
                                          name := "Row", next := 484386, 
                                          root := ~, start := 483964, 
                                          stop := 484385 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 6, 0, 22 ], 
                                          name := "HorLine", next := 484403, 
                                          root := ~, start := 484393, 
                                          stop := 484402 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "C\
ompleteSubgraphsOfGivenSize", count := [ "A", 6, 0, 23 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 6, 0, 23 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 484477, 
                                                          root := ~, 
                                                          start := 484442, 
                                                          stop := 484476 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 23 ], 
                                                  name := "Item", 
                                                  next := 484493, root := ~, 
                                                  start := 484425, 
                                                  stop := 484492 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Func := "Digraph\
Cliques" ), content := 0, count := [ "A", 6, 0, 25 ], mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 484547, 
                                                          root := ~, 
                                                          start := 484519, 
                                                          stop := 484546 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 25 ], 
                                                  name := "Item", 
                                                  next := 484563, root := ~, 
                                                  start := 484502, 
                                                  stop := 484562 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 6, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Much of the functionality of ", count := [ "A", 6, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "CompleteSubgraphsOfGivenSize", count := [ "A", 6, 0, 27 
                                                                             ]
                                                                            , 
                                                                          math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 6, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "C", next := 484683, root := ~, start := 484648, stop := 48468\
2 ), rec( HTML := true, content := " in\n            ", count := [ "A", 6, 0, 
                                                                      27 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Not := "Text" )
                                                                    , 
                                                                  content := 
                                                                    [ rec( 
                                                                          attr\
ibutes := rec( Text := "Grape" ), content := [ rec( HTML := true, content := "\
http://www.maths.qmul.ac.uk/~leonard/grape/", count := [ "A", 6, 0, 27 ], math\
mode := "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 6, 0, 27 ], 
                                                                          math\
mode := "Text", name := "URL", next := 87, root := ~, start := 17, stop := 86 
                                                                         ) ], 
                                                                  count := 
                                                                    [ "A", 6, 
                                                                      0, 27 ],
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 6, 0, 27 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 6, 0, 27 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 6, 0, 27 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is provided by ", count := [ "A", 6, 0, 27 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Func := "DigraphCliques" ), 
                                                                  content := 0
                                                                    , 
                                                                  count := 
                                                                    [ "A", 6, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "Ref", next := 484750, root := ~, start := 484722, 
                                                                  stop := 4847\
49 ), rec( HTML := true, content := " and ", count := [ "A", 6, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec( Func := "Digrap\
hMaximalCliques" ), content := 0, count := [ "A", 6, 0, 27 ], mathmode := "Tex\
t", name := "Ref", next := 484804, root := ~, start := 484755, stop := 484803 
                                                                 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
 in ", count := [ "A", 6, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec(  ), content := [ rec( HTML := true, content := "Digraphs", count := [ "\
A", 6, 0, 27 ], mathmode := "Text", name := "PCDATA", root := ~ ) ], 
                                                                  count := 
                                                                    [ "A", 6, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, except that the\n            functionality relating to vertex weights and pa\
rtial colourings is\n            not implemented.\n          ", count := 
                                                                    [ "A", 6, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 6, 0, 27 ], 
                                                          name := "Alt", 
                                                          next := 484960, 
                                                          root := ~, 
                                                          start := 484589, 
                                                          stop := 484959 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 6, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 6, 0, 27 ], 
                                                  name := "Item", 
                                                  next := 484976, root := ~, 
                                                  start := 484572, 
                                                  stop := 484975 ) ], 
                                          count := [ "A", 6, 0, 22 ], 
                                          name := "Row", next := 484989, 
                                          root := ~, start := 484411, 
                                          stop := 484988 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 6, 0, 28 ], 
                                          name := "HorLine", next := 485006, 
                                          root := ~, start := 484996, 
                                          stop := 485005 ) ], 
                                  count := [ "A", 6, 0, 4 ], 
                                  mathmode := "Text", name := "Table", 
                                  next := 485020, root := ~, start := 483131, 
                                  stop := 485019 ), 
                              rec( content := "\n  ", 
                                  count := [ "A", 6, 0, 29 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 6, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 485033, root := ~, start := 482892, 
                          stop := 485032 ), 
                      rec( content := "\n\n  ", count := [ "A", 6, 0, 29 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ), 
                      rec( attributes := rec(  ), 
                          content := 
                            [ 
                              rec( content := "\n    ", 
                                  count := [ "A", 7, 0, 1 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec(  ), 
                                  content := 
                                    [ 
                                      rec( 
                                          content := "\n      Automorphism grou\
ps and isomorphism testing for graphs\n    ", count := [ "A", 7, 0, 2 ], 
                                          mathmode := "Text", 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 7, 0, 2 ], 
                                  mathmode := "Text", name := "Heading", 
                                  next := 485136, root := ~, start := 485051, 
                                  stop := 485135 ), 
                              rec( content := "\n    ", 
                                  count := [ "A", 7, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Not := "HTML" ), 
                                  content := 
                                    [ 
                                      rec( content := "\n      ", 
                                          count := [ "A", 7, 0, 3 ], 
                                          name := "PCDATA", root := ~ ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( 
                                                  content := "\n        The tab\
le in this section contains more information when viewed in\n        html form\
at.\n      ", count := [ "A", 7, 0, 3 ], name := "PCDATA", root := ~ ) ], 
                                          count := [ "A", 7, 0, 3 ], 
                                          name := "E", next := 485274, 
                                          root := ~, start := 485164, 
                                          stop := 485273 ), 
                                      rec( content := "\n    ", 
                                          count := [ "A", 7, 0, 3 ], 
                                          name := "PCDATA", root := ~ ) ], 
                                  count := [ "A", 7, 0, 3 ], 
                                  mathmode := "Text", name := "Alt", 
                                  next := 485285, root := ~, start := 485141, 
                                  stop := 485284 ), 
                              rec( content := "\n\n    ", 
                                  count := [ "A", 7, 0, 3 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ), 
                              rec( attributes := rec( Align := "|l|l|l|" ), 
                                  content := 
                                    [ 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 7, 0, 4 ], 
                                          name := "HorLine", next := 485331, 
                                          root := ~, start := 485321, 
                                          stop := 485330 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Not := "Text" ),
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec( Text := "Grape" ), content := [ rec( content := "http://www.maths.qmul.a\
c.uk/~leonard/grape/", count := [ "A", 7, 0, 5 ], mathmode := "Text", name := \
"PCDATA", root := ~ ) ], count := [ "A", 7, 0, 5 ], mathmode := "Text", 
                                                                  name := "URL\
", next := 87, root := ~, start := 17, stop := 86 ) ], count := 
                                                            [ "A", 7, 0, 5 ], 
                                                          name := "Alt", 
                                                          next := 93, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 92 ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "Text" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  attributes :=\
 rec(  ), content := [ rec( content := "Grape", count := [ "A", 7, 0, 5 ], 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 5 ], name := "Package", 
                                                                  next := 137,
                                                                  root := ~, 
                                                                  start := 113
                                                                    , 
                                                                  stop := 136 
                                                                 ) ], 
                                                          count := 
                                                            [ "A", 7, 0, 5 ], 
                                                          mathmode := "Text", 
                                                          name := "Alt", 
                                                          next := 143, 
                                                          root := ~, 
                                                          start := 93, 
                                                          stop := 142 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 7, 0, 5 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 5 ], 
                                                  name := "Item", 
                                                  next := 485401, root := ~, 
                                                  start := 485353, 
                                                  stop := 485400 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "D\
igraphs", count := [ "A", 7, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 7, 0, 7 ], 
                                                          mathmode := "Text", 
                                                          name := "Package", 
                                                          next := 28, 
                                                          root := ~, 
                                                          start := 1, 
                                                          stop := 27 ), 
                                                      rec( 
                                                          content := " command\
\n        ", count := [ "A", 7, 0, 7 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 7 ], 
                                                  name := "Item", 
                                                  next := 485461, root := ~, 
                                                  start := 485410, 
                                                  stop := 485460 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            Comments\n          ", count := [ "A", 7, 0, 9 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 9 ], 
                                                          name := "Alt", 
                                                          next := 485542, 
                                                          root := ~, 
                                                          start := 485487, 
                                                          stop := 485541 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 9 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 9 ], 
                                                  name := "Item", 
                                                  next := 485558, root := ~, 
                                                  start := 485470, 
                                                  stop := 485557 ) ], 
                                          count := [ "A", 7, 0, 4 ], 
                                          name := "Row", next := 485571, 
                                          root := ~, start := 485339, 
                                          stop := 485570 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 7, 0, 10 ], 
                                          name := "HorLine", next := 485588, 
                                          root := ~, start := 485578, 
                                          stop := 485587 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "A\
utGroupGraph", count := [ "A", 7, 0, 11 ], mathmode := "Text", name := "PCDATA\
", root := ~ ) ], count := [ "A", 7, 0, 11 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 485647, 
                                                          root := ~, 
                                                          start := 485627, 
                                                          stop := 485646 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 11 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 11 ], 
                                                  name := "Item", 
                                                  next := 485663, root := ~, 
                                                  start := 485610, 
                                                  stop := 485662 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Attr := "Automor\
phismGroup", Label := "for a digraph" ), content := 0, count := 
                                                            [ "A", 7, 0, 13 ],
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 485742, 
                                                          root := ~, 
                                                          start := 485689, 
                                                          stop := 485741 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 13 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 13 ], 
                                                  name := "Item", 
                                                  next := 485758, root := ~, 
                                                  start := 485672, 
                                                  stop := 485757 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 7, 0, 15 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "AutGroupGraph", count := [ "A", 7, 0, 15 ], mathmode := "Text", name :\
= "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 15 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4858\
34, root := ~, start := 485814, stop := 485833 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 7, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 7, 0, 15 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 7, 0, 15 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 7, 0, 15 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 7, 0, 15 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 7, 0, 15 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 7, 0, 15 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to\n            ", count := [ "A", 7, 0, 15 ], mathmode := "Tex\
t", name := "PCDATA", root := ~ ), rec( attributes := rec( Attr := "Automorphi\
smGroup", Label := "for a digraph" ), content := 0, count := [ "A", 7, 0, 15 ]
                                                                    , 
                                                                  mathmode := \
"Text", name := "Ref", next := 485928, root := ~, start := 485875, 
                                                                  stop := 4859\
27 ), rec( HTML := true, content := " in ", count := [ "A", 7, 0, 15 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 7, 0, 15 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 15 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n          ", count := [ "A", 7, 0, 15 ], mathmode := "Text", name := "PCDAT\
A", root := ~ ) ], count := [ "A", 7, 0, 15 ], name := "Alt", next := 485960, 
                                                          root := ~, 
                                                          start := 485784, 
                                                          stop := 485959 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 15 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 15 ], 
                                                  name := "Item", 
                                                  next := 485976, root := ~, 
                                                  start := 485767, 
                                                  stop := 485975 ) ], 
                                          count := [ "A", 7, 0, 10 ], 
                                          name := "Row", next := 485989, 
                                          root := ~, start := 485596, 
                                          stop := 485988 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 7, 0, 16 ], 
                                          name := "HorLine", next := 486006, 
                                          root := ~, start := 485996, 
                                          stop := 486005 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
raphIsomorphism", count := [ "A", 7, 0, 17 ], mathmode := "Text", name := "PCD\
ATA", root := ~ ) ], count := [ "A", 7, 0, 17 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 486068, 
                                                          root := ~, 
                                                          start := 486045, 
                                                          stop := 486067 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 17 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 17 ], 
                                                  name := "Item", 
                                                  next := 486084, root := ~, 
                                                  start := 486028, 
                                                  stop := 486083 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs", Oper := "IsomorphismDigraphs" ), content := 0, count := 
                                                            [ "A", 7, 0, 19 ],
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 486164, 
                                                          root := ~, 
                                                          start := 486110, 
                                                          stop := 486163 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 19 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 19 ], 
                                                  name := "Item", 
                                                  next := 486180, root := ~, 
                                                  start := 486093, 
                                                  stop := 486179 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 7, 0, 21 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "GraphIsomorphism", count := [ "A", 7, 0, 21 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 21 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4862\
59, root := ~, start := 486236, stop := 486258 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 7, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 7, 0, 21 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 7, 0, 21 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 7, 0, 21 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 7, 0, 21 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 7, 0, 21 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 7, 0, 21 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to ", count := [ "A", 7, 0, 21 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Label := "for digraphs", Oper := "I\
somorphismDigraphs" ), content := 0, count := [ "A", 7, 0, 21 ], mathmode := "\
Text", name := "Ref", next := 486354, root := ~, start := 486288, stop := 4863\
53 ), rec( HTML := true, content := " in ", count := [ "A", 7, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 7, 0, 21 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 21 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n            Note however that ", count := [ "A", 7, 0, 21 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          HTML \
:= true, content := "GraphIsomorphism", count := [ "A", 7, 0, 21 ], mathmode :\
= "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "C", next := 486423, root := ~, start := 486400, stop := 48642\
2 ), rec( HTML := true, content := "'s optional argument\n            ", 
                                                                  count := 
                                                                    [ "A", 7, 
                                                                      0, 21 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "firstunbindcanon", count := [ "A", 7, 0, 21 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 21 ], 
                                                                  mathmode := \
"Text", name := "A", next := 486479, root := ~, start := 486456, stop := 48647\
8 ), rec( HTML := true, content := " is not applicable, since the canonical\n \
           labellings of a digraph are not portable between sessions.\n       \
   ", count := [ "A", 7, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 7, 0, 21 ],
                                                          name := "Alt", 
                                                          next := 486606, 
                                                          root := ~, 
                                                          start := 486206, 
                                                          stop := 486605 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 21 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 21 ], 
                                                  name := "Item", 
                                                  next := 486622, root := ~, 
                                                  start := 486189, 
                                                  stop := 486621 ) ], 
                                          count := [ "A", 7, 0, 16 ], 
                                          name := "Row", next := 486635, 
                                          root := ~, start := 486014, 
                                          stop := 486634 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 7, 0, 22 ], 
                                          name := "HorLine", next := 486652, 
                                          root := ~, start := 486642, 
                                          stop := 486651 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "I\
sIsomorphicGraph", count := [ "A", 7, 0, 23 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ) ], count := [ "A", 7, 0, 23 ], mathmode := "Text", 
                                                          name := "C", 
                                                          next := 486715, 
                                                          root := ~, 
                                                          start := 486691, 
                                                          stop := 486714 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 23 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 23 ], 
                                                  name := "Item", 
                                                  next := 486731, root := ~, 
                                                  start := 486674, 
                                                  stop := 486730 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Label := "for di\
graphs", Oper := "IsIsomorphicDigraph" ), content := 0, count := 
                                                            [ "A", 7, 0, 25 ],
                                                          mathmode := "Text", 
                                                          name := "Ref", 
                                                          next := 486811, 
                                                          root := ~, 
                                                          start := 486757, 
                                                          stop := 486810 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 25 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 25 ], 
                                                  name := "Item", 
                                                  next := 486827, root := ~, 
                                                  start := 486740, 
                                                  stop := 486826 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            ", count := [ "A", 7, 0, 27 ], mathmode := "Text", name := "PCDA\
TA", root := ~ ), rec( attributes := rec(  ), content := [ rec( HTML := true, 
                                                                          cont\
ent := "IsIsomorphicGraph", count := [ "A", 7, 0, 27 ], mathmode := "Text", 
                                                                          name\
 := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 27 ], mathmode := "Text", 
                                                                  name := "C",
                                                                  next := 4869\
07, root := ~, start := 486883, stop := 486906 ), rec( HTML := true, 
                                                                  content := "\
 in ", count := [ "A", 7, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ),
                                                              rec( 
                                                                  attributes :\
= rec( Not := "Text" ), content := [ rec( attributes := rec( Text := "Grape" )
                                                                            , 
                                                                          cont\
ent := [ rec( HTML := true, content := "http://www.maths.qmul.ac.uk/~leonard/g\
rape/", count := [ "A", 7, 0, 27 ], mathmode := "Text", name := "PCDATA", root\
 := ~ ) ], count := [ "A", 7, 0, 27 ], mathmode := "Text", name := "URL", next\
 := 87, root := ~, start := 17, stop := 86 ) ], count := [ "A", 7, 0, 27 ], 
                                                                  name := "Alt\
", next := 93, root := ~, start := 1, stop := 92 ), rec( attributes := 
                                                                    rec( 
                                                                      Only := \
"Text" ), content := [ rec( attributes := rec(  ), content := [ rec( HTML := t\
rue, content := "Grape", count := [ "A", 7, 0, 27 ], name := "PCDATA", root :=\
 ~ ) ], count := [ "A", 7, 0, 27 ], name := "Package", next := 137, root := ~,
                                                                          star\
t := 113, stop := 136 ) ], count := [ "A", 7, 0, 27 ], mathmode := "Text", 
                                                                  name := "Alt\
", next := 143, root := ~, start := 93, stop := 142 ), rec( HTML := true, 
                                                                  content := "\
 is equivalent to ", count := [ "A", 7, 0, 27 ], mathmode := "Text", 
                                                                  name := "PCD\
ATA", root := ~ ), rec( attributes := rec( Label := "for digraphs", Oper := "I\
sIsomorphicDigraph" ), content := 0, count := [ "A", 7, 0, 27 ], mathmode := "\
Text", name := "Ref", next := 487002, root := ~, start := 486936, stop := 4870\
01 ), rec( HTML := true, content := " in ", count := [ "A", 7, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 7, 0, 27 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 27 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
.\n            Note however that ", count := [ "A", 7, 0, 27 ], mathmode := "T\
ext", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), content := 
                                                                    [ 
                                                                      rec( 
                                                                          HTML \
:= true, content := "IsIsomorphicGraph", count := [ "A", 7, 0, 27 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "C", next := 487072, root := ~, start := 487048, stop := 48707\
1 ), rec( HTML := true, content := "'s optional argument\n            ", 
                                                                  count := 
                                                                    [ "A", 7, 
                                                                      0, 27 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "firstunbindcanon", count := [ "A", 7, 0, 27 ], mathmode \
:= "Text", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 27 ], 
                                                                  mathmode := \
"Text", name := "A", next := 487128, root := ~, start := 487105, stop := 48712\
7 ), rec( HTML := true, content := " is not applicable, since the canonical\n \
           labellings of a digraph are not portable between sessions.\n       \
   ", count := [ "A", 7, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 7, 0, 27 ],
                                                          name := "Alt", 
                                                          next := 487255, 
                                                          root := ~, 
                                                          start := 486853, 
                                                          stop := 487254 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 27 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 27 ], 
                                                  name := "Item", 
                                                  next := 487271, root := ~, 
                                                  start := 486836, 
                                                  stop := 487270 ) ], 
                                          count := [ "A", 7, 0, 22 ], 
                                          name := "Row", next := 487284, 
                                          root := ~, start := 486660, 
                                          stop := 487283 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 7, 0, 28 ], 
                                          name := "HorLine", next := 487301, 
                                          root := ~, start := 487291, 
                                          stop := 487300 ), 
                                      rec( attributes := rec(  ), 
                                          content := 
                                            [ 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec(  ), 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  content := "G\
raphIsomorphismClassRepresentatives", count := [ "A", 7, 0, 29 ], mathmode := \
"Text", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 29 ], 
                                                          mathmode := "Text", 
                                                          name := "C", 
                                                          next := 487383, 
                                                          root := ~, 
                                                          start := 487340, 
                                                          stop := 487382 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 29 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 29 ], 
                                                  name := "Item", 
                                                  next := 487399, root := ~, 
                                                  start := 487323, 
                                                  stop := 487398 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   None\n        ", count := [ "A", 7, 0, 31 ], mathmode := "Text", 
                                                          name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 31 ], 
                                                  name := "Item", 
                                                  next := 487445, root := ~, 
                                                  start := 487408, 
                                                  stop := 487444 ), 
                                              rec( attributes := rec(  ), 
                                                  content := 
                                                    [ 
                                                      rec( 
                                                          content := "\n       \
   ", count := [ "A", 7, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ), 
                                                      rec( 
                                                          attributes := 
                                                            rec( 
                                                              Only := "HTML" )
                                                            , 
                                                          content := 
                                                            [ 
                                                              rec( 
                                                                  HTML := true,
                                                                  content := "\
\n            There is no analogous function in ", count := [ "A", 7, 0, 33 ],
                                                                  mathmode := \
"Text", name := "PCDATA", root := ~ ), rec( attributes := rec(  ), 
                                                                  content := 
                                                                    [ rec( 
                                                                          HTML\
 := true, content := "Digraphs", count := [ "A", 7, 0, 33 ], mathmode := "Text\
", name := "PCDATA", root := ~ ) ], count := [ "A", 7, 0, 33 ], mathmode := "T\
ext", name := "Package", next := 28, root := ~, start := 1, stop := 27 ), 
                                                              rec( 
                                                                  HTML := true
                                                                    , 
                                                                  content := "\
, although this feature\n            might be implemented in the future.\n    \
      ", count := [ "A", 7, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                                  root := ~ ) 
                                                             ], 
                                                          count := 
                                                            [ "A", 7, 0, 33 ],
                                                          name := "Alt", 
                                                          next := 487633, 
                                                          root := ~, 
                                                          start := 487471, 
                                                          stop := 487632 ), 
                                                      rec( 
                                                          content := "\n      \
  ", count := [ "A", 7, 0, 33 ], mathmode := "Text", name := "PCDATA", 
                                                          root := ~ ) ], 
                                                  count := [ "A", 7, 0, 33 ], 
                                                  name := "Item", 
                                                  next := 487649, root := ~, 
                                                  start := 487454, 
                                                  stop := 487648 ) ], 
                                          count := [ "A", 7, 0, 28 ], 
                                          name := "Row", next := 487662, 
                                          root := ~, start := 487309, 
                                          stop := 487661 ), 
                                      rec( attributes := rec(  ), 
                                          content := 0, 
                                          count := [ "A", 7, 0, 34 ], 
                                          name := "HorLine", next := 487679, 
                                          root := ~, start := 487669, 
                                          stop := 487678 ) ], 
                                  count := [ "A", 7, 0, 4 ], 
                                  mathmode := "Text", name := "Table", 
                                  next := 487693, root := ~, start := 485291, 
                                  stop := 487692 ), 
                              rec( content := "\n  ", 
                                  count := [ "A", 7, 0, 35 ], 
                                  mathmode := "Text", name := "PCDATA", 
                                  root := ~ ) ], count := [ "A", 7, 0, 1 ], 
                          mathmode := "Text", name := "Section", 
                          next := 487706, root := ~, start := 485037, 
                          stop := 487705 ), 
                      rec( content := "\n", count := [ "A", 7, 0, 35 ], 
                          mathmode := "Text", name := "PCDATA", root := ~ ) ],
                  count := [ "A", 0, 0, 1 ], mathmode := "Text", 
                  name := "Appendix", next := 487718, root := ~, 
                  start := 454067, stop := 487717 ), 
              rec( content := " Grape to Digraphs command map ", 
                  count := [ "A", 7, 0, 35 ], mathmode := "Text", 
                  name := "XMLCOMMENT", root := ~ ), 
              rec( attributes := rec( Databases := "digraphs" ), 
                  content := 0, count := [ "Bib", 0, 0, 1 ], 
                  mathmode := "Text", name := "Bibliography", next := 487798, 
                  root := ~, start := 487761, stop := 487797 ), 
              rec( attributes := rec(  ), content := 0, 
                  count := [ "Ind", 0, 0, 1 ], mathmode := "Text", 
                  name := "TheIndex", next := 487810, root := ~, 
                  start := 487799, stop := 487809 ) ], 
          count := [ 0, 0, 0, 1 ], name := "Book", next := 487819, root := ~, 
          start := 1962, stop := 487818 ) ], count := [ 0, 0, 0, 1 ], 
  indent := "", 
  indextext := "<code class=\"code\">&lt;</code> (for digraphs)  <a href=\"cha\
p4_mj.html#X84E0B5B88358C96B\">4.1</a>  <br />\n<code class=\"code\">=</code> \
(for digraphs)  <a href=\"chap4_mj.html#X84E0B5B88358C96B\">4.1</a>  <br />\n<\
code class=\"func\">AdjacencyMatrix</code>  <a href=\"chap5_mj.html#X7DC2CD708\
30BEE60\">5.2-1</a>  <br />\n<code class=\"func\">AdjacencyMatrixMutableCopy</\
code>  <a href=\"chap5_mj.html#X7DC2CD70830BEE60\">5.2-1</a>  <br />\n<code cl\
ass=\"func\">AdjacencyMatrixUpperTriangleLineDecoder</code>  <a href=\"chap9_m\
j.html#X7DF22D1687D096D6\">9.2-10</a>  <br />\n<code class=\"func\">Articulati\
onPoints</code>  <a href=\"chap5_mj.html#X7DDE06E47E605DD7\">5.3-14</a>  <br /\
>\n<code class=\"func\">AsBinaryRelation</code>  <a href=\"chap3_mj.html#X7FBC\
4BDB82FBEDD2\">3.2-1</a>  <br />\n<code class=\"func\">AsDigraph</code>  <a hr\
ef=\"chap3_mj.html#X83CA27E67F685EB3\">3.2-2</a>  <br />\n<code class=\"func\"\
>AsGraph</code>  <a href=\"chap3_mj.html#X7C4F13E080EC16B0\">3.2-4</a>  <br />\
\n<code class=\"func\">AsMonoid</code>  <a href=\"chap5_mj.html#X87D5C60D7B0C1\
309\">5.5-1</a>  <br />\n<code class=\"func\">AsSemigroup</code>, for a filter\
 and a digraph  <a href=\"chap5_mj.html#X87D5C60D7B0C1309\">5.5-1</a>  <br />\
\n&nbsp;&nbsp;&nbsp;&nbsp;for a filter, semilattice digraph, and two lists  <a\
 href=\"chap5_mj.html#X7C6D5EC27C51066B\">5.5-2</a>  <br />\n<code class=\"fun\
c\">AsTransformation</code>  <a href=\"chap3_mj.html#X7C5360B2799943F3\">3.2-5\
</a>  <br />\n<code class=\"func\">AutomorphismGroup</code>, for a digraph  <a\
 href=\"chap7_mj.html#X858C32127A190175\">7.2-2</a>  <br />\n&nbsp;&nbsp;&nbsp\
;&nbsp;for a digraph and a homogeneous list  <a href=\"chap7_mj.html#X877732B1\
783C391B\">7.2-5</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph, homogeneo\
us list, and list  <a href=\"chap7_mj.html#X7DA2C4FE837FFE01\">7.2-6</a>  <br \
/>\n<code class=\"func\">BipartiteDoubleDigraph</code>  <a href=\"chap3_mj.htm\
l#X7C6E6CB284982C7A\">3.3-37</a>  <br />\n<code class=\"func\">BlissAutomorphi\
smGroup</code>, for a digraph  <a href=\"chap7_mj.html#X7E7B0D88865A89F6\">7.2\
-3</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph and homogenous list  <a \
href=\"chap7_mj.html#X7E7B0D88865A89F6\">7.2-3</a>  <br />\n&nbsp;&nbsp;&nbsp;\
&nbsp;for a digraph, homogenous list, and list  <a href=\"chap7_mj.html#X7E7B0\
D88865A89F6\">7.2-3</a>  <br />\n<code class=\"func\">BlissCanonicalDigraph</c\
ode>  <a href=\"chap7_mj.html#X877B1D377EC197D7\">7.2-9</a>  <br />\n<code cla\
ss=\"func\">BlissCanonicalLabelling</code>, for a digraph  <a href=\"chap7_mj.\
html#X7D676FE67A6684FF\">7.2-7</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digr\
aph and a list  <a href=\"chap7_mj.html#X87DA265D803DB337\">7.2-8</a>  <br />\
\n<code class=\"func\">BooleanAdjacencyMatrix</code>  <a href=\"chap5_mj.html#\
X8507DC4F794780C1\">5.2-3</a>  <br />\n<code class=\"func\">BooleanAdjacencyMa\
trixMutableCopy</code>  <a href=\"chap5_mj.html#X8507DC4F794780C1\">5.2-3</a> \
 <br />\n<code class=\"func\">Bridges</code>  <a href=\"chap5_mj.html#X84D5A12\
5848BD800\">5.3-15</a>  <br />\n<code class=\"func\">CayleyDigraph</code>  <a \
href=\"chap3_mj.html#X7FCADADC7EC28478\">3.1-12</a>  <br />\n<code class=\"fun\
c\">ChainDigraph</code>  <a href=\"chap3_mj.html#X870594FC866AC88E\">3.5-1</a>\
  <br />\n<code class=\"func\">CharacteristicPolynomial</code>  <a href=\"chap\
5_mj.html#X87FA0A727CDB060B\">5.2-2</a>  <br />\n<code class=\"func\">Chromati\
cNumber</code>  <a href=\"chap7_mj.html#X807D49358529A37C\">7.3-17</a>  <br />\
\n<code class=\"func\">CliqueNumber</code>  <a href=\"chap8_mj.html#X78427A8B8\
1FEB457\">8.1-5</a>  <br />\n<code class=\"func\">CliquesFinder</code>  <a hre\
f=\"chap8_mj.html#X7A3BC9FF8169ABCD\">8.1-2</a>  <br />\n<code class=\"func\">\
CompleteBipartiteDigraph</code>  <a href=\"chap3_mj.html#X8795B0AD856014FA\">3\
.5-3</a>  <br />\n<code class=\"func\">CompleteDigraph</code>  <a href=\"chap3\
_mj.html#X812417E278198D9C\">3.5-2</a>  <br />\n<code class=\"func\">CompleteM\
ultipartiteDigraph</code>  <a href=\"chap3_mj.html#X873F29CC863241F8\">3.5-4</\
a>  <br />\n<code class=\"func\">CycleDigraph</code>  <a href=\"chap3_mj.html#\
X80C29DDE876FFBEB\">3.5-5</a>  <br />\n<code class=\"func\">DegreeMatrix</code\
>  <a href=\"chap5_mj.html#X7BEAE1C78267F54D\">5.2-16</a>  <br />\n<code class\
=\"func\">Digraph</code>  <a href=\"chap3_mj.html#X834843057CE86655\">3.1-7</a\
>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a group, list, function, and function  \
<a href=\"chap3_mj.html#X834843057CE86655\">3.1-7</a>  <br />\n&nbsp;&nbsp;&nb\
sp;&nbsp;for a list and function  <a href=\"chap3_mj.html#X834843057CE86655\">\
3.1-7</a>  <br />\n<code class=\"func\">Digraph6String</code>  <a href=\"chap9\
_mj.html#X782A052979EA2376\">9.2-3</a>  <br />\n<code class=\"func\">DigraphAd\
dAllLoops</code>  <a href=\"chap3_mj.html#X8167A50A83256ED1\">3.3-38</a>  <br \
/>\n<code class=\"func\">DigraphAddAllLoopsAttr</code>  <a href=\"chap3_mj.htm\
l#X8167A50A83256ED1\">3.3-38</a>  <br />\n<code class=\"func\">DigraphAddEdge<\
/code>, for a digraph and an edge  <a href=\"chap3_mj.html#X7E58CC4880627658\"\
>3.3-16</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph, source, and range \
 <a href=\"chap3_mj.html#X7E58CC4880627658\">3.3-16</a>  <br />\n<code class=\
\"func\">DigraphAddEdgeOrbit</code>  <a href=\"chap3_mj.html#X7BE5C7028760B053\
\">3.3-17</a>  <br />\n<code class=\"func\">DigraphAddEdges</code>  <a href=\"\
chap3_mj.html#X8693A61B7F752C76\">3.3-18</a>  <br />\n<code class=\"func\">Dig\
raphAddVertex</code>  <a href=\"chap3_mj.html#X83B2506D79453208\">3.3-14</a>  \
<br />\n<code class=\"func\">DigraphAddVertices</code>, for a digraph and a li\
st of labels  <a href=\"chap3_mj.html#X8134BEE7786BD3A7\">3.3-15</a>  <br />\n\
&nbsp;&nbsp;&nbsp;&nbsp;for a digraph and an integer  <a href=\"chap3_mj.html#\
X8134BEE7786BD3A7\">3.3-15</a>  <br />\n<code class=\"func\">DigraphAdjacencyF\
unction</code>  <a href=\"chap5_mj.html#X7AFCE34A7A04D5C1\">5.2-4</a>  <br />\
\n<code class=\"func\">DigraphAllSimpleCircuits</code>  <a href=\"chap5_mj.htm\
l#X7ECD16838704FAAA\">5.3-24</a>  <br />\n<code class=\"func\">DigraphBicompon\
ents</code>  <a href=\"chap5_mj.html#X7F1B5A2782F598B1\">5.3-13</a>  <br />\n<\
code class=\"func\">DigraphByAdjacencyMatrix</code>  <a href=\"chap3_mj.html#X\
8023FE387A3AB609\">3.1-8</a>  <br />\n<code class=\"func\">DigraphByEdges</cod\
e>  <a href=\"chap3_mj.html#X7F37B6768349E269\">3.1-9</a>  <br />\n<code class\
=\"func\">DigraphByInNeighbors</code>  <a href=\"chap3_mj.html#X81BC49B57EAADE\
FB\">3.1-11</a>  <br />\n<code class=\"func\">DigraphByInNeighbours</code>  <a\
 href=\"chap3_mj.html#X81BC49B57EAADEFB\">3.1-11</a>  <br />\n<code class=\"fu\
nc\">DigraphByOutNeighboursType</code>  <a href=\"chap3_mj.html#X86E798B779515\
678\">3.1-6</a>  <br />\n<code class=\"func\">DigraphCartesianProduct</code>, \
for a list of digraphs  <a href=\"chap3_mj.html#X7D625CC87DBFFDED\">3.3-30</a>\
  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a positive number of digraphs  <a href=\
\"chap3_mj.html#X7D625CC87DBFFDED\">3.3-30</a>  <br />\n<code class=\"func\">D\
igraphCartesianProductProjections</code>  <a href=\"chap3_mj.html#X8795087A78F\
E7D54\">3.3-32</a>  <br />\n<code class=\"func\">DigraphClique</code>  <a href\
=\"chap8_mj.html#X789854AC7B466402\">8.1-3</a>  <br />\n<code class=\"func\">D\
igraphCliques</code>  <a href=\"chap8_mj.html#X84EA2F9482B8D4AF\">8.1-4</a>  <\
br />\n<code class=\"func\">DigraphCliquesReps</code>  <a href=\"chap8_mj.html\
#X84EA2F9482B8D4AF\">8.1-4</a>  <br />\n<code class=\"func\">DigraphClosure</c\
ode>  <a href=\"chap3_mj.html#X86F9CCEA839ABC48\">3.3-40</a>  <br />\n<code cl\
ass=\"func\">DigraphColouring</code>, for a digraph and a number of colours  <\
a href=\"chap7_mj.html#X86D0A74B83D6B9A7\">7.3-14</a>  <br />\n<code class=\"f\
unc\">DigraphConnectedComponent</code>  <a href=\"chap5_mj.html#X8484EC557810C\
D31\">5.3-10</a>  <br />\n<code class=\"func\">DigraphConnectedComponents</cod\
e>  <a href=\"chap5_mj.html#X842FAD6A7B835977\">5.3-9</a>  <br />\n<code class\
=\"func\">DigraphCopy</code>  <a href=\"chap3_mj.html#X83D93A8A8251E6F9\">3.3-\
1</a>  <br />\n<code class=\"func\">DigraphCopySameMutability</code>  <a href=\
\"chap3_mj.html#X83D93A8A8251E6F9\">3.3-1</a>  <br />\n<code class=\"func\">Di\
graphCore</code>  <a href=\"chap7_mj.html#X863487EF7D64EF56\">7.3-18</a>  <br \
/>\n<code class=\"func\">DigraphDegeneracy</code>  <a href=\"chap5_mj.html#X7B\
2E42327DA118E0\">5.3-27</a>  <br />\n<code class=\"func\">DigraphDegeneracyOrd\
ering</code>  <a href=\"chap5_mj.html#X827C2BD17A4547E3\">5.3-28</a>  <br />\n\
<code class=\"func\">DigraphDiameter</code>  <a href=\"chap5_mj.html#X7F16B9EB\
8398459C\">5.3-1</a>  <br />\n<code class=\"func\">DigraphDijkstra</code>, for\
 a source  <a href=\"chap5_mj.html#X79352A8286D1D8F6\">5.3-31</a>  <br />\n&nb\
sp;&nbsp;&nbsp;&nbsp;for a source and target  <a href=\"chap5_mj.html#X79352A8\
286D1D8F6\">5.3-31</a>  <br />\n<code class=\"func\">DigraphDirectProduct</cod\
e>, for a list of digraphs  <a href=\"chap3_mj.html#X84D24DC9833B54A5\">3.3-31\
</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a positive number of digraphs  <a hr\
ef=\"chap3_mj.html#X84D24DC9833B54A5\">3.3-31</a>  <br />\n<code class=\"func\
\">DigraphDirectProductProjections</code>  <a href=\"chap3_mj.html#X84FB64F185\
B804C2\">3.3-33</a>  <br />\n<code class=\"func\">DigraphDisjointUnion</code>,\
 for a list of digraphs  <a href=\"chap3_mj.html#X814F1DFC83DB273F\">3.3-27</a\
>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for an\n    arbitrary number of digraphs  <\
a href=\"chap3_mj.html#X814F1DFC83DB273F\">3.3-27</a>  <br />\n<code class=\"f\
unc\">DigraphDistanceSet</code>, for a digraph, a pos int, and a list  <a href\
=\"chap5_mj.html#X7CB7DDCD84621D38\">5.3-5</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbs\
p;for a digraph, a pos int, and an int  <a href=\"chap5_mj.html#X7CB7DDCD84621\
D38\">5.3-5</a>  <br />\n<code class=\"func\">DigraphDual</code>  <a href=\"ch\
ap3_mj.html#X7F71D99D852B130F\">3.3-10</a>  <br />\n<code class=\"func\">Digra\
phDualAttr</code>  <a href=\"chap3_mj.html#X7F71D99D852B130F\">3.3-10</a>  <br\
 />\n<code class=\"func\">DigraphEdgeLabel</code>  <a href=\"chap5_mj.html#X79\
FAEACC7F438C2F\">5.1-11</a>  <br />\n<code class=\"func\">DigraphEdgeLabels</c\
ode>  <a href=\"chap5_mj.html#X7C24851087D4A8FB\">5.1-12</a>  <br />\n<code cl\
ass=\"func\">DigraphEdges</code>  <a href=\"chap5_mj.html#X7D1C6A4D7ECEC317\">\
5.1-3</a>  <br />\n<code class=\"func\">DigraphEdgeUnion</code>, for a list of\
 digraphs  <a href=\"chap3_mj.html#X7DA997697D310E44\">3.3-28</a>  <br />\n&nb\
sp;&nbsp;&nbsp;&nbsp;for a positive number of digraphs  <a href=\"chap3_mj.htm\
l#X7DA997697D310E44\">3.3-28</a>  <br />\n<code class=\"func\">DigraphEmbeddin\
g</code>  <a href=\"chap7_mj.html#X7AD04CC186E86CCA\">7.3-8</a>  <br />\n<code\
 class=\"func\">DigraphEpimorphism</code>  <a href=\"chap7_mj.html#X7CB5AD9F86\
1684FD\">7.3-6</a>  <br />\n<code class=\"func\">DigraphFamily</code>  <a href\
=\"chap3_mj.html#X86E798B779515678\">3.1-6</a>  <br />\n<code class=\"func\">D\
igraphFile</code>  <a href=\"chap9_mj.html#X7845ACDA7D4D333D\">9.2-4</a>  <br \
/>\n<code class=\"func\">DigraphFloydWarshall</code>  <a href=\"chap5_mj.html#\
X864A31A8809F61C2\">5.3-18</a>  <br />\n<code class=\"func\">DigraphFromDigrap\
h6String</code>  <a href=\"chap9_mj.html#X873D6EB8836A3C61\">9.2-2</a>  <br />\
\n<code class=\"func\">DigraphFromDiSparse6String</code>  <a href=\"chap9_mj.h\
tml#X873D6EB8836A3C61\">9.2-2</a>  <br />\n<code class=\"func\">DigraphFromGra\
ph6String</code>  <a href=\"chap9_mj.html#X873D6EB8836A3C61\">9.2-2</a>  <br /\
>\n<code class=\"func\">DigraphFromPlainTextString</code>  <a href=\"chap9_mj.\
html#X8540FC21796A793F\">9.2-12</a>  <br />\n<code class=\"func\">DigraphFromS\
parse6String</code>  <a href=\"chap9_mj.html#X873D6EB8836A3C61\">9.2-2</a>  <b\
r />\n<code class=\"func\">DigraphGirth</code>  <a href=\"chap5_mj.html#X79A3D\
A4078CF3C90\">5.3-6</a>  <br />\n<code class=\"func\">DigraphGreedyColouring</\
code>, for a digraph  <a href=\"chap7_mj.html#X7AB7200D831013C1\">7.3-15</a>  \
<br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph and vertex order  <a href=\"chap\
7_mj.html#X7AB7200D831013C1\">7.3-15</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for \
a digraph and vertex order function  <a href=\"chap7_mj.html#X7AB7200D831013C1\
\">7.3-15</a>  <br />\n<code class=\"func\">DigraphGroup</code>  <a href=\"cha\
p7_mj.html#X803ACEDA7BBAC5B3\">7.2-10</a>  <br />\n<code class=\"func\">Digrap\
hHasLoops</code>  <a href=\"chap6_mj.html#X7D92935C7D535187\">6.1-1</a>  <br /\
>\n<code class=\"func\">DigraphHomomorphism</code>  <a href=\"chap7_mj.html#X8\
5E9B019877AD7FE\">7.3-2</a>  <br />\n<code class=\"func\">DigraphImmutableCopy\
</code>  <a href=\"chap3_mj.html#X83D93A8A8251E6F9\">3.3-1</a>  <br />\n<code \
class=\"func\">DigraphImmutableCopyIfImmutable</code>  <a href=\"chap3_mj.html\
#X8399F7427B227228\">3.3-2</a>  <br />\n<code class=\"func\">DigraphImmutableC\
opyIfMutable</code>  <a href=\"chap3_mj.html#X8399F7427B227228\">3.3-2</a>  <b\
r />\n<code class=\"func\">DigraphIndependentSet</code>  <a href=\"chap8_mj.ht\
ml#X84350678782BFAB7\">8.2-2</a>  <br />\n<code class=\"func\">DigraphIndepend\
entSets</code>  <a href=\"chap8_mj.html#X7D2C78EB81A798A9\">8.2-3</a>  <br />\
\n<code class=\"func\">DigraphIndependentSetsReps</code>  <a href=\"chap8_mj.h\
tml#X7D2C78EB81A798A9\">8.2-3</a>  <br />\n<code class=\"func\">DigraphInEdges\
</code>  <a href=\"chap5_mj.html#X7EFAF01B7A155157\">5.1-13</a>  <br />\n<code\
 class=\"func\">DigraphJoin</code>, for a list of digraphs  <a href=\"chap3_mj\
.html#X7DDFC759860E3390\">3.3-29</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a po\
sitive number of digraphs  <a href=\"chap3_mj.html#X7DDFC759860E3390\">3.3-29<\
/a>  <br />\n<code class=\"func\">DigraphLayers</code>  <a href=\"chap5_mj.htm\
l#X870E04307C5F213F\">5.3-26</a>  <br />\n<code class=\"func\">DigraphLongestD\
istanceFromVertex</code>  <a href=\"chap5_mj.html#X8223718079D98A82\">5.3-4</a\
>  <br />\n<code class=\"func\">DigraphLongestSimpleCircuit</code>  <a href=\"\
chap5_mj.html#X7C735C4E86BDD5F6\">5.3-25</a>  <br />\n<code class=\"func\">Dig\
raphLoops</code>  <a href=\"chap5_mj.html#X83271F607BD809CF\">5.2-14</a>  <br \
/>\n<code class=\"func\">DigraphMaximalClique</code>  <a href=\"chap8_mj.html#\
X789854AC7B466402\">8.1-3</a>  <br />\n<code class=\"func\">DigraphMaximalCliq\
ues</code>  <a href=\"chap8_mj.html#X84EA2F9482B8D4AF\">8.1-4</a>  <br />\n<co\
de class=\"func\">DigraphMaximalCliquesAttr</code>  <a href=\"chap8_mj.html#X8\
4EA2F9482B8D4AF\">8.1-4</a>  <br />\n<code class=\"func\">DigraphMaximalClique\
sReps</code>  <a href=\"chap8_mj.html#X84EA2F9482B8D4AF\">8.1-4</a>  <br />\n<\
code class=\"func\">DigraphMaximalCliquesRepsAttr</code>  <a href=\"chap8_mj.h\
tml#X84EA2F9482B8D4AF\">8.1-4</a>  <br />\n<code class=\"func\">DigraphMaximal\
IndependentSet</code>  <a href=\"chap8_mj.html#X84350678782BFAB7\">8.2-2</a>  \
<br />\n<code class=\"func\">DigraphMaximalIndependentSets</code>  <a href=\"c\
hap8_mj.html#X7D2C78EB81A798A9\">8.2-3</a>  <br />\n<code class=\"func\">Digra\
phMaximalIndependentSetsAttr</code>  <a href=\"chap8_mj.html#X7D2C78EB81A798A9\
\">8.2-3</a>  <br />\n<code class=\"func\">DigraphMaximalIndependentSetsReps</\
code>  <a href=\"chap8_mj.html#X7D2C78EB81A798A9\">8.2-3</a>  <br />\n<code cl\
ass=\"func\">DigraphMaximalIndependentSetsRepsAttr</code>  <a href=\"chap8_mj.\
html#X7D2C78EB81A798A9\">8.2-3</a>  <br />\n<code class=\"func\">DigraphMaxima\
lMatching</code>  <a href=\"chap5_mj.html#X7B7A67277B1C9A02\">5.1-17</a>  <br \
/>\n<code class=\"func\">DigraphMaximumMatching</code>  <a href=\"chap5_mj.htm\
l#X78E9847A858788D1\">5.1-18</a>  <br />\n<code class=\"func\">DigraphMonomorp\
hism</code>  <a href=\"chap7_mj.html#X82D0FCD87D47ACA8\">7.3-4</a>  <br />\n<c\
ode class=\"func\">DigraphMutableCopy</code>  <a href=\"chap3_mj.html#X83D93A8\
A8251E6F9\">3.3-1</a>  <br />\n<code class=\"func\">DigraphMutableCopyIfImmuta\
ble</code>  <a href=\"chap3_mj.html#X8399F7427B227228\">3.3-2</a>  <br />\n<co\
de class=\"func\">DigraphMutableCopyIfMutable</code>  <a href=\"chap3_mj.html#\
X8399F7427B227228\">3.3-2</a>  <br />\n<code class=\"func\">DigraphMycielskian\
</code>  <a href=\"chap3_mj.html#X7B5AC5FE859F4D80\">3.3-41</a>  <br />\n<code\
 class=\"func\">DigraphMycielskianAttr</code>  <a href=\"chap3_mj.html#X7B5AC5\
FE859F4D80\">3.3-41</a>  <br />\n<code class=\"func\">DigraphNrConnectedCompon\
ents</code>  <a href=\"chap5_mj.html#X842FAD6A7B835977\">5.3-9</a>  <br />\n<c\
ode class=\"func\">DigraphNrEdges</code>  <a href=\"chap5_mj.html#X85E1CFDD7E1\
64AD0\">5.1-4</a>  <br />\n<code class=\"func\">DigraphNrLoops</code>  <a href\
=\"chap5_mj.html#X7BDABAF07917462B\">5.1-5</a>  <br />\n<code class=\"func\">D\
igraphNrStronglyConnectedComponents</code>  <a href=\"chap5_mj.html#X833ECD6B7\
A84944C\">5.3-11</a>  <br />\n<code class=\"func\">DigraphNrVertices</code>  <\
a href=\"chap5_mj.html#X7C6F19B57CB2E882\">5.1-2</a>  <br />\n<code class=\"fu\
nc\">DigraphOddGirth</code>  <a href=\"chap5_mj.html#X8374B7357EC189C1\">5.3-7\
</a>  <br />\n<code class=\"func\">DigraphOrbitReps</code>  <a href=\"chap7_mj\
.html#X8386028782F2D3FF\">7.2-12</a>  <br />\n<code class=\"func\">DigraphOrbi\
ts</code>  <a href=\"chap7_mj.html#X8096C5287E459279\">7.2-11</a>  <br />\n<co\
de class=\"func\">DigraphOutEdges</code>  <a href=\"chap5_mj.html#X7BECFE6687E\
CD028\">5.1-14</a>  <br />\n<code class=\"func\">DigraphPath</code>  <a href=\
\"chap5_mj.html#X8039170B82A32257\">5.3-21</a>  <br />\n<code class=\"func\">D\
igraphPeriod</code>  <a href=\"chap5_mj.html#X853D0B0981A33433\">5.3-17</a>  <\
br />\n<code class=\"func\">DigraphPlainTextLineDecoder</code>  <a href=\"chap\
9_mj.html#X7AAA35867B5D8BF4\">9.2-8</a>  <br />\n<code class=\"func\">DigraphP\
lainTextLineEncoder</code>  <a href=\"chap9_mj.html#X7AAA35867B5D8BF4\">9.2-8<\
/a>  <br />\n<code class=\"func\">DigraphRange</code>  <a href=\"chap5_mj.html\
#X7FDEBF3279759961\">5.2-5</a>  <br />\n<code class=\"func\">DigraphReflexiveT\
ransitiveClosure</code>  <a href=\"chap3_mj.html#X7A6C419080AD41DE\">3.3-12</a\
>  <br />\n<code class=\"func\">DigraphReflexiveTransitiveClosureAttr</code>  \
<a href=\"chap3_mj.html#X7A6C419080AD41DE\">3.3-12</a>  <br />\n<code class=\"\
func\">DigraphReflexiveTransitiveReduction</code>  <a href=\"chap3_mj.html#X82\
AD17517E273600\">3.3-13</a>  <br />\n<code class=\"func\">DigraphReflexiveTran\
sitiveReductionAttr</code>  <a href=\"chap3_mj.html#X82AD17517E273600\">3.3-13\
</a>  <br />\n<code class=\"func\">DigraphRemoveAllMultipleEdges</code>  <a hr\
ef=\"chap3_mj.html#X7DCCD0247897A3DE\">3.3-25</a>  <br />\n<code class=\"func\
\">DigraphRemoveAllMultipleEdgesAttr</code>  <a href=\"chap3_mj.html#X7DCCD024\
7897A3DE\">3.3-25</a>  <br />\n<code class=\"func\">DigraphRemoveEdge</code>, \
for a digraph and an edge  <a href=\"chap3_mj.html#X8433E3BC7E5EA6BF\">3.3-21<\
/a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph, source, and range  <a href\
=\"chap3_mj.html#X8433E3BC7E5EA6BF\">3.3-21</a>  <br />\n<code class=\"func\">\
DigraphRemoveEdgeOrbit</code>  <a href=\"chap3_mj.html#X85981D9187F49018\">3.3\
-22</a>  <br />\n<code class=\"func\">DigraphRemoveEdges</code>  <a href=\"cha\
p3_mj.html#X87093FDA7F88E732\">3.3-23</a>  <br />\n<code class=\"func\">Digrap\
hRemoveLoops</code>  <a href=\"chap3_mj.html#X79324AF7818C0C02\">3.3-24</a>  <\
br />\n<code class=\"func\">DigraphRemoveLoopsAttr</code>  <a href=\"chap3_mj.\
html#X79324AF7818C0C02\">3.3-24</a>  <br />\n<code class=\"func\">DigraphRemov\
eVertex</code>  <a href=\"chap3_mj.html#X7B634A2B83C08B16\">3.3-19</a>  <br />\
\n<code class=\"func\">DigraphRemoveVertices</code>  <a href=\"chap3_mj.html#X\
7E290E847A5A299A\">3.3-20</a>  <br />\n<code class=\"func\">DigraphReverse</co\
de>  <a href=\"chap3_mj.html#X78DECD26811EFD7C\">3.3-9</a>  <br />\n<code clas\
s=\"func\">DigraphReverseAttr</code>  <a href=\"chap3_mj.html#X78DECD26811EFD7\
C\">3.3-9</a>  <br />\n<code class=\"func\">DigraphReverseEdge</code>, for a d\
igraph and an edge  <a href=\"chap3_mj.html#X7821753D85402A8C\">3.3-26</a>  <b\
r />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph, source, and range  <a href=\"chap\
3_mj.html#X7821753D85402A8C\">3.3-26</a>  <br />\n<code class=\"func\">Digraph\
ReverseEdges</code>, for a digraph and a list of edges  <a href=\"chap3_mj.htm\
l#X7821753D85402A8C\">3.3-26</a>  <br />\n<strong class=\"pkg\">Digraphs</stro\
ng> package overview  <a href=\"chap1_mj.html#X7F202ABA780E595D\">1.</a>  <br \
/>\n<code class=\"func\">DigraphSchreierVector</code>  <a href=\"chap7_mj.html\
#X8657604E87A25E5F\">7.2-13</a>  <br />\n<code class=\"func\">DigraphShortestD\
istance</code>, for a digraph and a list  <a href=\"chap5_mj.html#X8104A9D37BC\
D8A05\">5.3-2</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph and two verti\
ces  <a href=\"chap5_mj.html#X8104A9D37BCD8A05\">5.3-2</a>  <br />\n&nbsp;&nbs\
p;&nbsp;&nbsp;for a digraph, a list, and a list  <a href=\"chap5_mj.html#X8104\
A9D37BCD8A05\">5.3-2</a>  <br />\n<code class=\"func\">DigraphShortestDistance\
s</code>  <a href=\"chap5_mj.html#X81F99BC67E9D050F\">5.3-3</a>  <br />\n<code\
 class=\"func\">DigraphShortestPath</code>  <a href=\"chap5_mj.html#X80E9D6458\
43973A6\">5.3-22</a>  <br />\n<code class=\"func\">DigraphSinks</code>  <a hre\
f=\"chap5_mj.html#X85D5E08280914EE4\">5.1-6</a>  <br />\n<code class=\"func\">\
DigraphsMakeDoc</code>  <a href=\"chap2_mj.html#X870631C38610AC25\">2.4-1</a> \
 <br />\n<code class=\"func\">DigraphSource</code>  <a href=\"chap5_mj.html#X7\
FDEBF3279759961\">5.2-5</a>  <br />\n<code class=\"func\">DigraphSources</code\
>  <a href=\"chap5_mj.html#X7F5C6268839BE98C\">5.1-7</a>  <br />\n<code class=\
\"func\">DigraphsRespectsColouring</code>  <a href=\"chap7_mj.html#X7F80709A80\
CBFA98\">7.3-12</a>  <br />\n<code class=\"func\">DigraphStabilizer</code>  <a\
 href=\"chap7_mj.html#X78913684795FB256\">7.2-14</a>  <br />\n<code class=\"fu\
nc\">DigraphsTestExtreme</code>  <a href=\"chap2_mj.html#X7885EF3E785D4298\">2\
.5-3</a>  <br />\n<code class=\"func\">DigraphsTestInstall</code>  <a href=\"c\
hap2_mj.html#X86AF4DAE80B978DA\">2.5-1</a>  <br />\n<code class=\"func\">Digra\
phsTestStandard</code>  <a href=\"chap2_mj.html#X7A20088B7C406C4A\">2.5-2</a> \
 <br />\n<code class=\"func\">DigraphStronglyConnectedComponent</code>  <a hre\
f=\"chap5_mj.html#X7EFCB5017D662254\">5.3-12</a>  <br />\n<code class=\"func\"\
>DigraphStronglyConnectedComponents</code>  <a href=\"chap5_mj.html#X833ECD6B7\
A84944C\">5.3-11</a>  <br />\n<code class=\"func\">DigraphsUseBliss</code>  <a\
 href=\"chap7_mj.html#X83E593F3855B122E\">7.2-1</a>  <br />\n<code class=\"fun\
c\">DigraphsUseNauty</code>  <a href=\"chap7_mj.html#X83E593F3855B122E\">7.2-1\
</a>  <br />\n<code class=\"func\">DigraphSymmetricClosure</code>  <a href=\"c\
hap3_mj.html#X874883DD7DD450C4\">3.3-11</a>  <br />\n<code class=\"func\">Digr\
aphSymmetricClosureAttr</code>  <a href=\"chap3_mj.html#X874883DD7DD450C4\">3.\
3-11</a>  <br />\n<code class=\"func\">DigraphTopologicalSort</code>  <a href=\
\"chap5_mj.html#X785C30378064CF47\">5.1-8</a>  <br />\n<code class=\"func\">Di\
graphTransitiveClosure</code>  <a href=\"chap3_mj.html#X7A6C419080AD41DE\">3.3\
-12</a>  <br />\n<code class=\"func\">DigraphTransitiveClosureAttr</code>  <a \
href=\"chap3_mj.html#X7A6C419080AD41DE\">3.3-12</a>  <br />\n<code class=\"fun\
c\">DigraphTransitiveReduction</code>  <a href=\"chap3_mj.html#X82AD17517E2736\
00\">3.3-13</a>  <br />\n<code class=\"func\">DigraphTransitiveReductionAttr</\
code>  <a href=\"chap3_mj.html#X82AD17517E273600\">3.3-13</a>  <br />\n<code c\
lass=\"func\">DigraphUndirectedGirth</code>  <a href=\"chap5_mj.html#X84688B33\
7BDDBB09\">5.3-8</a>  <br />\n<code class=\"func\">DigraphVertexLabel</code>  \
<a href=\"chap5_mj.html#X7CA91E4B7904F793\">5.1-9</a>  <br />\n<code class=\"f\
unc\">DigraphVertexLabels</code>  <a href=\"chap5_mj.html#X7E51F2FE87140B32\">\
5.1-10</a>  <br />\n<code class=\"func\">DigraphVertices</code>  <a href=\"cha\
p5_mj.html#X7C45F7D878D896AC\">5.1-1</a>  <br />\n<code class=\"func\">Digraph\
WelshPowellOrder</code>  <a href=\"chap7_mj.html#X7F9CB3B27B9590DB\">7.3-16</a\
>  <br />\n<code class=\"func\">DiSparse6String</code>  <a href=\"chap9_mj.htm\
l#X782A052979EA2376\">9.2-3</a>  <br />\n<code class=\"func\">DistanceDigraph<\
/code>, for digraph and int  <a href=\"chap3_mj.html#X865436437DF95FEF\">3.3-3\
9</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for digraph and list  <a href=\"chap3_m\
j.html#X865436437DF95FEF\">3.3-39</a>  <br />\n<code class=\"func\">DotColored\
Digraph</code>  <a href=\"chap9_mj.html#X7F9B99C478EE093A\">9.1-2</a>  <br />\
\n<code class=\"func\">DotDigraph</code>  <a href=\"chap9_mj.html#X7F9B99C478E\
E093A\">9.1-2</a>  <br />\n<code class=\"func\">DotEdgeColoredDigraph</code>  \
<a href=\"chap9_mj.html#X7F9B99C478EE093A\">9.1-2</a>  <br />\n<code class=\"f\
unc\">DotHighlightedDigraph</code>  <a href=\"chap9_mj.html#X808D12CF81E2C19F\
\">9.1-6</a>  <br />\n<code class=\"func\">DotPartialOrderDigraph</code>  <a h\
ref=\"chap9_mj.html#X84120D447E2CAC23\">9.1-4</a>  <br />\n<code class=\"func\
\">DotPreorderDigraph</code>  <a href=\"chap9_mj.html#X7F5653C8854FAEA6\">9.1-\
5</a>  <br />\n<code class=\"func\">DotQuasiorderDigraph</code>  <a href=\"cha\
p9_mj.html#X7F5653C8854FAEA6\">9.1-5</a>  <br />\n<code class=\"func\">DotSymm\
etricColoredDigraph</code>  <a href=\"chap9_mj.html#X78DA31D1869D2F94\">9.1-3<\
/a>  <br />\n<code class=\"func\">DotSymmetricDigraph</code>  <a href=\"chap9_\
mj.html#X78DA31D1869D2F94\">9.1-3</a>  <br />\n<code class=\"func\">DotSymmetr\
icEdgeColoredDigraph</code>  <a href=\"chap9_mj.html#X78DA31D1869D2F94\">9.1-3\
</a>  <br />\n<code class=\"func\">DotSymmetricVertexColoredDigraph</code>  <a\
 href=\"chap9_mj.html#X78DA31D1869D2F94\">9.1-3</a>  <br />\n<code class=\"fun\
c\">DotVertexColoredDigraph</code>  <a href=\"chap9_mj.html#X7F9B99C478EE093A\
\">9.1-2</a>  <br />\n<code class=\"func\">DotVertexLabelledDigraph</code>  <a\
 href=\"chap9_mj.html#X7F9B99C478EE093A\">9.1-2</a>  <br />\n<code class=\"fun\
c\">DoubleDigraph</code>  <a href=\"chap3_mj.html#X7FB8B48C87C0ED16\">3.3-36</\
a>  <br />\n<code class=\"func\">EdgeDigraph</code>  <a href=\"chap3_mj.html#X\
8595BF937B749F22\">3.3-34</a>  <br />\n<code class=\"func\">EdgeOrbitsDigraph<\
/code>  <a href=\"chap3_mj.html#X7B75C1D680757D6F\">3.1-10</a>  <br />\n<code \
class=\"func\">EdgeUndirectedDigraph</code>  <a href=\"chap3_mj.html#X8364C6F1\
7A1680CB\">3.3-35</a>  <br />\n<code class=\"func\">EmbeddingsDigraphs</code> \
 <a href=\"chap7_mj.html#X82EBDF137EEDC5FD\">7.3-9</a>  <br />\n<code class=\"\
func\">EmbeddingsDigraphsRepresentatives</code>  <a href=\"chap7_mj.html#X82EB\
DF137EEDC5FD\">7.3-9</a>  <br />\n<code class=\"func\">EmptyDigraph</code>  <a\
 href=\"chap3_mj.html#X80DAE31A79FEFD40\">3.5-6</a>  <br />\n<code class=\"fun\
c\">EpimorphismsDigraphs</code>  <a href=\"chap7_mj.html#X7DFB1F5D873937B3\">7\
.3-7</a>  <br />\n<code class=\"func\">EpimorphismsDigraphsRepresentatives</co\
de>  <a href=\"chap7_mj.html#X7DFB1F5D873937B3\">7.3-7</a>  <br />\n<code clas\
s=\"func\">GeneralisedPetersenGraph</code>  <a href=\"chap3_mj.html#X7B5441F38\
6BD105E\">3.5-9</a>  <br />\n<code class=\"func\">GeneratorsOfCayleyDigraph</c\
ode>  <a href=\"chap5_mj.html#X8528455987D7D2BF\">5.4-2</a>  <br />\n<code cla\
ss=\"func\">GeneratorsOfEndomorphismMonoid</code>  <a href=\"chap7_mj.html#X7E\
93B268823F6478\">7.3-13</a>  <br />\n<code class=\"func\">GeneratorsOfEndomorp\
hismMonoidAttr</code>  <a href=\"chap7_mj.html#X7E93B268823F6478\">7.3-13</a> \
 <br />\n<code class=\"func\">Graph</code>  <a href=\"chap3_mj.html#X7B3353428\
39E5146\">3.2-3</a>  <br />\n<code class=\"func\">Graph6String</code>  <a href\
=\"chap9_mj.html#X782A052979EA2376\">9.2-3</a>  <br />\n<code class=\"func\">G\
roupOfCayleyDigraph</code>  <a href=\"chap5_mj.html#X7A000B1D7CCF7093\">5.4-1<\
/a>  <br />\n<code class=\"func\">HamiltonianPath</code>  <a href=\"chap5_mj.h\
tml#X863FDFC4839A3B82\">5.3-29</a>  <br />\n<code class=\"func\">HomomorphismD\
igraphsFinder</code>  <a href=\"chap7_mj.html#X79ABF0E783FD67C7\">7.3-1</a>  <\
br />\n<code class=\"func\">HomomorphismsDigraphs</code>  <a href=\"chap7_mj.h\
tml#X8653EDA183E06D05\">7.3-3</a>  <br />\n<code class=\"func\">HomomorphismsD\
igraphsRepresentatives</code>  <a href=\"chap7_mj.html#X8653EDA183E06D05\">7.3\
-3</a>  <br />\n<code class=\"func\">InDegreeOfVertex</code>  <a href=\"chap5_\
mj.html#X7C9CD0527CB9E6EF\">5.2-12</a>  <br />\n<code class=\"func\">InDegrees\
</code>  <a href=\"chap5_mj.html#X7ADDFBFD7A365775\">5.2-9</a>  <br />\n<code \
class=\"func\">InDegreeSequence</code>  <a href=\"chap5_mj.html#X7ADDFBFD7A365\
775\">5.2-9</a>  <br />\n<code class=\"func\">InDegreeSet</code>  <a href=\"ch\
ap5_mj.html#X7ADDFBFD7A365775\">5.2-9</a>  <br />\n<code class=\"func\">Induce\
dSubdigraph</code>  <a href=\"chap3_mj.html#X83C51DA182CCEA2F\">3.3-3</a>  <br\
 />\n<code class=\"func\">InNeighbors</code>  <a href=\"chap5_mj.html#X85C7AA5\
A81DA6E11\">5.2-7</a>  <br />\n<code class=\"func\">InNeighborsMutableCopy</co\
de>  <a href=\"chap5_mj.html#X85C7AA5A81DA6E11\">5.2-7</a>  <br />\n<code clas\
s=\"func\">InNeighborsOfVertex</code>  <a href=\"chap5_mj.html#X7C0DA18B8291F3\
02\">5.2-13</a>  <br />\n<code class=\"func\">InNeighbours</code>  <a href=\"c\
hap5_mj.html#X85C7AA5A81DA6E11\">5.2-7</a>  <br />\n<code class=\"func\">InNei\
ghboursMutableCopy</code>  <a href=\"chap5_mj.html#X85C7AA5A81DA6E11\">5.2-7</\
a>  <br />\n<code class=\"func\">InNeighboursOfVertex</code>  <a href=\"chap5_\
mj.html#X7C0DA18B8291F302\">5.2-13</a>  <br />\n<code class=\"func\">IsAcyclic\
Digraph</code>  <a href=\"chap6_mj.html#X7BD08D4478218F77\">6.3-1</a>  <br />\
\n<code class=\"func\">IsAntisymmetricDigraph</code>  <a href=\"chap6_mj.html#\
X7DB1BC2286FC08E2\">6.1-2</a>  <br />\n<code class=\"func\">IsAntiSymmetricDig\
raph</code>  <a href=\"chap6_mj.html#X7DB1BC2286FC08E2\">6.1-2</a>  <br />\n<c\
ode class=\"func\">IsAperiodicDigraph</code>  <a href=\"chap6_mj.html#X80E8839\
67EBE839E\">6.3-7</a>  <br />\n<code class=\"func\">IsBiconnectedDigraph</code\
>  <a href=\"chap6_mj.html#X838FAF2D825977BE\">6.3-4</a>  <br />\n<code class=\
\"func\">IsBipartiteDigraph</code>  <a href=\"chap6_mj.html#X860CFB0C8665F356\
\">6.1-3</a>  <br />\n<code class=\"func\">IsBridgelessDigraph</code>  <a href\
=\"chap6_mj.html#X7D2A6572820B7F24\">6.3-5</a>  <br />\n<code class=\"func\">I\
sCayleyDigraph</code>  <a href=\"chap3_mj.html#X7E749324800B38A5\">3.1-4</a>  \
<br />\n<code class=\"func\">IsChainDigraph</code>  <a href=\"chap6_mj.html#X7\
9563B297C220FB5\">6.3-2</a>  <br />\n<code class=\"func\">IsClique</code>  <a \
href=\"chap8_mj.html#X80670E3E7C36183F\">8.1-1</a>  <br />\n<code class=\"func\
\">IsCompleteBipartiteDigraph</code>  <a href=\"chap6_mj.html#X790A4DBF8533516\
E\">6.1-4</a>  <br />\n<code class=\"func\">IsCompleteDigraph</code>  <a href=\
\"chap6_mj.html#X81F28D4D879FE3B2\">6.1-5</a>  <br />\n<code class=\"func\">Is\
CompleteMultipartiteDigraph</code>  <a href=\"chap6_mj.html#X7FD1A15779FEC341\
\">6.1-6</a>  <br />\n<code class=\"func\">IsConnectedDigraph</code>  <a href=\
\"chap6_mj.html#X83C08C0B7EC1A91F\">6.3-3</a>  <br />\n<code class=\"func\">Is\
CycleDigraph</code>  <a href=\"chap6_mj.html#X7E91320B8028F5D8\">6.3-12</a>  <\
br />\n<code class=\"func\">IsDigraph</code>  <a href=\"chap3_mj.html#X7877ADC\
77F85E630\">3.1-1</a>  <br />\n<code class=\"func\">IsDigraphAutomorphism</cod\
e>  <a href=\"chap7_mj.html#X80183D4A7C51365A\">7.2-20</a>  <br />\n&nbsp;&nbs\
p;&nbsp;&nbsp;for a digraph and a transformation or permutation  <a href=\"cha\
p7_mj.html#X80183D4A7C51365A\">7.2-20</a>  <br />\n<code class=\"func\">IsDigr\
aphColouring</code>  <a href=\"chap7_mj.html#X7F16B8B3825A627A\">7.2-21</a>  <\
br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a transformation  <a href=\"chap7_mj.html#X\
7F16B8B3825A627A\">7.2-21</a>  <br />\n<code class=\"func\">IsDigraphCore</cod\
e>  <a href=\"chap6_mj.html#X78C0B2637985648B\">6.5-1</a>  <br />\n<code class\
=\"func\">IsDigraphEdge</code>, for digraph and list  <a href=\"chap5_mj.html#\
X7BB8ED88835F07B4\">5.1-15</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for digraph an\
d two pos ints  <a href=\"chap5_mj.html#X7BB8ED88835F07B4\">5.1-15</a>  <br />\
\n<code class=\"func\">IsDigraphEmbedding</code>  <a href=\"chap7_mj.html#X7D6\
B5A0887903810\">7.3-11</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for digraphs and a\
 permutation or transformation  <a href=\"chap7_mj.html#X7D6B5A0887903810\">7.\
3-11</a>  <br />\n<code class=\"func\">IsDigraphEndomorphism</code>  <a href=\
\"chap7_mj.html#X80FE9FCB79718A61\">7.3-10</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbs\
p;for digraphs and a permutation or transformation  <a href=\"chap7_mj.html#X8\
0FE9FCB79718A61\">7.3-10</a>  <br />\n<code class=\"func\">IsDigraphEpimorphis\
m</code>  <a href=\"chap7_mj.html#X80FE9FCB79718A61\">7.3-10</a>  <br />\n&nbs\
p;&nbsp;&nbsp;&nbsp;for digraphs and a permutation or transformation  <a href=\
\"chap7_mj.html#X80FE9FCB79718A61\">7.3-10</a>  <br />\n<code class=\"func\">I\
sDigraphHomomorphism</code>  <a href=\"chap7_mj.html#X80FE9FCB79718A61\">7.3-1\
0</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for digraphs and a permutation or trans\
formation  <a href=\"chap7_mj.html#X80FE9FCB79718A61\">7.3-10</a>  <br />\n<co\
de class=\"func\">IsDigraphIsomorphism</code>  <a href=\"chap7_mj.html#X80183D\
4A7C51365A\">7.2-20</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for digraphs and tran\
sformation or permutation  <a href=\"chap7_mj.html#X80183D4A7C51365A\">7.2-20<\
/a>  <br />\n<code class=\"func\">IsDigraphMonomorphism</code>  <a href=\"chap\
7_mj.html#X80FE9FCB79718A61\">7.3-10</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for \
digraphs and a permutation or transformation  <a href=\"chap7_mj.html#X80FE9FC\
B79718A61\">7.3-10</a>  <br />\n<code class=\"func\">IsDigraphWithAdjacencyFun\
ction</code>  <a href=\"chap3_mj.html#X80F1B6D28478D8B9\">3.1-5</a>  <br />\n<\
code class=\"func\">IsDirectedTree</code>  <a href=\"chap6_mj.html#X7B46EA6C7B\
2DF2FB\">6.3-8</a>  <br />\n<code class=\"func\">IsDistanceRegularDigraph</cod\
e>  <a href=\"chap6_mj.html#X7E2082AC7CAE59CD\">6.2-4</a>  <br />\n<code class\
=\"func\">IsEdgeTransitive</code>  <a href=\"chap6_mj.html#X8361CA6E8401FF26\"\
>6.5-2</a>  <br />\n<code class=\"func\">IsEmptyDigraph</code>  <a href=\"chap\
6_mj.html#X7E894CCF7B1C27AE\">6.1-7</a>  <br />\n<code class=\"func\">IsEquiva\
lenceDigraph</code>  <a href=\"chap6_mj.html#X83762C257DED2751\">6.1-8</a>  <b\
r />\n<code class=\"func\">IsEulerianDigraph</code>  <a href=\"chap6_mj.html#X\
79DFBB198525544E\">6.3-10</a>  <br />\n<code class=\"func\">IsFunctionalDigrap\
h</code>  <a href=\"chap6_mj.html#X7E8F37E585DAED52\">6.1-9</a>  <br />\n<code\
 class=\"func\">IsHamiltonianDigraph</code>  <a href=\"chap6_mj.html#X79EFEBC3\
7C2D262D\">6.3-11</a>  <br />\n<code class=\"func\">IsImmutableDigraph</code> \
 <a href=\"chap3_mj.html#X7CAFAA89804F80BD\">3.1-3</a>  <br />\n<code class=\"\
func\">IsIndependentSet</code>  <a href=\"chap8_mj.html#X790733B67B0BC894\">8.\
2-1</a>  <br />\n<code class=\"func\">IsInRegularDigraph</code>  <a href=\"cha\
p6_mj.html#X7A3F78B37E31D9E1\">6.2-1</a>  <br />\n<code class=\"func\">IsIsomo\
rphicDigraph</code>, for digraphs  <a href=\"chap7_mj.html#X7B4F24B283C9EE28\"\
>7.2-15</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for digraphs and homogeneous list\
s  <a href=\"chap7_mj.html#X7D4A1FA8868DA930\">7.2-16</a>  <br />\n<code class\
=\"func\">IsJoinSemilatticeDigraph</code>  <a href=\"chap6_mj.html#X78D3E17B7F\
737516\">6.1-17</a>  <br />\n<code class=\"func\">IsLatticeDigraph</code>  <a \
href=\"chap6_mj.html#X78D3E17B7F737516\">6.1-17</a>  <br />\n<code class=\"fun\
c\">IsMatching</code>  <a href=\"chap5_mj.html#X848FED0B7B4ACD1F\">5.1-16</a> \
 <br />\n<code class=\"func\">IsMaximalClique</code>  <a href=\"chap8_mj.html#\
X80670E3E7C36183F\">8.1-1</a>  <br />\n<code class=\"func\">IsMaximalIndepende\
ntSet</code>  <a href=\"chap8_mj.html#X790733B67B0BC894\">8.2-1</a>  <br />\n<\
code class=\"func\">IsMaximalMatching</code>  <a href=\"chap5_mj.html#X848FED0\
B7B4ACD1F\">5.1-16</a>  <br />\n<code class=\"func\">IsMaximumMatching</code> \
 <a href=\"chap5_mj.html#X848FED0B7B4ACD1F\">5.1-16</a>  <br />\n<code class=\
\"func\">IsMeetSemilatticeDigraph</code>  <a href=\"chap6_mj.html#X78D3E17B7F7\
37516\">6.1-17</a>  <br />\n<code class=\"func\">IsMultiDigraph</code>  <a hre\
f=\"chap6_mj.html#X7BB84CFC7E8B2B26\">6.1-10</a>  <br />\n<code class=\"func\"\
>IsMutableDigraph</code>  <a href=\"chap3_mj.html#X7D7EDF83820ED6F5\">3.1-2</a\
>  <br />\n<code class=\"func\">IsNullDigraph</code>  <a href=\"chap6_mj.html#\
X7E894CCF7B1C27AE\">6.1-7</a>  <br />\n<code class=\"func\">IsomorphismDigraph\
s</code>, for digraphs  <a href=\"chap7_mj.html#X8219FE6C839D9457\">7.2-17</a>\
  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for digraphs and homogeneous lists  <a href=\
\"chap7_mj.html#X7ED93C0F86D9D34F\">7.2-18</a>  <br />\n<code class=\"func\">I\
sOuterPlanarDigraph</code>  <a href=\"chap6_mj.html#X8251E8B187E7F059\">6.4-2<\
/a>  <br />\n<code class=\"func\">IsOutRegularDigraph</code>  <a href=\"chap6_\
mj.html#X7F0A806E7BCB413C\">6.2-2</a>  <br />\n<code class=\"func\">IsPartialO\
rderDigraph</code>  <a href=\"chap6_mj.html#X82BAE6D37D49A145\">6.1-16</a>  <b\
r />\n<code class=\"func\">IsPerfectMatching</code>  <a href=\"chap5_mj.html#X\
848FED0B7B4ACD1F\">5.1-16</a>  <br />\n<code class=\"func\">IsPlanarDigraph</c\
ode>  <a href=\"chap6_mj.html#X8606D415858C40AA\">6.4-1</a>  <br />\n<code cla\
ss=\"func\">IsPreorderDigraph</code>  <a href=\"chap6_mj.html#X8617726C7829F79\
6\">6.1-15</a>  <br />\n<code class=\"func\">IsQuasiorderDigraph</code>  <a hr\
ef=\"chap6_mj.html#X8617726C7829F796\">6.1-15</a>  <br />\n<code class=\"func\
\">IsReachable</code>  <a href=\"chap5_mj.html#X7FBAB09E7C0BE5CF\">5.3-19</a> \
 <br />\n<code class=\"func\">IsReflexiveDigraph</code>  <a href=\"chap6_mj.ht\
ml#X8462D8E2792B23F6\">6.1-11</a>  <br />\n<code class=\"func\">IsRegularDigra\
ph</code>  <a href=\"chap6_mj.html#X7AF9DB1E7DB12306\">6.2-3</a>  <br />\n<cod\
e class=\"func\">IsStronglyConnectedDigraph</code>  <a href=\"chap6_mj.html#X7\
B37B9467C68C208\">6.3-6</a>  <br />\n<code class=\"func\">IsSubdigraph</code> \
 <a href=\"chap4_mj.html#X829B911D7EFD2D85\">4.1-1</a>  <br />\n<code class=\"\
func\">IsSymmetricDigraph</code>  <a href=\"chap6_mj.html#X81B3EA7887219860\">\
6.1-12</a>  <br />\n<code class=\"func\">IsTournament</code>  <a href=\"chap6_\
mj.html#X7DD8D1A185EBE865\">6.1-13</a>  <br />\n<code class=\"func\">IsTransit\
iveDigraph</code>  <a href=\"chap6_mj.html#X7F0835667F29F0C0\">6.1-14</a>  <br\
 />\n<code class=\"func\">IsUndirectedForest</code>  <a href=\"chap6_mj.html#X\
80FC20FA7AC4BC2A\">6.3-9</a>  <br />\n<code class=\"func\">IsUndirectedSpannin\
gForest</code>  <a href=\"chap4_mj.html#X833C3299787E2309\">4.1-2</a>  <br />\
\n<code class=\"func\">IsUndirectedSpanningTree</code>  <a href=\"chap4_mj.htm\
l#X833C3299787E2309\">4.1-2</a>  <br />\n<code class=\"func\">IsUndirectedTree\
</code>  <a href=\"chap6_mj.html#X80FC20FA7AC4BC2A\">6.3-9</a>  <br />\n<code \
class=\"func\">IsVertexTransitive</code>  <a href=\"chap6_mj.html#X7B26E4447A1\
611E9\">6.5-3</a>  <br />\n<code class=\"func\">IteratorFromDigraphFile</code>\
  <a href=\"chap9_mj.html#X86D531B287733561\">9.2-7</a>  <br />\n<code class=\
\"func\">IteratorOfPaths</code>  <a href=\"chap5_mj.html#X7C0416FE7A69CA2C\">5\
.3-23</a>  <br />\n<code class=\"func\">JohnsonDigraph</code>  <a href=\"chap3\
_mj.html#X80ED9CE785819607\">3.5-7</a>  <br />\n<code class=\"func\">Kuratowsk\
iOuterPlanarSubdigraph</code>  <a href=\"chap5_mj.html#X78E8F09A8286501B\">5.6\
-2</a>  <br />\n<code class=\"func\">KuratowskiPlanarSubdigraph</code>  <a hre\
f=\"chap5_mj.html#X7DC478637E8C190D\">5.6-1</a>  <br />\n<code class=\"func\">\
LaplacianMatrix</code>  <a href=\"chap5_mj.html#X865390B08331936B\">5.2-17</a>\
  <br />\n<code class=\"func\">LineDigraph</code>  <a href=\"chap3_mj.html#X85\
95BF937B749F22\">3.3-34</a>  <br />\n<code class=\"func\">LineUndirectedDigrap\
h</code>  <a href=\"chap3_mj.html#X8364C6F17A1680CB\">3.3-35</a>  <br />\n<cod\
e class=\"func\">MaximalAntiSymmetricSubdigraph</code>  <a href=\"chap3_mj.htm\
l#X79BA6A66846D5A95\">3.3-6</a>  <br />\n<code class=\"func\">MaximalAntiSymme\
tricSubdigraphAttr</code>  <a href=\"chap3_mj.html#X79BA6A66846D5A95\">3.3-6</\
a>  <br />\n<code class=\"func\">MaximalSymmetricSubdigraph</code>  <a href=\"\
chap3_mj.html#X829E3EAC7C4B3B1E\">3.3-5</a>  <br />\n<code class=\"func\">Maxi\
malSymmetricSubdigraphAttr</code>  <a href=\"chap3_mj.html#X829E3EAC7C4B3B1E\"\
>3.3-5</a>  <br />\n<code class=\"func\">MaximalSymmetricSubdigraphWithoutLoop\
s</code>  <a href=\"chap3_mj.html#X829E3EAC7C4B3B1E\">3.3-5</a>  <br />\n<code\
 class=\"func\">MaximalSymmetricSubdigraphWithoutLoopsAttr</code>  <a href=\"c\
hap3_mj.html#X829E3EAC7C4B3B1E\">3.3-5</a>  <br />\n<code class=\"func\">Monom\
orphismsDigraphs</code>  <a href=\"chap7_mj.html#X84B4BDB984C2A9A8\">7.3-5</a>\
  <br />\n<code class=\"func\">MonomorphismsDigraphsRepresentatives</code>  <a\
 href=\"chap7_mj.html#X84B4BDB984C2A9A8\">7.3-5</a>  <br />\n<code class=\"fun\
c\">NautyAutomorphismGroup</code>  <a href=\"chap7_mj.html#X857758B18144C0CD\"\
>7.2-4</a>  <br />\n<code class=\"func\">NautyCanonicalDigraph</code>  <a href\
=\"chap7_mj.html#X877B1D377EC197D7\">7.2-9</a>  <br />\n<code class=\"func\">N\
autyCanonicalLabelling</code>, for a digraph  <a href=\"chap7_mj.html#X7D676FE\
67A6684FF\">7.2-7</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph and a lis\
t  <a href=\"chap7_mj.html#X87DA265D803DB337\">7.2-8</a>  <br />\n<code class=\
\"func\">NrSpanningTrees</code>  <a href=\"chap5_mj.html#X82F30D5681466BC6\">5\
.3-30</a>  <br />\n<code class=\"func\">NullDigraph</code>  <a href=\"chap3_mj\
.html#X80DAE31A79FEFD40\">3.5-6</a>  <br />\n<code class=\"func\">OnDigraphs</\
code>, for a digraph and a perm  <a href=\"chap7_mj.html#X808972017C486F1F\">7\
.1-1</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph and a transformation  \
<a href=\"chap7_mj.html#X808972017C486F1F\">7.1-1</a>  <br />\n<code class=\"f\
unc\">OnMultiDigraphs</code>  <a href=\"chap7_mj.html#X7AFBA7608498F9CE\">7.1-\
2</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph, perm, and perm  <a href=\
\"chap7_mj.html#X7AFBA7608498F9CE\">7.1-2</a>  <br />\n<code class=\"func\">Ou\
tDegreeOfVertex</code>  <a href=\"chap5_mj.html#X7A09EB648070276D\">5.2-10</a>\
  <br />\n<code class=\"func\">OutDegrees</code>  <a href=\"chap5_mj.html#X7F5\
ACE807D1BC2E2\">5.2-8</a>  <br />\n<code class=\"func\">OutDegreeSequence</cod\
e>  <a href=\"chap5_mj.html#X7F5ACE807D1BC2E2\">5.2-8</a>  <br />\n<code class\
=\"func\">OutDegreeSet</code>  <a href=\"chap5_mj.html#X7F5ACE807D1BC2E2\">5.2\
-8</a>  <br />\n<code class=\"func\">OuterPlanarEmbedding</code>  <a href=\"ch\
ap5_mj.html#X85DFB8C18088711F\">5.6-4</a>  <br />\n<code class=\"func\">OutNei\
ghbors</code>  <a href=\"chap5_mj.html#X7E9880767AE68E00\">5.2-6</a>  <br />\n\
<code class=\"func\">OutNeighborsMutableCopy</code>  <a href=\"chap5_mj.html#X\
7E9880767AE68E00\">5.2-6</a>  <br />\n<code class=\"func\">OutNeighborsOfVerte\
x</code>  <a href=\"chap5_mj.html#X83315B0186850806\">5.2-11</a>  <br />\n<cod\
e class=\"func\">OutNeighbours</code>  <a href=\"chap5_mj.html#X7E9880767AE68E\
00\">5.2-6</a>  <br />\n<code class=\"func\">OutNeighboursMutableCopy</code>  \
<a href=\"chap5_mj.html#X7E9880767AE68E00\">5.2-6</a>  <br />\n<code class=\"f\
unc\">OutNeighboursOfVertex</code>  <a href=\"chap5_mj.html#X83315B0186850806\
\">5.2-11</a>  <br />\n<code class=\"func\">PartialOrderDigraphJoinOfVertices<\
/code>  <a href=\"chap5_mj.html#X7DDB33B686B3A2C6\">5.2-15</a>  <br />\n<code \
class=\"func\">PartialOrderDigraphMeetOfVertices</code>  <a href=\"chap5_mj.ht\
ml#X7DDB33B686B3A2C6\">5.2-15</a>  <br />\n<code class=\"func\">PetersenGraph<\
/code>  <a href=\"chap3_mj.html#X823F43217A6C375D\">3.5-8</a>  <br />\n<code c\
lass=\"func\">PlainTextString</code>  <a href=\"chap9_mj.html#X8540FC21796A793\
F\">9.2-12</a>  <br />\n<code class=\"func\">PlanarEmbedding</code>  <a href=\
\"chap5_mj.html#X84E3947E7D39BA64\">5.6-3</a>  <br />\n<code class=\"func\">Pr\
intString</code>  <a href=\"chap9_mj.html#X81FB5BE27903EC32\">9.2-1</a>  <br /\
>\n<code class=\"func\">QuotientDigraph</code>  <a href=\"chap3_mj.html#X7D1D2\
6D27F5B56C2\">3.3-8</a>  <br />\n<code class=\"func\">RandomDigraph</code>  <a\
 href=\"chap3_mj.html#X86CF9F66788B2A24\">3.4-1</a>  <br />\n<code class=\"fun\
c\">RandomLattice</code>  <a href=\"chap3_mj.html#X7A023E4787682475\">3.4-4</a\
>  <br />\n<code class=\"func\">RandomMultiDigraph</code>  <a href=\"chap3_mj.\
html#X78FE275E7E77D56F\">3.4-2</a>  <br />\n<code class=\"func\">RandomTournam\
ent</code>  <a href=\"chap3_mj.html#X7D36B5E57F055051\">3.4-3</a>  <br />\n<co\
de class=\"func\">ReadDigraphs</code>  <a href=\"chap9_mj.html#X7E8142007ED0CB\
9F\">9.2-5</a>  <br />\n<code class=\"func\">ReadDIMACSDigraph</code>  <a href\
=\"chap9_mj.html#X804FDF6A7ED64049\">9.2-14</a>  <br />\n<code class=\"func\">\
ReadPlainTextDigraph</code>  <a href=\"chap9_mj.html#X81BD23697857B244\">9.2-1\
3</a>  <br />\n<code class=\"func\">ReducedDigraph</code>  <a href=\"chap3_mj.\
html#X7CAF093B85A93D2F\">3.3-4</a>  <br />\n<code class=\"func\">ReducedDigrap\
hAttr</code>  <a href=\"chap3_mj.html#X7CAF093B85A93D2F\">3.3-4</a>  <br />\n<\
code class=\"func\">RepresentativeOutNeighbours</code>  <a href=\"chap7_mj.htm\
l#X7E1C806D81DFE15E\">7.2-19</a>  <br />\n<code class=\"func\">SemigroupOfCayl\
eyDigraph</code>  <a href=\"chap5_mj.html#X7A000B1D7CCF7093\">5.4-1</a>  <br /\
>\n<code class=\"func\">SetDigraphEdgeLabel</code>  <a href=\"chap5_mj.html#X7\
9FAEACC7F438C2F\">5.1-11</a>  <br />\n<code class=\"func\">SetDigraphEdgeLabel\
s</code>, for a digraph and a function  <a href=\"chap5_mj.html#X7C24851087D4A\
8FB\">5.1-12</a>  <br />\n&nbsp;&nbsp;&nbsp;&nbsp;for a digraph and a list of \
lists  <a href=\"chap5_mj.html#X7C24851087D4A8FB\">5.1-12</a>  <br />\n<code c\
lass=\"func\">SetDigraphVertexLabel</code>  <a href=\"chap5_mj.html#X7CA91E4B7\
904F793\">5.1-9</a>  <br />\n<code class=\"func\">SetDigraphVertexLabels</code\
>  <a href=\"chap5_mj.html#X7E51F2FE87140B32\">5.1-10</a>  <br />\n<code class\
=\"func\">Sparse6String</code>  <a href=\"chap9_mj.html#X782A052979EA2376\">9.\
2-3</a>  <br />\n<code class=\"func\">Splash</code>  <a href=\"chap9_mj.html#X\
83B3318784E78415\">9.1-1</a>  <br />\n<code class=\"func\">String</code>  <a h\
ref=\"chap9_mj.html#X81FB5BE27903EC32\">9.2-1</a>  <br />\n<code class=\"func\
\">StrongOrientation</code>  <a href=\"chap5_mj.html#X865590147BD1C507\">5.3-1\
6</a>  <br />\n<code class=\"func\">StrongOrientationAttr</code>  <a href=\"ch\
ap5_mj.html#X865590147BD1C507\">5.3-16</a>  <br />\n<code class=\"func\">Subdi\
graphHomeomorphicToK23</code>  <a href=\"chap5_mj.html#X806D2D6B85E0B269\">5.6\
-5</a>  <br />\n<code class=\"func\">SubdigraphHomeomorphicToK33</code>  <a hr\
ef=\"chap5_mj.html#X806D2D6B85E0B269\">5.6-5</a>  <br />\n<code class=\"func\"\
>SubdigraphHomeomorphicToK4</code>  <a href=\"chap5_mj.html#X806D2D6B85E0B269\
\">5.6-5</a>  <br />\n<code class=\"func\">TCodeDecoder</code>  <a href=\"chap\
9_mj.html#X875393338486D77D\">9.2-11</a>  <br />\n<code class=\"func\">Tournam\
entLineDecoder</code>  <a href=\"chap9_mj.html#X7808D99079295C22\">9.2-9</a>  \
<br />\n<code class=\"func\">UndirectedSpanningForest</code>  <a href=\"chap3_\
mj.html#X7DD9766C86D3ED20\">3.3-7</a>  <br />\n<code class=\"func\">Undirected\
SpanningForestAttr</code>  <a href=\"chap3_mj.html#X7DD9766C86D3ED20\">3.3-7</\
a>  <br />\n<code class=\"func\">UndirectedSpanningTree</code>  <a href=\"chap\
3_mj.html#X7DD9766C86D3ED20\">3.3-7</a>  <br />\n<code class=\"func\">Undirect\
edSpanningTreeAttr</code>  <a href=\"chap3_mj.html#X7DD9766C86D3ED20\">3.3-7</\
a>  <br />\n<code class=\"func\">VerticesReachableFrom</code>  <a href=\"chap5\
_mj.html#X7CAE81D97B43DDF3\">5.3-20</a>  <br />\n<code class=\"func\">WriteDig\
raphs</code>  <a href=\"chap9_mj.html#X82A4F0767C9EFC87\">9.2-6</a>  <br />\n<\
code class=\"func\">WriteDIMACSDigraph</code>  <a href=\"chap9_mj.html#X804FDF\
6A7ED64049\">9.2-14</a>  <br />\n<code class=\"func\">WritePlainTextDigraph</c\
ode>  <a href=\"chap9_mj.html#X81BD23697857B244\">9.2-13</a>  <br />\n", 
  input := "<!DOCTYPE Book SYSTEM \"gapdoc.dtd\"\n   [ <!ENTITY Digraphs \"<Pa\
ckage>Digraphs</Package>\">\n     <!ENTITY Grape \"<Alt Not='Text'><URL\n   Te\
xt='Grape'>http://www.maths.qmul.ac.uk/~leonard/grape/</URL></Alt><Alt\n   Onl\
y='Text'><Package>Grape</Package></Alt>\">\n     <!ENTITY bliss \"<Alt Not='Te\
xt'><URL\n   Text='bliss'>http://www.tcs.tkk.fi/Software/bliss/</URL></Alt><Al\
t\n   Only='Text'><Package>bliss</Package></Alt>\">\n     <!ENTITY edge-additi\
on-planarity-suite \"<Alt Not='Text'><URL \n         Text='edge-addition-plana\
rity-suite'>https://github.com/graph-algorithms/edge-addition-planarity-suite<\
/URL></Alt><Alt\n       Only='Text'><Package>edge-addition-planarity-suite</Pa\
ckage></Alt>\">\n     <!ENTITY nauty \"<Alt Not='Text'><URL\n   Text='nauty'>h\
ttp://pallini.di.uniroma1.it/</URL></Alt><Alt\n   Only='Text'><Package>nauty</\
Package></Alt>\">\n     <!ENTITY NautyTracesInterface \"<Alt Not='Text'><URL\n\
   Text='NautyTracesInterface'>https://github.com/gap-packages/NautyTracesInte\
rface</URL></Alt><Alt\n   Only='Text'><Package>NautyTracesInterface</Package><\
/Alt>\">\n     <!ENTITY IO \"<Alt Not='Text'><URL Text='IO'>\n     http://gap-\
packages.github.io/io/\n</URL></Alt><Alt Only='Text'><Package>IO</Package></Al\
t>\">\n     <!ENTITY Orb \"<Alt Not='Text'><URL Text='Orb'>\n     http://http:\
//gap-packages.github.io/orb/</URL>\n     </Alt><Alt Only='Text'><Package>Orb<\
/Package></Alt>\">\n     <!ENTITY datastructures \"<Alt Not='Text'><URL\n     \
  Text='datastructures'>https://github.com/gap-packages/datastructures</URL></\
Alt><Alt\n   Only='Text'><Package>datastructures</Package></Alt>\">\n     <!EN\
TITY VERSION                  \"1.4.0\">\n<!ENTITY GAPVERS                  \"\
4.10.0\">\n<!ENTITY GRAPEVERS                \"4.8.1\">\n<!ENTITY IOVERS      \
             \"4.5.1\">\n<!ENTITY ORBVERS                  \"4.8.2\">\n<!ENTIT\
Y DATASTRUCTURESVERS       \"0.2.5\">\n<!ENTITY NAUTYTRACESINTERFACEVERS \"0.2\
\">\n<!ENTITY ARCHIVENAME    \"digraphs-1.4.0\">\n<!ENTITY COPYRIGHTYEARS \"20\
14-20\">\n\n   ]>\n\n<Book Name=\"digraphs\">\n<TitlePage>\n  <Title>&Digraphs\
;</Title>\n  <Version>Version &VERSION;</Version>\n\n  <Author>Jan De Beule\n \
   <Email>jdebeule@cage.ugent.be</Email>\n    <Homepage>http://homepages.vub.a\
c.be/~jdbeule</Homepage>\n  </Author>\n\n  <Author>Julius Jonu&#353;as\n    <E\
mail>julius.jonusas@tuwien.ac.at</Email>\n    <Homepage>http://julius.jonusas.\
work</Homepage>\n  </Author>\n\n  <Author>James D. Mitchell\n    <Email>jdm3@s\
t-and.ac.uk</Email>\n    <Homepage>https://jdbm.me</Homepage>\n  </Author>\n\n\
  <Author>Michael Torpey\n    <Email>mct25@st-andrews.ac.uk</Email>\n    <Home\
page>https://mtorpey.github.io</Homepage>\n  </Author>\n\n  <Author>Wilf A. Wi\
lson\n    <Email>gap@wilf-wilson.net</Email>\n    <Homepage>http://wilf.me</Ho\
mepage>\n  </Author>\n\n  <Author>Stuart Burrell</Author>\n\n  <Author>Reinis \
Cirpons</Author>\n\n  <Author>Luke Elliott</Author>\n\n  <Author>Max Horn</Aut\
hor>\n\n  <Author>Christopher Jefferson</Author>\n\n  <Author>Markus Pfeiffer<\
/Author>\n\n  <Author>Chris Russell</Author>\n\n  <Author>Finn Smith</Author>\
\n\n  <Author>Murray White</Author>\n\n  <Copyright>&copyright; &COPYRIGHTYEAR\
S; by\n    Jan De Beule, Julius Jonu&#353;as, James D. Mitchell, Michael\n    \
Torpey, Wilf A. Wilson et al.<P/>\n\n    &Digraphs; is free software; you can \
redistribute it and/or modify it\n    under the terms of the <URL Text=\"GNU G\
eneral Public License\">\n    http://www.fsf.org/licenses/gpl.html</URL> as pu\
blished by the Free Software\n    Foundation; either version 3 of the License,\
 or (at your option) any later\n    version.\n  </Copyright>\n\n  <Abstract>\n\
    The &Digraphs; package is a &GAP; package containing methods for graphs,\n\
    digraphs, and multidigraphs.\n  </Abstract>\n\n  <Acknowledgements>\n    W\
e would like to thank Christopher Jefferson for his help in including \n    &b\
liss; in &Digraphs;.\n\n    This package's methods for computing digraph homom\
orphisms are based on work\n    by Max Neunh&#246;ffer, and independently Artu\
r Sch&#228;fer.\n  </Acknowledgements>\n\n</TitlePage>\n\n\n<TableOfContents/>\
\n\n<Body>\n  <Chapter Label=\"The Digraphs package\">\n  <Heading>\n    The &\
Digraphs; package\n  </Heading>\n  <Index Key=\"Digraphs\">&Digraphs; package \
overview</Index>\n\n<Section><Heading>Introduction</Heading>\n\n  This is the \
manual for version &VERSION; of the &Digraphs; package.\n  This package was de\
veloped at the University of St Andrews by:\n  <List>\n    <Item>Jan De Beule,\
</Item>\n    <Item>Julius Jonu&#353;as,</Item>\n    <Item>James D. Mitchell,</\
Item>\n    <Item>Michael C. Torpey, and</Item>\n    <Item>Wilf A. Wilson.</Ite\
m>\n  </List>\n  Additional contributions were made by:\n  <List>\n    <Item>S\
tuart Burrell,</Item>\n    <Item>Reinis Cirpons,</Item>\n    <Item>Luke Elliot\
t,</Item>\n    <Item>Max Horn,</Item>\n    <Item>Christopher Jefferson,</Item>\
\n    <Item>Markus Pfeiffer,</Item>\n    <Item>Chris Russell,</Item>\n    <Ite\
m>Finn Smith, and</Item>\n    <Item>Maria Tsalakou,</Item>\n    <Item>Murray W\
hyte.</Item>\n  </List>\n\n  The &Digraphs; package contains a variety of meth\
ods for efficiently creating\n  and storing mutable and immutable digraphs and\
 computing information about\n    them.  Full explanations of all the function\
s contained in the package are\n    provided below. <P/>\n\n  If the &Grape; p\
ackage is available, it will be loaded automatically.\n  Digraphs created with\
 the &Digraphs; package can be converted to &Grape;\n  graphs with <Ref Oper=\
\"Graph\"/>, and conversely &Grape; graphs can be\n  converted to &Digraphs; o\
bjects with <Ref Oper=\"Digraph\"/>.  &Grape; is not\n  required for &Digraphs\
; to run. <P/>\n\n  The &bliss; tool <Cite Key=\"JK07\"/> is included in this \
package.  It\n  is an open-source tool for computing automorphism groups and c\
anonical forms\n  of graphs, written by Tommi Junttila and Petteri Kaski. Seve\
ral of the methods\n  in the &Digraphs; package rely on &bliss;. If the &Nauty\
TracesInterface;\n  package for GAP is available then it is also possible to u\
se &nauty; <Cite\n    Key=\"MP14\"/> for computing automorphism groups and can\
onical forms\n  in &Digraphs;. See Section \n  <Ref Sect=\"Isomorphisms and ca\
nonical labellings\"/> for more details.  \n  <P/>\n\n  From version 1.0.0 of \
this package, digraphs can be either mutable or immutable.\n  Mutable digraphs\
 can be changed in-place by many of the methods in the\n  package, which avoid\
s unnecessary copying. Immutable digraphs cannot be\n  changed in-place, but t\
heir advantage is that the value of an attribute of\n  an immutable digraph is\
 only ever computed once. Mutable digraphs can be\n  converted into immutable \
digraphs in-place using <Ref Func=\"MakeImmutable\"\n  BookName = \"ref\"/>.  \
One of the motivations for introducing mutable\n  digraphs in version 1.0.0 wa\
s that in practice the authors often wanted\n  to create a digraph and immedia\
tely modify it (removing certain edges,\n  loops, and so on). Before version 1\
.0.0, this involved copying the digraph\n  several times, with each copy being\
 discarded almost immediately.\n  From version 1.0.0, this unnecessary copying\
 can be eliminated by\n  first creating a mutable digraph, then changing it in\
-place, and  finally\n  converting the mutable digraph to an immutable one in-\
place\n  (if desirable).\n\n  <Subsection Label=\"Definitions\"><Heading>Defin\
itions</Heading>\n\n    For the purposes of this package and its documentation\
, the following\n    definitions apply: <P/>\n\n    A <E>digraph</E> <M>E=(E^0\
,E^1,r,s)</M>, also known as a <E>directed\n      graph</E>, consists of a set\
 of vertices <M>E^0</M> and a set of edges\n    <M>E^1</M> together with funct\
ions <M>s, r: E^1 \\to E^0</M>, called the\n    <E>source</E> and <E>range</E>\
, respectively.\n\n    The source and range of an edge is respectively the val\
ues of <M>s, r</M> at\n    that edge.\n\n    An edge is called a <E>loop</E> i\
f its source and range are the same.\n\n    A digraph is called a <E>multidigr\
aph</E> if there exist two or more edges\n    with the same source and the sam\
e range. <P/>\n\n    A <E>directed walk</E> on a digraph is a sequence of alte\
rnating vertices\n    and edges <M>(v_1, e_1, v_2, e_2, ..., e_{n-1}, v_n)</M>\
 such that each edge\n    <M>e_i</M> has source <M>v_i</M> and range <M>v_{i+1\
}</M>. A <E>directed\n      path</E> is a directed walk where no vertex (and h\
ence no edge) is\n    repeated.  A <E>directed circuit</E> is a directed walk \
where <M>v_1 =\n      v_n</M>, and a <E>directed cycle</E> is a directed circu\
it where where no\n    vertex is repeated, except for <M>v_1 = v_n</M>.  <P/>\
\n\n    The <E>length</E> of a directed walk <M>(v_1, e_1, v_2, e_2, ..., e_{n\
-1},\n      v_n)</M> is equal to <M>n-1</M>, the number of edges it contains. \
 A\n    directed walk (or path) <M>(v_1, e_1, v_2, e_2, ..., e_{n-1}, v_n)</M>\
 is\n    sometimes called a directed walk (or path) <E>from vertex <M>v_1</M> \
to\n      vertex <M>v_n</M></E>.  A directed walk of zero length, i.e. a seque\
nce\n    <M>(v)</M> for some vertex <M>v</M>, is called <E>trivial</E>. A triv\
ial\n    directed walk is considered to be both a circuit and a cycle, as is t\
he\n    empty directed walk <M>()</M>. A <E>simple circuit</E> is another name\
 for a\n    non-trivial and non-empty directed cycle.<P/>\n\n  </Subsection>\n\
  </Section>\n</Chapter>\n <!-- intro -->\n  <Chapter Label=\"Installing Digra\
phs\">\n  <Heading>Installing &Digraphs;</Heading>\n\n  <Section Label=\"For t\
hose in a hurry\">\n    <Heading>For those in a hurry</Heading>\n    In this s\
ection we give a brief description of how to start using\n    &Digraphs;.<P/>\
\n\n    It is assumed that you have a working copy of &GAP; with version numbe\
r\n    &GAPVERS; or higher. The most up-to-date version of &GAP; and instructi\
ons\n    on how to install it can be obtained from the main &GAP; webpage\n   \
 <URL>http://www.gap-system.org</URL>.<P/>\n\n    The following is a summary o\
f the steps that should lead to a\n    successful installation of &Digraphs;:\
\n\n    <List>\n\n      <Item>\n        ensure that the &IO; package version &\
IOVERS; or higher is available.\n        &IO; must be compiled before &Digraph\
s; can be loaded.\n      </Item>\n\n      <Item>\n        ensure that the &Orb\
; package version &ORBVERS; or higher is available.\n        &Orb; has better \
performance when compiled, but although compilation is\n        recommended, i\
t is not required to be compiled for &Digraphs; to be\n        loaded.\n      \
</Item>\n\n      <Item> ensure that the &datastructures; package version\n    \
    &DATASTRUCTURESVERS; or higher is available. \n    </Item>\n\n      <Item>\
\n        <B>This step is optional:</B> certain functions in &Digraphs; requir\
e\n        the &Grape; package to be available; see Section\n        <Ref Subs\
ect=\"The Grape package\"/> for full details.  To use these\n        functions\
 make sure\n        that the &Grape; package version &GRAPEVERS; or higher is \
available.\n        If &Grape; is not available, then &Digraphs; can be used a\
s normal with\n        the exception that the functions listed in Subsection\n\
        <Ref Subsect=\"The Grape package\"/> will not work.\n      </Item>\n  \
    \n      <Item>\n        <B>This step is optional:</B> certain functions in\
 &Digraphs; require\n          the &NautyTracesInterface; package to be availa\
ble.\n        <!-- TODO \n          see Section\n        <Ref Subsect=\"The Gr\
ape package\"/> for full details.  -->\n        If you want to make use of the\
se functions, please ensure that the\n        &NautyTracesInterface; package v\
ersion &NAUTYTRACESINTERFACEVERS; or\n        higher is available.  If &NautyT\
racesInterface; is not available,\n        then &Digraphs; can be used as norm\
al with the exception that \n          functions whose names contain <Q>Nauty<\
/Q> will not work.\n      </Item>\n\n      <Item>\n        download the packag\
e archive <F>&ARCHIVENAME;.tar.gz</F> from\n        <URL Text=\"the Digraph pa\
ckage webpage\">http://digraphs.github.io/Digraphs/</URL>.\n      </Item>\n\n \
     <Item>\n        unzip and untar the file, this should create a directory \
called\n        <F>&ARCHIVENAME;</F>.\n      </Item>\n\n      <Item>\n        \
locate the <F>pkg</F> directory of your &GAP; directory, which contains\n     \
   the directories <F>lib</F>, <F>doc</F> and so on. Move the directory\n     \
   <F>&ARCHIVENAME;</F> into the <F>pkg</F> directory.\n      </Item>\n\n     \
 <Item>\n        it is necessary to compile the &Digraphs; package.\n        I\
nside the <F>pkg/&ARCHIVENAME;</F> directory, type\n        <Listing>\n<![CDAT\
A[./configure\nmake]]></Listing>\n        Further information about this step \
can be found in Section\n        <Ref Sect=\"Compiling the kernel module\"/>.\
\n      </Item>\n\n      <Item>\n        start &GAP; in the usual way (i.e. ty\
pe <C>gap</C> at the command line).\n      </Item>\n\n      <Item>\n        ty\
pe <C>LoadPackage(\"digraphs\");</C>\n      </Item>\n    </List>\n\n    If you\
 want to check that the package is working correctly, you\n    should run some\
 of the tests described in Section\n    <Ref Sect=\"Testing your installation\
\"/>.\n  </Section>\n\n  <!--*************************************************\
*********************-->\n  <!--**********************************************\
************************-->\n\n  <Section Label=\"Optional package dependencie\
s\">\n    <Heading>Optional package dependencies</Heading>\n\n    <!--********\
************************************************************-->\n\n    The &Di\
graphs; package is written in &GAP; and C code and requires the\n    &IO; pack\
age.  The &IO; package is used to read and write transformations,\n    partial\
 permutations, and bipartitions to a file. <P/>\n\n    <!--*******************\
*************************************************-->\n\n    <Subsection Label=\
\"The Grape package\">\n      <Heading>The Grape package</Heading>\n\n      Th\
e &Grape; package must be available for the following operations to be\n      \
available:\n\n      <List>\n        <Item><Ref Oper=\"Graph\"/> with a digraph\
 argument</Item>\n        <Item><Ref Attr=\"AsGraph\"/> with a digraph argumen\
t</Item>\n        <Item><Ref Oper=\"Digraph\"/> with a &Grape; graph argument<\
/Item>\n      </List>\n\n      If &Grape; is not available, then &Digraphs; ca\
n be used as normal with\n      the exception that the functions above will no\
t work.\n    </Subsection>\n  </Section>\n\n  <!--****************************\
******************************************-->\n  <!--*************************\
*********************************************-->\n\n  <Section Label=\"Compili\
ng the kernel module\">\n    <Heading>Compiling the kernel module</Heading>\n \
   The &Digraphs; package has a &GAP; kernel component in\n    C which should \
be compiled. This component contains certain low-level\n    functions required\
 by &Digraphs;.\n    <P/>\n\n    It is not possible to use the &Digraphs; pack\
age without compiling it.<P/>\n\n    To compile the kernel component inside th\
e <F>pkg/&ARCHIVENAME;</F>\n    directory, type\n<Listing>\n<![CDATA[\n./confi\
gure\nmake]]></Listing>\n    <P/>\n\n    If you installed the package in anoth\
er 'pkg' directory than the standard 'pkg'\n    directory in your &GAP; instal\
lation, then you have to do two things. Firstly\n    during compilation you ha\
ve to use the option '--with-gaproot=PATH' of the\n    'configure' script wher\
e 'PATH' is a path to the main GAP root directory (if\n    not given the defau\
lt '../..' is assumed).<P/>\n\n    If you installed &GAP; on several architect\
ures, you must execute the\n    configure/make step for each of the architectu\
res. You can either do this\n    immediately after configuring and compiling G\
AP itself on this architecture, or\n    alternatively set the environment\n   \
 variable 'CONFIGNAME' to the name of the configuration you used when compilin\
g\n    GAP before running './configure'.  Note however that your compiler choi\
ce and\n    flags (environment variables 'CC' and 'CFLAGS') need to be chosen \
to match the\n    setup of the original GAP compilation. For example you have \
to specify 32-bit\n    or 64-bit mode correctly!\n  </Section>\n\n  <!--******\
****************************************************************-->\n  <!--***\
*******************************************************************-->\n\n  <S\
ection Label=\"Rebuilding the documentation\">\n    <Heading>Rebuilding the do\
cumentation</Heading>\n    The &Digraphs; package comes complete with pdf, htm\
l, and text versions of\n    the documentation. However, you might find it nec\
essary, at some point, to\n    rebuild the documentation. To rebuild the docum\
entation, please use the\n    function <Ref Func=\"DigraphsMakeDoc\"/>.\n\n   \
 <ManSection>\n  <Func Name=\"DigraphsMakeDoc\" Arg=\"\"/>\n  <Returns>Nothing\
</Returns>\n  <Description>\n    This function should be called with no argume\
nt to compile the &Digraphs;\n    documentation.\n  </Description>\n</ManSecti\
on>\n\n  </Section>\n\n  <!--*************************************************\
*********************-->\n  <!--**********************************************\
************************-->\n\n  <Section Label=\"Testing your installation\">\
\n    <Heading>Testing your installation</Heading>\n\n    In this section we d\
escribe how to test that &Digraphs; is working as\n    intended.  To test that\
 &Digraphs; is installed correctly use\n    <Ref Func=\"DigraphsTestInstall\"/\
> or for more extensive tests use\n    <Ref Func=\"DigraphsTestStandard\"/>. <\
P/>\n\n    If something goes wrong, then please review the instructions in Sec\
tion <Ref\n      Sect=\"For those in a hurry\"/> and ensure that &Digraphs; ha\
s been\n    properly installed.  If you continue having problems, please use t\
he <URL\n      Text=\"issue tracker\">https://github.com/digraphs/Digraphs/iss\
ues</URL>\n    to report the issues you are having.\n\n    <ManSection>\n  <Fu\
nc Name=\"DigraphsTestInstall\" Arg=\"\"/>\n  <Returns><K>true</K> or <K>false\
</K>.</Returns>\n  <Description>\n    This function can be called without argu\
ments to test your installation of\n    &Digraphs; is working correctly. These\
 tests should take no more than a\n    few seconds to complete.  To test more \
comprehensively that\n    &Digraphs; is working correctly, use <Ref Func=\"Dig\
raphsTestStandard\"/>.\n  </Description>\n</ManSection>\n\n    <ManSection>\n \
 <Func Name=\"DigraphsTestStandard\" Arg=\"\"/>\n  <Returns><K>true</K> or <K>\
false</K>.</Returns>\n  <Description>\n    This function can be called without\
 arguments to test all of the methods\n    included in &Digraphs;.\n    These \
tests should take less than a minute to complete. <P/>\n\n    To quickly test \
that &Digraphs; is installed correctly use <Ref\n    Func=\"DigraphsTestInstal\
l\"/>.  For a more thorough test, use <Ref\n    Func=\"DigraphsTestExtreme\"/>\
.\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Func Name=\"Digraph\
sTestExtreme\" Arg=\"\"/>\n  <Returns>Nothing.</Returns>\n  <Description>\n   \
 This function should be called with no argument. It executes a series of\n   \
 very demanding tests, which measure the performance of a variety of\n    func\
tions on large examples.  These tests take a long time to\n    complete, at le\
ast several minutes. <P/>\n\n    For these tests to complete, the digraphs lib\
rary <C>digraphs-lib</C> must\n    be downloaded and placed in the <C>digraphs\
</C> directory in a subfolder\n    named <F>digraphs-lib</F>.\n    This librar\
y can be found on the &Digraphs; website.\n  </Description>\n</ManSection>\n\n\
\n  </Section>\n\n  <!--******************************************************\
****************-->\n  <!--***************************************************\
*******************-->\n\n\n</Chapter>\n <!-- installing -->\n  <Chapter Label\
=\"Creating digraphs\"><Heading>Creating digraphs</Heading>\n\n  In this chapt\
er we describe how to create digraphs.<P/>\n\n  <Section><Heading>Creating dig\
raphs</Heading>\n    <ManSection>\n  <Filt Name=\"IsDigraph\" Type='Category'/\
>\n  <Description>\n    Every  digraph in  &Digraphs;  belongs  to  the  categ\
ory\n    <C>IsDigraph</C>.  Some basic attributes and operations for digraphs\
\n    are <Ref Attr=\"DigraphVertices\"/>, <Ref Attr=\"DigraphEdges\"/>, and\n\
    <Ref Attr=\"OutNeighbours\"/>.\n    </Description>\n</ManSection>\n\n    <\
ManSection>\n  <Filt Name=\"IsMutableDigraph\" Type='Category'/>\n  <Descripti\
on>\n    <C>IsMutableDigraph</C> is a synonym for <Ref Filt=\"IsDigraph\" /> a\
nd <Ref\n    Filt=\"IsMutable\" BookName=\"ref\" />.  A mutable digraph may be\
 changed\n    in-place by methods in the &Digraphs; package, and is not attrib\
ute-storing\n    – see <Ref Filt=\"IsAttributeStoringRep\" BookName=\"ref\" \
/>.\n    <P/>\n\n    A mutable digraph may be converted into an immutable attr\
ibute-storing\n    digraph by calling <Ref Func=\"MakeImmutable\" BookName=\"r\
ef\"/> on the\n    digraph.\n    </Description>\n</ManSection>\n\n    <ManSect\
ion>\n  <Filt Name=\"IsImmutableDigraph\" Type='Category'/>\n  <Description>\n\
    <C>IsImmutableDigraph</C> is a subcategory of <Ref Filt=\"IsDigraph\" />.\
\n    Digraphs that lie in <C>IsImmutableDigraph</C> are immutable and\n    at\
tribute-storing. In particular, they lie in\n    <Ref Filt=\"IsAttributeStorin\
gRep\" BookName=\"ref\" />. <P/>\n\n    A mutable digraph may be converted to \
an immutable\n    digraph that lies in the category <C>IsImmutableDigraph</C> \
by calling\n    <Ref Func=\"MakeImmutable\" BookName=\"ref\"/> on the digraph.\
<P/>\n\n    The operation <Ref Oper=\"DigraphMutableCopy\"/> can be used\n    \
to construct a mutable copy of an immutable digraph. It is however not\n    po\
ssible to convert an immutable digraph into a mutable digraph in-place.\n  </D\
escription>\n</ManSection>\n\n    <ManSection>\n  <Filt Name=\"IsCayleyDigraph\
\" Type='Category'/>\n  <Description>\n    <C>IsCayleyDigraph</C> is a subcate\
gory of <C>IsDigraph</C>. Digraphs that\n    are Cayley digraphs of a group an\
d that are constructed by the operation\n    <Ref Oper=\"CayleyDigraph\"/> are\
 constructed in this category, and are\n    always immutable.\n    </Descripti\
on>\n</ManSection>\n\n    <ManSection>\n  <Filt Name=\"IsDigraphWithAdjacencyF\
unction\" Type='Category'/>\n  <Description>\n    <C>IsDigraphWithAdjacencyFun\
ction</C> is a subcategory of <C>IsDigraph</C>.\n    Digraphs that are <E>crea\
ted</E> using an adjacency function are constructed\n    in this category.\n  \
</Description>\n</ManSection>\n\n    <ManSection>\n  <Var Name=\"DigraphByOutN\
eighboursType\"/>\n  <Fam Name=\"DigraphFamily\"/>\n  <Description>\n    The t\
ype of all digraphs is <C>DigraphByOutNeighboursType</C>.\n    The family of a\
ll digraphs is <C>DigraphFamily</C>.\n  </Description>\n</ManSection>\n\n    <\
ManSection>\n  <Oper Name = \"Digraph\" Arg = \"[filt,] obj[, source, range]\"\
/>\n  <Oper Name = \"Digraph\" Arg = \"[filt,] list, func\" \n    Label = \"fo\
r a list and function\"/>\n  <Oper Name = \"Digraph\" Arg = \"[filt,] G, list,\
 act, adj\"\n    Label = \"for a group, list, function, and function\"/>\n  <R\
eturns>A digraph.</Returns>\n  <Description>\n    If the optional first argume\
nt <A>filt</A> is present, then this should\n    specify the category or repre\
sentation the digraph being created will\n    belong to. For example, if <A>fi\
lt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then the digraph being create\
d will be mutable, if <A>filt</A> is <Ref\n    Filt=\"IsImmutableDigraph\"/>, \
then the digraph will be immutable. \n    If the optional first argument <A>fi\
lt</A> is not present, then <Ref\n    Filt=\"IsImmutableDigraph\"/> is used by\
 default.\n    <List>\n      <Mark>for a list (i.e. an adjacency list)</Mark>\
\n      <Item>\n        if <A>obj</A> is a list of lists of positive integers \
in\n        the range from <C>1</C> to <C>Length(<A>obj</A>)</C>, then this fu\
nction\n        returns the digraph with vertices\n        <M>E ^ 0 = </M><C>[\
1 .. Length(<A>obj</A>)]</C>,\n        and edges corresponding to the entries \
of <A>obj</A>. <P/>\n\n        More precisely, there is an edge from vertex <C\
>i</C> to <C>j</C> if and\n        only if <C>j</C> is in <C><A>obj</A>[i]</C>\
; the source of this edge is\n        <C>i</C> and the range is <C>j</C>. If <\
C>j</C> occurs in\n        <C><A>obj</A>[i]</C> with multiplicity <C>k</C>, th\
en there are <C>k</C>\n        edges from <C>i</C> to <C>j</C>.\n      </Item>\
\n\n      <Mark>for three lists</Mark>\n      <Item>\n        if <A>obj</A> is\
 a duplicate-free list, and <A>source</A> and\n        <A>range</A> are lists \
of equal length consisting of positive integers\n        in the list <C>[1 .. \
Length(<A>obj</A>)]</C>, then this function\n        returns a digraph with ve\
rtices\n        <M>E ^ 0 = </M><C>[1 .. Length(<A>obj</A>)]</C>, and\n        \
<C>Length(<A>source</A>)</C> edges.  For each <C>i</C> in\n        <C>[1 .. Le\
ngth(<A>source</A>)]</C> there exists an edge with source\n        vertex <C>s\
ource[i]</C> and range vertex <C>range[i]</C>.\n        See <Ref Attr=\"Digrap\
hSource\"/> and <Ref Attr=\"DigraphRange\"/>.\n        <P/>\n\n        The ver\
tices of the digraph will be labelled by the elements of\n        <A>obj</A>.\
\n      </Item>\n\n      <Mark>for an integer, and two lists</Mark>\n      <It\
em>\n        if <A>obj</A> is an integer, and <A>source</A> and\n        <A>ra\
nge</A> are lists of equal length consisting of positive integers\n        in \
the list <C>[1 .. <A>obj</A>]</C>, then this function\n        returns a digra\
ph with vertices\n        <M>E ^ 0 = </M><C>[1 .. <A>obj</A>]</C>, and\n      \
  <C>Length(<A>source</A>)</C> edges.  For each <C>i</C> in\n        <C>[1 .. \
Length(<A>source</A>)]</C> there exists an edge with source\n        vertex <C\
>source[i]</C> and range vertex <C>range[i]</C>.\n        See <Ref Attr=\"Digr\
aphSource\"/> and <Ref Attr=\"DigraphRange\"/>.\n      </Item>\n\n      <Mark>\
for a list and a function</Mark>\n      <Item>\n        if <A>list</A> is a li\
st and <A>func</A> is a function taking 2\n        arguments that are elements\
 of <A>list</A>, and <A>func</A> returns\n        <K>true</K> or <K>false</K>,\
 then this operation creates a digraph with\n        vertices <C>[1 .. Length(\
<A>list</A>)]</C> and an edge from vertex\n        <C>i</C> to vertex <C>j</C>\
 if and only if\n        <C><A>func</A>(<A>list</A>[i], <A>list</A>[j])</C> re\
turns <K>true</K>.\n      </Item>\n\n      <Mark>for a group, a list, and two \
functions</Mark>\n      <Item>\n        The arguments will be <A>G, list, act,\
 adj</A>. <P/>\n\n        Let <A>G</A> be a group acting on the objects in <A>\
list</A> via\n        the action <A>act</A>, and let <A>adj</A> be a function \
taking\n        two objects from <A>list</A> as arguments and returning <C>tru\
e</C> or\n        <C>false</C>. The function <A>adj</A> will describe the adja\
cency\n        between objects from <A>list</A>, which is invariant under the \
action of\n        <A>G</A>. This variant of the constructor returns a digraph\
 with\n        vertices the objects of <A>list</A> and directed edges <C>[x, y\
]</C>\n        when <C>f(x, y)</C> is <C>true</C>. <P/>\n\n        The action \
of the group <A>G</A> on the objects in <A>list</A> is stored\n        in the \
attribute <Ref Attr=\"DigraphGroup\"/>, and is used to speed up\n        opera\
tions like <Ref Attr=\"DigraphDiameter\"/>.\n      </Item>\n\n      <Mark>for \
a Grape package graph</Mark>\n      <Item>\n        if <A>obj</A> is a &Grape;\
 package graph (i.e. a record for which the\n        function <C>IsGraph</C> r\
eturns <K>true</K>), then this function returns\n        a digraph isomorphic \
to <A>obj</A>.\n      </Item>\n\n      <Mark>for a binary relation</Mark>\n   \
   <Item>\n        if <A>obj</A> is a binary relation on the points <C>[1 .. n\
]</C> for\n        some posititve integer <M>n</M>, then this function returns\
 the digraph\n        defined by <A>obj</A>. Specifically, this function retur\
ns a digraph\n        which has <M>n</M> vertices, and which has an edge with \
source <C>i</C>\n        and range <C>j</C> if and only if <C>[i,j]</C> is a p\
air in\n        the binary relation <A>obj</A>.\n      </Item>\n    </List>\n\
\n    <Example><![CDATA[\ngap> gr := Digraph([\n> [2, 5, 8, 10], [2, 3, 4, 2, \
5, 6, 8, 9, 10], [1],\n> [3, 5, 7, 8, 10], [2, 5, 7], [3, 6, 7, 9, 10], [1, 4]\
,\n> [1, 5, 9], [1, 2, 7, 8], [3, 5]]);\n<immutable multidigraph with 10 verti\
ces, 38 edges>\ngap> gr := Digraph([\"a\", \"b\", \"c\"], [\"a\"], [\"b\"]);\n\
<immutable digraph with 3 vertices, 1 edge>\ngap> gr := Digraph(5, [1, 2, 2, 4\
, 1, 1], [2, 3, 5, 5, 1, 1]);\n<immutable multidigraph with 5 vertices, 6 edge\
s>\ngap> Petersen := Graph(SymmetricGroup(5), [[1, 2]], OnSets,\n> function(x,\
 y) return Intersection(x, y) = []; end);;\ngap> Digraph(Petersen);\n<immutabl\
e digraph with 10 vertices, 30 edges>\ngap> gr := Digraph([1 .. 10], ReturnTru\
e);\n<immutable digraph with 10 vertices, 100 edges>]]></Example>\n\n      The\
 next example illustrates the uses of the fourth and fifth variants of\n      \
this constructor. The resulting digraph is a strongly regular graph, and\n    \
  it is actually the point graph of the van Lint-Schrijver partial\n      geom\
etry, <Cite Key=\"vLS81\"/>.  The algebraic description\n      is taken from t\
he seminal paper of Calderbank and Kantor <Cite\n        Key=\"CK86\"/>.\n<Exa\
mple><![CDATA[\ngap> f := GF(3 ^ 4);\nGF(3^4)\ngap> gamma := First(f, x -> Ord\
er(x) = 5);\nZ(3^4)^64\ngap> L := Union([Zero(f)], List(Group(gamma)));\n[ 0*Z\
(3), Z(3)^0, Z(3^4)^16, Z(3^4)^32, Z(3^4)^48, Z(3^4)^64 ]\ngap> omega := Union\
(List(L, x -> List(Difference(L, [x]), y -> x - y)));\n[ Z(3)^0, Z(3), Z(3^4)^\
5, Z(3^4)^7, Z(3^4)^8, Z(3^4)^13, Z(3^4)^15, \n  Z(3^4)^16, Z(3^4)^21, Z(3^4)^\
23, Z(3^4)^24, Z(3^4)^29, Z(3^4)^31, \n  Z(3^4)^32, Z(3^4)^37, Z(3^4)^39, Z(3^\
4)^45, Z(3^4)^47, Z(3^4)^48, \n  Z(3^4)^53, Z(3^4)^55, Z(3^4)^56, Z(3^4)^61, Z\
(3^4)^63, Z(3^4)^64, \n  Z(3^4)^69, Z(3^4)^71, Z(3^4)^72, Z(3^4)^77, Z(3^4)^79\
 ]\ngap> adj := function(x, y)\n>   return x - y in omega;\n> end;\nfunction( \
x, y ) ... end\ngap> digraph := Digraph(AsList(f), adj);\n<immutable digraph w\
ith 81 vertices, 2430 edges>\ngap> group := Group(Z(3));;\ngap> act := \\*;\n<\
Operation \"*\">\ngap> digraph := Digraph(group, List(f), act, adj);\n<immutab\
le digraph with 81 vertices, 2430 edges>\n]]></Example>\n  </Description>\n</M\
anSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphByAdjacencyMatrix\" Arg=\
\"[filt, ]list\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If t\
he optional first argument <A>filt</A> is present, then this should\n    speci\
fy the category or representation the digraph being created will\n    belong t\
o. For example, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then \
the digraph being created will be mutable, if <A>filt</A> is <Ref\n    Filt=\"\
IsImmutableDigraph\"/>, then the digraph will be immutable. \n    If the optio\
nal first argument <A>filt</A> is not present, then <Ref\n    Filt=\"IsImmutab\
leDigraph\"/> is used by default.<P/>\n\n    If <A>list</A> is the adjacency m\
atrix of a digraph in the sense of\n    <Ref Attr=\"AdjacencyMatrix\"/>, then \
this operation returns the digraph\n    which is defined by <A>list</A>. <P/>\
\n\n    Alternatively, if <A>list</A> is a square boolean matrix, then this\n \
   operation returns the digraph with <C>Length(</C><A>list</A><C>)</C>\n    v\
ertices which has the edge <C>[i,j]</C> if and only if\n    <A>list</A><C>[i][\
j]</C> is <K>true</K>. <P/>\n\n    <Example><![CDATA[\ngap> DigraphByAdjacency\
Matrix([\n> [0, 1, 0, 2, 0],\n> [1, 1, 1, 0, 1],\n> [0, 3, 2, 1, 1],\n> [0, 0,\
 1, 0, 1],\n> [2, 0, 0, 0, 0]]);\n<immutable multidigraph with 5 vertices, 18 \
edges>\ngap> D := DigraphByAdjacencyMatrix([\n> [true, false, true],\n> [false\
, false, true],\n> [false, true, false]]);\n<immutable digraph with 3 vertices\
, 4 edges>\ngap> OutNeighbours(D);\n[ [ 1, 3 ], [ 3 ], [ 2 ] ]\ngap> D := Digr\
aphByAdjacencyMatrix(IsMutableDigraph, \n> [[true, false, true],\n>  [false, f\
alse, true],\n>  [false, true, false]]);\n<mutable digraph with 3 vertices, 4 \
edges>\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  \
<Oper Name=\"DigraphByEdges\" Arg=\"[filt, ]list[, n]\"/>\n  <Returns>A digrap\
h.</Returns>\n  <Description>\n    If the optional first argument <A>filt</A> \
is present, then this should\n    specify the category or representation the d\
igraph being created will\n    belong to. For example, if <A>filt</A> is <Ref \
Filt=\"IsMutableDigraph\"/>,\n    then the digraph being created will be mutab\
le, if <A>filt</A> is <Ref\n    Filt=\"IsImmutableDigraph\"/>, then the digrap\
h will be immutable. \n    If the optional first argument <A>filt</A> is not p\
resent, then <Ref\n    Filt=\"IsImmutableDigraph\"/> is used by default.<P/>\n\
\n    If <A>list</A> is list of pairs of positive integers, then this function\
\n    returns the digraph with the minimum number of vertices <C>m</C> such th\
at\n    its list equal <A>list</A>.<P/>\n\n    If the optional second argument\
 <A>n</A> is a positive integer with\n    <C><A>n</A> >= m</C> (with <C>m</C> \
defined as above),\n    then this function returns the digraph with <A>n</A> v\
ertices and list\n    <A>list</A>. <P/>\n\n    See <Ref Attr=\"DigraphEdges\"/\
>.\n\n    <Example><![CDATA[\ngap> DigraphByEdges(\n> [[1, 3], [2, 1], [2, 3],\
 [2, 5], [3, 6],\n>  [4, 6], [5, 2], [5, 4], [5, 6], [6, 6]]);\n<immutable dig\
raph with 6 vertices, 10 edges>\ngap> DigraphByEdges(\n> [[1, 3], [2, 1], [2, \
3], [2, 5], [3, 6],\n>  [4, 6], [5, 2], [5, 4], [5, 6], [6, 6]], 12);\n<immuta\
ble digraph with 12 vertices, 10 edges>\ngap> DigraphByEdges(IsMutableDigraph,\
 \n> [[1, 3], [2, 1], [2, 3], [2, 5], [3, 6],\n>  [4, 6], [5, 2], [5, 4], [5, \
6], [6, 6]], 12);\n<mutable digraph with 12 vertices, 10 edges>\n]]></Example>\
\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"EdgeOrbi\
tsDigraph\" Arg=\"G, edges[, n]\"/>\n  <Returns>\n    An immutable digraph.\n \
 </Returns>\n  <Description>\n    If <A>G</A> is a permutation group, <A>edges\
</A> is an edge or list of\n    edges, and <A>n</A> is a non-negative integer \
such that <A>G</A> fixes\n    <C>[1 .. <A>n</A>]</C> setwise, then\n    this o\
peration returns an immutable digraph with <A>n</A> vertices and the union\n  \
  of the orbits of the edges in <A> edges </A> under the action of the\n    pe\
rmutation group <A>G</A>.  An edge in this context is simply a pair of\n    po\
sitive integers.\n    <P/>\n\n    If the optional third argument <A>n</A> is n\
ot present, then the largest\n    moved point of the permutation group <A>G</A\
> is used by default.<P/>\n\n    <Example><![CDATA[\ngap> digraph := EdgeOrbit\
sDigraph(Group((1, 3), (1, 2)(3, 4)),\n>                                 [[1, \
2], [4, 5]], 5);\n<immutable digraph with 5 vertices, 12 edges>\ngap> OutNeigh\
bours(digraph);\n[ [ 2, 4, 5 ], [ 1, 3, 5 ], [ 2, 4, 5 ], [ 1, 3, 5 ], [  ] ]\
\ngap> RepresentativeOutNeighbours(digraph);\n[ [ 2, 4, 5 ], [  ] ]\n]]></Exam\
ple>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"Digr\
aphByInNeighbours\" Arg=\"[filt, ]list\"/>\n  <Oper Name=\"DigraphByInNeighbor\
s\" Arg=\"[filt, ]list\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n\
  If the optional first argument <A>filt</A> is present, then this should\n  s\
pecify the category or representation the digraph being created will\n  belong\
 to. For example, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n  then \
the digraph being created will be mutable, if <A>filt</A> is <Ref\n  Filt=\"Is\
ImmutableDigraph\"/>, then the digraph will be immutable. \n  If the optional \
first argument <A>filt</A> is not present, then <Ref\n  Filt=\"IsImmutableDigr\
aph\"/> is used by default.<P/>\n\n  If <A>list</A> is a list of lists of posi\
tive integers list the range\n  <C>[1 .. Length(<A>list</A>)]</C>, then this f\
unction returns the\n  digraph with vertices <M>E^0=</M><C>[1 .. Length(<A>lis\
t</A>)]</C>, and\n  edges corresponding to the entries of <A>list</A>. More pr\
ecisely, there is an\n  edge with source vertex <C>i</C> and range vertex <C>j\
</C> if <C>i</C> is list\n  <C><A>list</A>[j]</C>. <P/>\n\n  If <C>i</C> occur\
s list <C><A>list</A>[j]</C> with multiplicity <C>k</C>,\n  then there are <C>\
k</C> multiple edges from <C>i</C> to <C>j</C>. <P/>\n\n  See <Ref Attr=\"InNe\
ighbours\"/>.\n\n    <Example><![CDATA[\ngap> D := DigraphByInNeighbours([\n> \
[2, 5, 8, 10], [2, 3, 4, 5, 6, 8, 9, 10],\n> [1], [3, 5, 7, 8, 10], [2, 5, 7],\
 [3, 6, 7, 9, 10], [1, 4],\n> [1, 5, 9], [1, 2, 7, 8], [3, 5]]);\n<immutable d\
igraph with 10 vertices, 37 edges>\ngap> D := DigraphByInNeighbours([[2, 3, 2]\
, [1], [1, 2, 3]]);\n<immutable multidigraph with 3 vertices, 7 edges>\ngap> D\
 := DigraphByInNeighbours(IsMutableDigraph, \n>                               \
[[2, 3, 2], [1], [1, 2, 3]]);\n<mutable multidigraph with 3 vertices, 7 edges>\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper \
Name=\"CayleyDigraph\" Arg=\"G[, gens]\"/>\n  <Returns>An immutable digraph.</\
Returns>\n  <Description>\n    Let <A>G</A> be any group and let <A>gens</A> b\
e a list of elements of\n    <A>G</A>. This operation returns an immutable dig\
raph that corresponds to\n    the Cayley graph of <A>G</A> with respect\n    <\
A>gens</A>. The vertices are the elements of <A>G</A>. There exists an edge\n \
   from the vertex <C>u</C> to the vertex <C>v</C> if and only if there exists\
\n    a generator <C>g</C> in <A>gens</A> such that <C>x * g = y</C>. <P/>\n\n\
    <!-- FIXME What is the correspondence between vertices and elements? -->\n\
\n    If the optional second argument <A>gens</A> is not present, then the\n  \
  generators of <A>G</A> are used by default.<P/>\n\n    The digraph created b\
y this operation belongs to the category <Ref\n      Filt=\"IsCayleyDigraph\"/\
>, the group <A>G</A> can be recovered from the\n    digraph using <Ref Attr=\
\"GroupOfCayleyDigraph\"/>, and the generators\n    <A>gens</A> can be obtaine\
d using <Ref Attr=\"GeneratorsOfCayleyDigraph\"/>.<P/>\n\n    Note that this f\
unction can only return an immutable digraph.\n\n    <Example><![CDATA[\ngap> \
G := DihedralGroup(8);\n<pc group of size 8 with 3 generators>\ngap> CayleyDig\
raph(G);\n<immutable digraph with 8 vertices, 24 edges>\ngap> G := DihedralGro\
up(IsPermGroup, 8);\nGroup([ (1,2,3,4), (2,4) ])\ngap> CayleyDigraph(G);\n<imm\
utable digraph with 8 vertices, 16 edges>\ngap> digraph := CayleyDigraph(G, [(\
)]);\n<immutable digraph with 8 vertices, 8 edges>\ngap> GroupOfCayleyDigraph(\
digraph) = G;\ntrue\ngap> GeneratorsOfCayleyDigraph(digraph);\n[ () ]]]></Exam\
ple>\n  </Description>\n</ManSection>\n\n  </Section>\n\n  <Section><Heading>C\
hanging representations</Heading>\n    <ManSection>\n  <Oper Name=\"AsBinaryRe\
lation\" Arg=\"digraph\"/>\n  <Returns>A binary relation.</Returns>\n  <Descri\
ption>\n    If <A>digraph</A> is a digraph with a positive number of vertices\
\n    <M>n</M>, and no multiple edges, then this operation returns a binary\n \
   relation on the points <C>[1..n]</C>.\n    The pair <C>[i,j]</C> is in the \
binary relation if and only if\n    <C>[i,j]</C> is an edge in <A>digraph</A>.\
\n    <P/>\n<Example><![CDATA[\ngap> D := Digraph([[3, 2], [1, 2], [2], [3, 4]\
]);\n<immutable digraph with 4 vertices, 7 edges>\ngap> AsBinaryRelation(D);\n\
Binary Relation on 4 points\n]]></Example>\n  </Description>\n</ManSection>\n\
\n    <ManSection>\n  <Oper Name=\"AsDigraph\" Arg=\"[filt, ]trans[, n]\"/>\n \
 <Returns>A digraph, or <K>fail</K>.</Returns>\n  <Description>\n    If the op\
tional first argument <A>filt</A> is present, then this should\n    specify th\
e category or representation the digraph being created will\n    belong to. Fo\
r example, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then the d\
igraph being created will be mutable, if <A>filt</A> is <Ref\n    Filt=\"IsImm\
utableDigraph\"/>, then the digraph will be immutable. \n    If the optional f\
irst argument <A>filt</A> is not present, then <Ref\n    Filt=\"IsImmutableDig\
raph\"/> is used by default.<P/>\n\n    If <A>trans</A> is a transformation, a\
nd <A>n</A> is a non-negative integer\n    such that the restriction of <A>tra\
ns</A> to <C>[1 .. <A>n</A>]</C> defines\n    a transformation of <C>[1 .. <A>\
n</A>]</C>, then <C>AsDigraph</C>\n    returns the functional digraph with <A>\
n</A> vertices defined by\n    <A>trans</A>. See <Ref Prop=\"IsFunctionalDigra\
ph\"/>.\n    <P/>\n\n    Specifically, the digraph returned by <C>AsDigraph</C\
> has  <A>n</A> edges:\n    for each vertex <C>x</C> in <C>[1 .. <A>n</A>]</C>\
, there is a unique edge\n    with source <C>x</C>; this edge has range <C>x^<\
A>trans</A></C>.\n    <P/>\n\n    If the optional second argument <A>n</A> is \
not supplied, then the degree of\n    the transformation <A>trans</A> is used \
by default.  If the restriction of\n    <A>trans</A> to <C>[1 .. <A>n</A>]</C>\
 does not define a transformation of\n    <C>[1 .. <A>n</A>]</C>, then <C>AsDi\
graph(<A>trans</A>, <A>n</A>)</C>\n    returns <K>fail</K>.\n\n    <Example><!\
[CDATA[\ngap> f := Transformation([4, 3, 3, 1, 7, 9, 10, 4, 2, 3]);\nTransform\
ation( [ 4, 3, 3, 1, 7, 9, 10, 4, 2, 3 ] )\ngap> AsDigraph(f);\n<immutable fun\
ctional digraph with 10 vertices>\ngap> AsDigraph(f, 4);\n<immutable functiona\
l digraph with 4 vertices>\ngap> AsDigraph(f, 5);\nfail\ngap> b := BinaryRelat\
ionOnPoints(\n> [[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\nBinary Relation\
 on 5 points\ngap> D := AsDigraph(b);\n<immutable digraph with 5 vertices, 11 \
edges>\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  \
<Oper Name=\"Graph\" Arg=\"digraph\"/>\n  <Returns>A &Grape; package graph.</R\
eturns>\n  <Description>\n    If <A>digraph</A> is a mutable or immutable digr\
aph without multiple edges, then this operation\n    returns a &Grape; package\
 graph that is isomorphic to <A>digraph</A>. <P/>\n\n    If <A>digraph</A> is \
a multidigraph, then since &Grape; does not support\n    multiple edges, the m\
ultiple edges will be reduced to a single edge in the\n    result. In order wo\
rds, for a multidigraph this operation will return the\n    same as <C>Graph(D\
igraphRemoveAllMultipleEdges(</C><A>digraph</A><C>))</C>.\n\n    <Example><![C\
DATA[\ngap> Petersen := Graph(SymmetricGroup(5), [[1, 2]], OnSets,\n> function\
(x, y) return Intersection(x, y) = []; end);;\ngap> Display(Petersen);\nrec(\n\
  adjacencies := [ [ 3, 5, 8 ] ],\n  group := \n   Group( [ ( 1, 2, 3, 5, 7)( \
4, 6, 8, 9,10), ( 2, 4)( 6, 9)( 7,10) \n     ] ),\n  isGraph := true,\n  names\
 := [ [ 1, 2 ], [ 2, 3 ], [ 3, 4 ], [ 1, 3 ], [ 4, 5 ], \n      [ 2, 4 ], [ 1,\
 5 ], [ 3, 5 ], [ 1, 4 ], [ 2, 5 ] ],\n  order := 10,\n  representatives := [ \
1 ],\n  schreierVector := [ -1, 1, 1, 2, 1, 1, 1, 1, 2, 2 ] )\ngap> Digraph(Pe\
tersen);\n<immutable digraph with 10 vertices, 30 edges>\ngap> Graph(last) = P\
etersen;\ntrue]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSectio\
n>\n  <Attr Name=\"AsGraph\" Arg=\"digraph\"/>\n  <Returns>A &Grape; package g\
raph.</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph, then thi\
s method returns the same as\n    <Ref Oper=\"Graph\"/>, except that if <A>dig\
raph</A> is immutable, then the\n    result will be stored as a mutable attrib\
ute of <A>digraph</A>.\n    In this latter case, when <C>AsGraph(</C><A>digrap\
h</A><C>)</C> is called\n    subsequently, the same &GAP; object will be retur\
ned as before.\n\n    <Example><![CDATA[\ngap> D := Digraph([[1, 2], [3], []])\
;\n<immutable digraph with 3 vertices, 3 edges>\ngap> G := AsGraph(D);\nrec( a\
djacencies := [ [ 1, 2 ], [ 3 ], [  ] ], group := Group(()), \n  isGraph := tr\
ue, names := [ 1 .. 3 ], order := 3, \n  representatives := [ 1, 2, 3 ], schre\
ierVector := [ -1, -2, -3 ] )\n]]></Example>\n  </Description>\n</ManSection>\
\n\n    <ManSection>\n  <Attr Name=\"AsTransformation\" Arg=\"digraph\"/>\n  <\
Returns>A transformation, or <K>fail</K></Returns>\n  <Description>\n    If <A\
>digraph</A> is a functional digraph, then <C>AsTransformation</C>\n    return\
s the transformation which is defined by <A>digraph</A>.  See <Ref\n      Prop\
=\"IsFunctionalDigraph\"/>. Otherwise,\n    <C>AsTransformation(</C><A>digraph\
</A><C>)</C> returns <K>fail</K>.  <P/>\n\n    If <A>digraph</A> is a function\
al digraph with <M>n</M> vertices, then\n    <C>AsTransformation(</C><A>digrap\
h</A><C>)</C> will return the\n    transformation <C>f</C> of degree at most <\
M>n</M> where for each <M>1\n      \\leq i \\leq n</M>, <C>i ^ f</C> is equal \
to the unique out-neighbour of\n    vertex <C>i</C> in <A>digraph</A>.\n\n    \
<Example><![CDATA[\ngap> D := Digraph([[1], [3], [2]]);\n<immutable digraph wi\
th 3 vertices, 3 edges>\ngap> AsTransformation(D);\nTransformation( [ 1, 3, 2 \
] )\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 ver\
tices, 3 edges>\ngap> AsTransformation(D);\nTransformation( [ 2, 3, 1 ] )\ngap\
> AsPermutation(last);\n(1,2,3)\ngap> D := Digraph([[2, 3], [], []]);\n<immuta\
ble digraph with 3 vertices, 2 edges>\ngap> AsTransformation(D);\nfail]]></Exa\
mple>\n  </Description>\n</ManSection>\n\n  </Section>\n\n  <Section><Heading>\
New digraphs from old</Heading>\n    <ManSection>\n  <Oper Name=\"DigraphImmut\
ableCopy\" Arg=\"digraph\"/>\n  <Oper Name=\"DigraphMutableCopy\" Arg=\"digrap\
h\"/>\n  <Oper Name=\"DigraphCopySameMutability\" Arg=\"digraph\"/>\n  <Oper N\
ame=\"DigraphCopy\" Arg=\"digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Des\
cription>\n    Each of these operations returns a new copy of <A>digraph</A>,\
\n    of the appropriate mutability, retaining none of the attributes or\n    \
properties of <A>digraph</A>. <P/>\n\n    <C>DigraphCopy</C> is a synonym for \
<C>DigraphCopySameMutability</C>.\n<Example><![CDATA[\ngap> D := CycleDigraph(\
10);\n<immutable cycle digraph with 10 vertices>\ngap> DigraphCopy(D) = D;\ntr\
ue\ngap> IsIdenticalObj(DigraphCopy(D), D);\nfalse\ngap> DigraphMutableCopy(D)\
;\n<mutable digraph with 10 vertices, 10 edges>\n]]></Example>\n  </Descriptio\
n>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphImmutableCopyIfIm\
mutable\" Arg=\"digraph\"/>\n  <Oper Name=\"DigraphImmutableCopyIfMutable\" Ar\
g=\"digraph\"/>\n  <Oper Name=\"DigraphMutableCopyIfMutable\" Arg=\"digraph\"/\
>\n  <Oper Name=\"DigraphMutableCopyIfImmutable\" Arg=\"digraph\"/>\n  <Return\
s>A digraph.</Returns>\n  <Description>\n    Each of these operations returns \
either the original argument\n    <A>digraph</A>, or a new copy of <A>digraph<\
/A> of the appropriate\n    mutability, according to the mutability of <A>digr\
aph</A>.\n<Example><![CDATA[\ngap> C := CycleDigraph(10);\n<immutable cycle di\
graph with 10 vertices>\ngap> D := DigraphImmutableCopyIfImmutable(C);\n<immut\
able digraph with 10 vertices, 10 edges>\ngap> IsIdenticalObj(C, D);\nfalse\ng\
ap> C = D;\ntrue\ngap> D := DigraphImmutableCopyIfMutable(C);\n<immutable cycl\
e digraph with 10 vertices>\ngap> IsIdenticalObj(C, D);\ntrue\ngap> C = D;\ntr\
ue\ngap> D := DigraphMutableCopyIfMutable(C);\n<immutable cycle digraph with 1\
0 vertices>\ngap> IsMutableDigraph(D);\nfalse\ngap> D := DigraphMutableCopyIfI\
mmutable(C);\n<mutable digraph with 10 vertices, 10 edges>\ngap> IsMutableDigr\
aph(D);\ntrue\ngap> C := CycleDigraph(IsMutableDigraph, 10);\n<mutable digraph\
 with 10 vertices, 10 edges>\ngap> D := DigraphImmutableCopyIfImmutable(C);\n<\
mutable digraph with 10 vertices, 10 edges>\ngap> IsIdenticalObj(C, D);\ntrue\
\ngap> C = D;\ntrue\ngap> D := DigraphImmutableCopyIfMutable(C);\n<immutable d\
igraph with 10 vertices, 10 edges>\ngap> IsIdenticalObj(C, D);\nfalse\ngap> C \
= D;\ntrue\ngap> D := DigraphMutableCopyIfMutable(C);\n<mutable digraph with 1\
0 vertices, 10 edges>\ngap> IsMutableDigraph(D);\ntrue\ngap> D := DigraphMutab\
leCopyIfImmutable(C);\n<mutable digraph with 10 vertices, 10 edges>\ngap> IsId\
enticalObj(C, D);\ntrue\ngap> IsMutableDigraph(D);\ntrue]]></Example>\n  </Des\
cription>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"InducedSubdigraph\
\" Arg=\"digraph, verts\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\
\n    If <A>digraph</A> is a digraph, and <A>verts</A> is a subset of the\n   \
 vertices of <A>digraph</A>, then this operation returns a digraph\n    constr\
ucted from <A>digraph</A> by retaining precisely those vertices in\n    <A>ver\
ts</A>, and those edges whose source and range vertices are both\n    containe\
d in <A>verts</A>. <P/>\n\n    The vertices of the induced subdigraph are\n   \
 <C>[1..Length(verts)]</C> but the original vertex labels can be\n    accessed\
 via <Ref Oper=\"DigraphVertexLabels\"/>. <P/>\n\n    If <A>digraph</A> belong\
s to <Ref Filt=\"IsMutableDigraph\"/>, then\n    <A>digraph</A> is modified in\
 place. If <A>digraph</A> belongs to <Ref\n      Filt=\"IsImmutableDigraph\"/>\
, a new immutable digraph containing the\n    appropriate\n    vertices and ed\
ges is returned.<P/>\n\n    <Example><![CDATA[\ngap> D := Digraph([[1, 1, 2, 3\
, 4, 4], [1, 3, 4], [3, 1], [1, 1]]);\n<immutable multidigraph with 4 vertices\
, 13 edges>\ngap> InducedSubdigraph(D, [1, 3, 4]);\n<immutable multidigraph wi\
th 3 vertices, 9 edges>\ngap> DigraphVertices(last);\n[ 1 .. 3 ]\ngap> D := Di\
graphMutableCopy(D);\n<mutable multidigraph with 4 vertices, 13 edges>\ngap> n\
ew := InducedSubdigraph(D, [1, 3, 4]);\n<mutable multidigraph with 3 vertices,\
 9 edges>\ngap> D = new;\ntrue\n]]></Example>\n  </Description>\n</ManSection>\
\n\n    <ManSection>\n  <Oper Name=\"ReducedDigraph\" Arg=\"digraph\"/>\n  <At\
tr Name=\"ReducedDigraphAttr\" Arg=\"digraph\"/>\n  <Returns>A digraph.</Retur\
ns>\n  <Description>\n    This function returns a digraph isomorphic to the su\
bdigraph of\n    <A>digraph</A> induced by the set of non-isolated vertices,\n\
    i.e. the set of those vertices of <A>digraph</A> which are the source or\n\
    range of some edge in <A>digraph</A>.\n    See <Ref Oper=\"InducedSubdigra\
ph\"/>.\n    <P/>\n\n    The ordering of the remaining vertices of <A>digraph<\
/A> is preserved, as are\n    the labels of the remaining vertices and edges;\
\n    see <Ref Oper=\"DigraphVertexLabels\"/> and <Ref Oper=\"DigraphEdgeLabel\
s\"/>.\n    This can allow one to match a vertex in the reduced digraph to the\
\n    corresponding vertex in <A>digraph</A>.\n    <P/>\n\n    If <A>digraph</\
A> is immutable, then a new immutable digraph is returned.\n    Otherwise, the\
 isolated vertices of the mutable digraph <A>digraph</A> are\n    removed in-p\
lace.\n    <Example><![CDATA[\ngap> D := Digraph([[1, 2], [], [], [1, 4], []])\
;\n<immutable digraph with 5 vertices, 4 edges>\ngap> R := ReducedDigraph(D);\
\n<immutable digraph with 3 vertices, 4 edges>\ngap> OutNeighbours(R);\n[ [ 1,\
 2 ], [  ], [ 1, 3 ] ]\ngap> DigraphEdges(D);\n[ [ 1, 1 ], [ 1, 2 ], [ 4, 1 ],\
 [ 4, 4 ] ]\ngap> DigraphEdges(R);\n[ [ 1, 1 ], [ 1, 2 ], [ 3, 1 ], [ 3, 3 ] ]\
\ngap> DigraphVertexLabel(R, 3);\n4\ngap> DigraphVertexLabel(R, 2);\n2\ngap> D\
 := Digraph(IsMutableDigraph, [[], [3], [2]]);\n<mutable digraph with 3 vertic\
es, 2 edges>\ngap> ReducedDigraph(D);\n<mutable digraph with 2 vertices, 2 edg\
es>\ngap> D;\n<mutable digraph with 2 vertices, 2 edges>\n]]></Example>\n  </D\
escription>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"MaximalSymmetri\
cSubdigraph\" Arg=\"digraph\"/>\n  <Attr Name=\"MaximalSymmetricSubdigraphAttr\
\" Arg=\"digraph\"/>\n  <Oper Name=\"MaximalSymmetricSubdigraphWithoutLoops\" \
Arg=\"digraph\"/>\n  <Attr Name=\"MaximalSymmetricSubdigraphWithoutLoopsAttr\"\
 Arg=\"digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If <\
A>digraph</A> is a digraph, then <C>MaximalSymmetricSubdigraph</C>\n    return\
s a symmetric digraph without multiple edges which has the same\n    vertex se\
t as <A>digraph</A>, and whose edge list is formed from\n    <A>digraph</A> by\
 ignoring the multiplicity of edges, and by ignoring\n    edges <C>[u,v]</C> f\
or which there does not exist an edge <C>[v,u]</C>.\n    <P/>\n\n    The digra\
ph returned by <C>MaximalSymmetricSubdigraphWithoutLoops</C> is\n    the same,\
 except that loops are removed.<P/>\n    \n    If <A>digraph</A> is immutable,\
 then a new immutable digraph is returned.\n    Otherwise, the mutable digraph\
 <A>digraph</A> is changed in-place into such\n    a digraph described above.<\
P/>\n\n    See <Ref Prop=\"IsSymmetricDigraph\"/>, <Ref Prop=\"IsMultiDigraph\
\"/>, and\n    <Ref Prop=\"DigraphHasLoops\"/> for more information.\n    <Exa\
mple><![CDATA[\ngap> D := Digraph([[2, 2], [1, 3], [4], [3, 1]]);\n<immutable \
multidigraph with 4 vertices, 7 edges>\ngap> not IsSymmetricDigraph(D) and IsM\
ultiDigraph(D);\ntrue\ngap> OutNeighbours(D);\n[ [ 2, 2 ], [ 1, 3 ], [ 4 ], [ \
3, 1 ] ]\ngap> S := MaximalSymmetricSubdigraph(D);\n<immutable symmetric digra\
ph with 4 vertices, 4 edges>\ngap> IsSymmetricDigraph(S) and not IsMultiDigrap\
h(S);\ntrue\ngap> OutNeighbours(S);\n[ [ 2 ], [ 1 ], [ 4 ], [ 3 ] ]\ngap> D :=\
 CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges\
>\ngap> MaximalSymmetricSubdigraph(D);\n<mutable empty digraph with 3 vertices\
>\ngap> D;\n<mutable empty digraph with 3 vertices>\n]]></Example>\n  </Descri\
ption>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"MaximalAntiSymmetric\
Subdigraph\" Arg=\"digraph\"/>\n  <Attr Name=\"MaximalAntiSymmetricSubdigraphA\
ttr\" Arg=\"digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n   \
 If <A>digraph</A> is a digraph, then <C>MaximalAntiSymmetricSubdigraph</C>\n \
   returns an anti-symmetric subdigraph of <A>digraph</A> formed by\n    retai\
ning the vertices of <A>digraph</A>, discarding any duplicate edges,\n    and \
discarding any edge <C>[i,j]</C> of <A>digraph</A> where <C>i > j</C>\n    and\
 the reverse edge <C>[j,i]</C> is an edge of <A>digraph</A>.\n    In other wor\
ds, for every\n    symmetric pair of edges <C>[i,j]</C> and <C>[j,i]</C> in <A\
>digraph</A>, where \n    <C>i</C> and <C>j</C> are distinct, it discards the \
the edge\n    <M>[\\max(i,j),\\min(i,j)]</M>.\n    <P/>\n\n    If <A>digraph</\
A> is immutable, then a new immutable digraph is returned.\n    Otherwise, the\
 mutable digraph <A>digraph</A> is changed in-place. <P/>\n\n    See <Ref Prop\
=\"IsAntisymmetricDigraph\"/> for more information.\n    <Example><![CDATA[\ng\
ap> D := Digraph([[2, 2], [1, 3], [4], [3, 1]]);\n<immutable multidigraph with\
 4 vertices, 7 edges>\ngap> not IsAntiSymmetricDigraph(D) and IsMultiDigraph(D\
);\ntrue\ngap> OutNeighbours(D);\n[ [ 2, 2 ], [ 1, 3 ], [ 4 ], [ 3, 1 ] ]\ngap\
> D := MaximalAntiSymmetricSubdigraph(D);\n<immutable antisymmetric digraph wi\
th 4 vertices, 4 edges>\ngap> IsAntiSymmetricDigraph(D) and not IsMultiDigraph\
(D);\ntrue\ngap> OutNeighbours(D);\n[ [ 2 ], [ 3 ], [ 4 ], [ 1 ] ]\ngap> D := \
Digraph(IsMutableDigraph, [[2], [1]]);\n<mutable digraph with 2 vertices, 2 ed\
ges>\ngap> MaximalAntiSymmetricSubdigraph(D);\n<mutable digraph with 2 vertice\
s, 1 edge>\ngap> D;\n<mutable digraph with 2 vertices, 1 edge>\n]]></Example>\
\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"Undirect\
edSpanningForest\" Arg=\"digraph\"/>\n  <Attr Name=\"UndirectedSpanningForestA\
ttr\" Arg=\"digraph\"/>\n  <Oper Name=\"UndirectedSpanningTree\" Arg=\"digraph\
\"/>\n  <Attr Name=\"UndirectedSpanningTreeAttr\" Arg=\"digraph\"/>\n  <Return\
s>A digraph, or <K>fail</K>.</Returns>\n  <Description>\n    If <A>digraph</A>\
 is a digraph with at least one vertex, then\n    <C>UndirectedSpanningForest<\
/C> returns an undirected spanning forest of\n    <A>digraph</A>, otherwise th\
is attribute returns <K>fail</K>. See <Ref\n      Oper=\"IsUndirectedSpanningF\
orest\" /> for the definition of an undirected\n    spanning forest.<P/>\n\n  \
  If <A>digraph</A> is a digraph with at least one vertex and whose <Ref\n    \
  Oper=\"MaximalSymmetricSubdigraph\"/> is connected (see <Ref\n      Prop=\"I\
sConnectedDigraph\" />), then <C>UndirectedSpanningTree</C> returns\n    an un\
directed spanning tree of <A>digraph</A>, otherwise this attribute\n    return\
s <K>fail</K>.  See <Ref Oper=\"IsUndirectedSpanningTree\" /> for the\n    def\
inition of an undirected spanning tree.<P/>\n\n    If <A>digraph</A> is immuta\
ble, then an immutable digraph is returned.\n    Otherwise, the mutable digrap\
h <A>digraph</A> is changed in-place into an\n    undirected spanning tree of \
<A>digraph</A>.<P/>\n\n    Note that for an immutable digraph that has known u\
ndirected spanning tree,\n    the attribute <C>UndirectedSpanningTree</C> retu\
rns the same digraph as\n    the attribute <C>UndirectedSpanningForest</C>.\n\
\n    <Example><![CDATA[\ngap> D := Digraph([[1, 2, 1, 3], [1], [4], [3, 4, 3]\
]);\n<immutable multidigraph with 4 vertices, 9 edges>\ngap> UndirectedSpannin\
gTree(D);\nfail\ngap> forest := UndirectedSpanningForest(D);\n<immutable symme\
tric digraph with 4 vertices, 4 edges>\ngap> OutNeighbours(forest);\n[ [ 2 ], \
[ 1 ], [ 4 ], [ 3 ] ]\ngap> IsUndirectedSpanningForest(D, forest);\ntrue\ngap>\
 DigraphConnectedComponents(forest).comps;\n[ [ 1, 2 ], [ 3, 4 ] ]\ngap> Digra\
phConnectedComponents(MaximalSymmetricSubdigraph(D)).comps;\n[ [ 1, 2 ], [ 3, \
4 ] ]\ngap> UndirectedSpanningForest(MaximalSymmetricSubdigraph(D))\n> = fores\
t;\ntrue\ngap> D := CompleteDigraph(4);\n<immutable complete digraph with 4 ve\
rtices>\ngap> tree := UndirectedSpanningTree(D);\n<immutable symmetric digraph\
 with 4 vertices, 6 edges>\ngap> IsUndirectedSpanningTree(D, tree);\ntrue\ngap\
> tree = UndirectedSpanningForest(D);\ntrue\ngap> UndirectedSpanningForest(Emp\
tyDigraph(0));\nfail\ngap> D := PetersenGraph(IsMutableDigraph);\n<mutable dig\
raph with 10 vertices, 30 edges>\ngap> UndirectedSpanningTree(D);\n<mutable di\
graph with 10 vertices, 18 edges>\ngap> D;\n<mutable digraph with 10 vertices,\
 18 edges>\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\
\n  <Oper Name=\"QuotientDigraph\" Arg=\"digraph, p\"/>\n  <Returns>A digraph.\
</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph, and <A>p</A> \
is a partition of the vertices\n    of <A>digraph</A>, then this operation ret\
urns a digraph constructed by\n    amalgamating all vertices of <A>digraph</A>\
 which lie in the same part of\n    <A>p</A>.\n    <P/>\n\n    A partition of \
the vertices of <A>digraph</A> is a list of non-empty\n    disjoint lists, suc\
h that the union of all the sub-lists is equal\n    to vertex set of <A>digrap\
h</A>. In particular, each vertex must appear\n    in precisely one sub-list.\
\n    <P/>\n\n    The vertices of <A>digraph</A> in part <C>i</C> of <A>p</A> \
will become\n    vertex <C>i</C> in the quotient, and there exists some edge i\
n <A>digraph</A>\n    with source in part <C>i</C> and range in part <C>j</C> \
if and only if there\n    is an edge from <C>i</C> to <C>j</C> in the quotient\
.\n    In particular, this means that the quotient of a digraph has no multipl\
e edges.\n    which was a change introduced in version 1.0.0 of the &Digraphs;\
 package.\n    <P/>\n\n    If <A>digraph</A> belongs to <Ref Filt=\"IsMutableD\
igraph\"/>, then\n    <A>digraph</A> is modified in place. If <A>digraph</A> b\
elongs to <Ref\n      Filt=\"IsImmutableDigraph\"/>, a new immutable digraph w\
ith the above\n    properties is returned.<P/>\n\n    <Example><![CDATA[\ngap>\
 D := Digraph([[2, 1], [4], [1], [1, 3, 4]]);\n<immutable digraph with 4 verti\
ces, 7 edges>\ngap> DigraphVertices(D);\n[ 1 .. 4 ]\ngap> DigraphEdges(D);\n[ \
[ 1, 2 ], [ 1, 1 ], [ 2, 4 ], [ 3, 1 ], [ 4, 1 ], [ 4, 3 ], \n  [ 4, 4 ] ]\nga\
p> p := [[1], [2, 4], [3]];\n[ [ 1 ], [ 2, 4 ], [ 3 ] ]\ngap> quo := QuotientD\
igraph(D, p);\n<immutable digraph with 3 vertices, 6 edges>\ngap> DigraphVerti\
ces(quo);\n[ 1 .. 3 ]\ngap> DigraphEdges(quo);\n[ [ 1, 1 ], [ 1, 2 ], [ 2, 1 ]\
, [ 2, 2 ], [ 2, 3 ], [ 3, 1 ] ]\ngap> QuotientDigraph(EmptyDigraph(0), []);\n\
<immutable empty digraph with 0 vertices>\n]]></Example>\n  </Description>\n</\
ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphReverse\" Arg=\"digraph\
\"/>\n  <Attr Name=\"DigraphReverseAttr\" Arg=\"digraph\"/>\n  <Returns>A digr\
aph.</Returns>\n  <Description>\n    The reverse of a digraph is the digraph f\
ormed by reversing the orientation\n    of each of its edges, i.e. for every e\
dge <C>[i, j]</C> of a digraph, the\n    reverse contains the corresponding ed\
ge <C>[j, i]</C>.<P/>\n\n    <C>DigraphReverse</C> returns the reverse of the \
digraph <A>digraph</A>. If\n    <A>digraph</A> is immutable, then a new immuta\
ble digraph is returned. Otherwise,\n    the mutable digraph <A>digraph</A> is\
 changed in-place into its reverse.\n    <Example><![CDATA[\ngap> D := Digraph\
([[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\n<immutable digraph with 5 vert\
ices, 11 edges>\ngap> DigraphReverse(D);\n<immutable digraph with 5 vertices, \
11 edges>\ngap> OutNeighbours(last);\n[ [ 2, 3, 4 ], [ 4, 5 ], [ 1, 2, 5 ], [ \
4 ], [ 2, 5 ] ]\ngap> D := Digraph([[2, 4], [1], [4], [3, 4]]);\n<immutable di\
graph with 4 vertices, 6 edges>\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 4 ], \
[ 2, 1 ], [ 3, 4 ], [ 4, 3 ], [ 4, 4 ] ]\ngap> DigraphEdges(DigraphReverse(D))\
;\n[ [ 1, 2 ], [ 2, 1 ], [ 3, 4 ], [ 4, 1 ], [ 4, 3 ], [ 4, 4 ] ]\ngap> D := C\
ycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\
\ngap> OutNeighbours(D);\n[ [ 2 ], [ 3 ], [ 1 ] ]\ngap> DigraphReverse(D);\n<m\
utable digraph with 3 vertices, 3 edges>\ngap> OutNeighbours(D);\n[ [ 3 ], [ 1\
 ], [ 2 ] ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection\
>\n  <Oper Name=\"DigraphDual\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphDualA\
ttr\" Arg=\"digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n   \
 The <E>dual</E> of <A>digraph</A> has the same vertices as <A>digraph</A>,\n \
   and there is an edge in the dual from <C>i</C> to <C>j</C>\n    whenever th\
ere is no edge from <C>i</C> to <C>j</C> in <A>digraph</A>.\n    The <E>dual</\
E> is sometimes called the <E>complement</E>.<P/>\n\n    <C>DigraphDual</C> re\
turns the dual of the digraph <A>digraph</A>. If\n    <A>digraph</A> is an imm\
utable digraph, then a new immutable digraph is\n    returned. Otherwise, the \
mutable digraph <A>digraph</A> is changed in-place\n    into its dual.\n    <E\
xample><![CDATA[\ngap> D := Digraph([[2, 3], [], [4, 6], [5], [],\n> [7, 8, 9]\
, [], [], []]);\n<immutable digraph with 9 vertices, 8 edges>\ngap> DigraphDua\
l(D);\n<immutable digraph with 9 vertices, 73 edges>\ngap> D := CycleDigraph(I\
sMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> Digraph\
Dual(D);\n<mutable digraph with 3 vertices, 6 edges>\ngap> D;\n<mutable digrap\
h with 3 vertices, 6 edges>\n]]></Example>\n  </Description>\n</ManSection>\n\
\n    <ManSection>\n  <Oper Name=\"DigraphSymmetricClosure\" Arg=\"digraph\"/>\
\n  <Attr Name=\"DigraphSymmetricClosureAttr\" Arg=\"digraph\"/>\n  <Returns>A\
 digraph.</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph, then\
 this attribute gives the minimal\n    symmetric digraph which has the same ve\
rtices and contains all the edges of\n    <A>digraph</A>.<P/>\n    \n    A dig\
raph is <E>symmetric</E> if its adjacency matrix \n    <Ref Attr=\"AdjacencyMa\
trix\"/> is symmetric. For a digraph with multiple\n    edges this means that \
there are the same number of edges from a vertex\n    <C>u</C> to a vertex <C>\
v</C> as there are from <C>v</C> to <C>u</C>; \n    see <Ref Prop=\"IsSymmetri\
cDigraph\"/>.<P/>\n\n    If <A>digraph</A> is immutable, then a new immutable \
digraph is returned.\n    Otherwise, the mutable digraph <A>digraph</A> is cha\
nged in-place into its\n    symmetric closure.\n<Example><![CDATA[\ngap> D := \
Digraph([[1, 2, 3], [2, 4], [1], [3, 4]]);\n<immutable digraph with 4 vertices\
, 8 edges>\ngap> D := DigraphSymmetricClosure(D);\n<immutable symmetric digrap\
h with 4 vertices, 11 edges>\ngap> IsSymmetricDigraph(D);\ntrue\ngap> List(Out\
Neighbours(D), AsSet);\n[ [ 1, 2, 3 ], [ 1, 2, 4 ], [ 1, 4 ], [ 2, 3, 4 ] ]\ng\
ap> D := Digraph([[2, 2], [1]]);\n<immutable multidigraph with 2 vertices, 3 e\
dges>\ngap> D := DigraphSymmetricClosure(D);\n<immutable symmetric multidigrap\
h with 2 vertices, 4 edges>\ngap> OutNeighbours(D);\n[ [ 2, 2 ], [ 1, 1 ] ]\ng\
ap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices,\
 3 edges>\ngap> DigraphSymmetricClosure(D);\n<mutable digraph with 3 vertices,\
 6 edges>\ngap> D;\n<mutable digraph with 3 vertices, 6 edges>\n]]></Example>\
\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphT\
ransitiveClosure\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphTransitiveClosureA\
ttr\" Arg=\"digraph\"/>\n  <Oper Name=\"DigraphReflexiveTransitiveClosure\" Ar\
g=\"digraph\"/>\n  <Attr Name=\"DigraphReflexiveTransitiveClosureAttr\" Arg=\"\
digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If <A>digra\
ph</A> is a digraph with no multiple edges, then these\n    attributes return \
the (reflexive) transitive closure of <A>digraph</A>.<P/>\n\n    A digraph is \
<E>reflexive</E> if it has a loop at every vertex, and it is\n    <E>transitiv\
e</E> if whenever <C>[i,j]</C> and <C>[j,k]</C> are edges of\n    <A>digraph</\
A>, <C>[i,k]</C> is also an edge.  The <E>(reflexive)\n      transitive closur\
e</E> of a digraph <A>digraph</A> is the least\n    (reflexive and) transitive\
 digraph containing <A>digraph</A>.<P/>\n\n    If <A>digraph</A> is immutable,\
 then a new immutable digraph is returned.\n    Otherwise, the mutable digraph\
 <A>digraph</A> is changed in-place into its\n    (reflexive) transitive closu\
re.<P/>\n\n    Let <M>n</M> be the number of vertices of <A>digraph</A>, and l\
et\n    <M>m</M> be the number of edges.  For an arbitrary digraph, these\n   \
 attributes will use a version of the Floyd-Warshall algorithm, with\n    comp\
lexity <M>O(n^3)</M>.\n\n    However, for a topologically sortable digraph [se\
e <Ref\n      Attr=\"DigraphTopologicalSort\"/>], these attributes will use me\
thods\n    with complexity <M>O(m + n + m \\cdot n)</M> when this is faster.<P\
/>\n\n    <Example><![CDATA[\ngap> D := DigraphFromDiSparse6String(\".H`eOWR`U\
l^\");\n<immutable digraph with 9 vertices, 8 edges>\ngap> IsReflexiveDigraph(\
D) or IsTransitiveDigraph(D);\nfalse\ngap> OutNeighbours(D);\n[ [ 4, 6 ], [ 1,\
 3 ], [  ], [ 5 ], [  ], [ 7, 8, 9 ], [  ], [  ], \n  [  ] ]\ngap> T := Digrap\
hTransitiveClosure(D);\n<immutable transitive digraph with 9 vertices, 18 edge\
s>\ngap> OutNeighbours(T);\n[ [ 4, 6, 5, 7, 8, 9 ], [ 1, 3, 4, 5, 6, 7, 8, 9 ]\
, [  ], [ 5 ], \n  [  ], [ 7, 8, 9 ], [  ], [  ], [  ] ]\ngap> RT := DigraphRe\
flexiveTransitiveClosure(D);\n<immutable preorder digraph with 9 vertices, 27 \
edges>\ngap> OutNeighbours(RT);\n[ [ 4, 6, 5, 7, 8, 9, 1 ], [ 1, 3, 4, 5, 6, 7\
, 8, 9, 2 ], [ 3 ], \n  [ 5, 4 ], [ 5 ], [ 7, 8, 9, 6 ], [ 7 ], [ 8 ], [ 9 ] ]\
\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertic\
es, 3 edges>\ngap> DigraphReflexiveTransitiveClosure(D);\n<mutable digraph wit\
h 3 vertices, 9 edges>\ngap> D;\n<mutable digraph with 3 vertices, 9 edges>\n]\
]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Nam\
e=\"DigraphTransitiveReduction\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphTran\
sitiveReductionAttr\" Arg=\"digraph\"/>\n  <Oper Name=\"DigraphReflexiveTransi\
tiveReduction\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphReflexiveTransitiveRe\
ductionAttr\" Arg=\"digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Descripti\
on>\n    If <A>digraph</A> is a topologically sortable digraph\n    [see <Ref \
Attr=\"DigraphTopologicalSort\"/>]\n    with no multiple edges, then these  op\
erations return the\n    (reflexive) transitive reduction of <A>digraph</A>.<P\
/>\n\n    The (reflexive) transitive reduction of such a digraph is the unique\
\n    least subgraph such that the (reflexive) transitive closure of the\n    \
subgraph is equal to the (reflexive) transitive closure of <A>digraph</A>\n   \
 [see <Ref Oper=\"DigraphReflexiveTransitiveClosure\"/>].\n    In order words,\
 it is the least subgraph of <A>digraph</A> which\n    retains the same reacha\
bility as <A>digraph</A>.<P/>\n\n    If <A>digraph</A> is immutable, then a ne\
w immutable digraph is returned.\n    Otherwise, the mutable digraph <A>digrap\
h</A> is changed in-place into its\n    (reflexive) transitive reduction.<P/>\
\n\n    Let <M>n</M> be the number of vertices of an arbitrary digraph, and le\
t\n        <M>m</M> be the number of edges.\n    Then these operations\n    us\
e methods with complexity <M>O(m + n + m \\cdot n)</M>.\n    <P/>\n    <Exampl\
e><![CDATA[\ngap> D := Digraph([[1, 2, 3], [3], [3]]);;\ngap> DigraphHasLoops(\
D);\ntrue\ngap> D1 := DigraphReflexiveTransitiveReduction(D);\n<immutable digr\
aph with 3 vertices, 2 edges>\ngap> DigraphHasLoops(D1);\nfalse\ngap> OutNeigh\
bours(D1);\n[ [ 2 ], [ 3 ], [  ] ]\ngap> D2 := DigraphTransitiveReduction(D);\
\n<immutable digraph with 3 vertices, 4 edges>\ngap> DigraphHasLoops(D2);\ntru\
e\ngap> OutNeighbours(D2);\n[ [ 2, 1 ], [ 3 ], [ 3 ] ]\ngap> DigraphReflexiveT\
ransitiveClosure(D)\n>  = DigraphReflexiveTransitiveClosure(D1);\ntrue\ngap> D\
igraphTransitiveClosure(D)\n>  = DigraphTransitiveClosure(D2);\ntrue\ngap> D :\
= Digraph(IsMutableDigraph, [[1], [1], [1, 2, 3]]);\n<mutable digraph with 3 v\
ertices, 5 edges>\ngap> DigraphReflexiveTransitiveReduction(D);\n<mutable digr\
aph with 3 vertices, 2 edges>\ngap> D;\n<mutable digraph with 3 vertices, 2 ed\
ges>\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <O\
per Name=\"DigraphAddVertex\" Arg=\"digraph[, label ]\"/>\n  <Returns>A digrap\
h.</Returns>\n  <Description>\n    The operation returns a digraph constructed\
 from <A>digraph</A> by adding a\n    single new vertex, and no new edges. <P/\
>\n\n    If the optional second argument <A>label</A> is a &GAP; object,\n    \
then the new vertex will be labelled <A>label</A>.\n    <P/>\n\n    If <A>digr\
aph</A> belongs to <Ref Filt=\"IsMutableDigraph\"/>, then the\n    vertex is a\
dded directly to <A>digraph</A>. If <A>digraph</A> belongs to\n    <Ref Filt=\
\"IsImmutableDigraph\"/>, an immutable copy of <A>digraph</A> with\n    the ad\
ditional vertex is returned.<P/>\n\n    <Example><![CDATA[\ngap> D := Complete\
Digraph(3);\n<immutable complete digraph with 3 vertices>\ngap> new := Digraph\
AddVertex(D);\n<immutable digraph with 4 vertices, 6 edges>\ngap> D = new;\nfa\
lse\ngap> DigraphVertices(new);\n[ 1 .. 4 ]\ngap> new := DigraphAddVertex(D, G\
roup([(1, 2)]));\n<immutable digraph with 4 vertices, 6 edges>\ngap> DigraphVe\
rtexLabels(new);\n[ 1, 2, 3, Group([ (1,2) ]) ]\ngap> D := CompleteBipartiteDi\
graph(IsMutableDigraph, 2, 3);\n<mutable digraph with 5 vertices, 12 edges>\ng\
ap> new := DigraphAddVertex(D);\n<mutable digraph with 6 vertices, 12 edges>\n\
gap> D = new;\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\n    <Ma\
nSection>\n  <Oper Name=\"DigraphAddVertices\" Arg=\"digraph, m\"\n    Label=\
\"for a digraph and an integer\"/>\n  <Oper Name=\"DigraphAddVertices\" Arg=\"\
digraph, labels\"\n    Label=\"for a digraph and a list of labels\"/>\n  <!-- \
The 3-argument version is deliberately undocumented. It is redundant,\n       \
but it is included for backwards compatibility. -->\n  <Returns>A digraph.</Re\
turns>\n  <Description>\n    For a non-negative integer <A>m</A>, this operati\
on returns a digraph\n    constructed from <A>digraph</A> by adding <A>m</A> n\
ew vertices.\n    <P/>\n\n    Otherwise, if <A>labels</A> is a list\n    consi\
sting of <C>k</C> &GAP; objects, then this operation returns a\n    digraph co\
nstructed from <A>digraph</A> by adding <C>k</C> new vertices,\n    which are \
labelled according to this list.\n    <P/>\n\n    If <A>digraph</A> belongs to\
 <Ref Filt=\"IsMutableDigraph\"/>, then the\n    vertices are added directly t\
o <A>digraph</A>, which is changed in-place.\n    If <A>digraph</A> belongs to\
 <Ref Filt=\"IsImmutableDigraph\"/>, then\n    <A>digraph</A> itself is return\
ed if no vertices are added\n    (i.e. <C><A>m</A>=0</C> or <A>labels</A> is e\
mpty), otherwise\n    the result is a new immutable digraph.\n    <P/>\n\n    \
<Example><![CDATA[\ngap> D := CompleteDigraph(3);\n<immutable complete digraph\
 with 3 vertices>\ngap> new := DigraphAddVertices(D, 3);\n<immutable digraph w\
ith 6 vertices, 6 edges>\ngap> DigraphVertices(new);\n[ 1 .. 6 ]\ngap> new := \
DigraphAddVertices(D, [Group([(1, 2)]), \"d\"]);\n<immutable digraph with 5 ve\
rtices, 6 edges>\ngap> DigraphVertexLabels(new);\n[ 1, 2, 3, Group([ (1,2) ]),\
 \"d\" ]\ngap> DigraphAddVertices(D, 0) = D;\ntrue\ngap> D := CompleteBipartit\
eDigraph(IsMutableDigraph, 2, 3);\n<mutable digraph with 5 vertices, 12 edges>\
\ngap> new := DigraphAddVertices(D, 4);\n<mutable digraph with 9 vertices, 12 \
edges>\ngap> D = new;\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\
\n    <ManSection>\n  <Oper Name=\"DigraphAddEdge\" Arg=\"digraph, edge\"\n   \
 Label=\"for a digraph and an edge\"/>\n  <Oper Name=\"DigraphAddEdge\" Arg=\"\
digraph, src, ran\"\n    Label=\"for a digraph, source, and range\"/>\n  <Retu\
rns>A digraph.</Returns>\n  <Description>\n    If <A>edge</A> is a pair of ver\
tices of <A>digraph</A>, or <A>src</A> and\n    <A>ran</A> are vertices of <A>\
digraph</A>,\n    then this operation returns a digraph constructed from <A>di\
graph</A>\n    by adding a new edge with source <A>edge</A><C>[1]</C> [<A>src<\
/A>] and range\n    <A>edge</A><C>[2]</C> [<A>ran</A>].\n    <P/>\n    \n    I\
f <A>digraph</A> belongs to <Ref Filt=\"IsMutableDigraph\"/>, then the edge\n \
   is added directly to <A>digraph</A>. If <A>digraph</A> belongs to <Ref\n   \
   Filt=\"IsImmutableDigraph\"/>, then an immutable copy of <A>digraph</A> wit\
h the\n    additional edge is returned.  <P/>\n\n    <Example><![CDATA[\ngap> \
D1 := Digraph([[2], [3], []]);\n<immutable digraph with 3 vertices, 2 edges>\n\
gap> DigraphEdges(D1);\n[ [ 1, 2 ], [ 2, 3 ] ]\ngap> D2 := DigraphAddEdge(D1, \
[3, 1]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> DigraphEdges(D2);\
\n[ [ 1, 2 ], [ 2, 3 ], [ 3, 1 ] ]\ngap> D3 := DigraphAddEdge(D2, [2, 3]);\n<i\
mmutable multidigraph with 3 vertices, 4 edges>\ngap> DigraphEdges(D3);\n[ [ 1\
, 2 ], [ 2, 3 ], [ 2, 3 ], [ 3, 1 ] ]\ngap> D := CycleDigraph(IsMutableDigraph\
, 4);\n<mutable digraph with 4 vertices, 4 edges>\ngap> new := DigraphAddEdge(\
D, [1, 3]);\n<mutable digraph with 4 vertices, 5 edges>\ngap> DigraphEdges(new\
);\n[ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 4, 1 ] ]\ngap> D = new;\ntrue\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper \
Name=\"DigraphAddEdgeOrbit\" Arg=\"digraph, edge\"/>\n  <Returns>\n    A new d\
igraph.\n  </Returns>\n  <Description>\n    This operation returns a new digra\
ph with the same vertices and edges as\n    <A>digraph</A> and with additional\
 edges consisting of the orbit of the\n    edge <A>edge</A> under the action o\
f the <Ref Attr=\"DigraphGroup\"/> of\n    <A>digraph</A>.  If <A>edge</A> is \
already an edge in <A>digraph</A>, then\n    <A>digraph</A> is returned unchan\
ged. The argument <A>digraph</A> must be\n    an immutable digraph.\n    <P/>\
\n\n    An edge is simply a pair of vertices of <A>digraph</A>.\n\n    <Exampl\
e><![CDATA[\ngap> gr1 := CayleyDigraph(DihedralGroup(8));\n<immutable digraph \
with 8 vertices, 24 edges>\ngap> gr2 := DigraphAddEdgeOrbit(gr1, [1, 8]);\n<im\
mutable digraph with 8 vertices, 32 edges>\ngap> DigraphEdges(gr1);\n[ [ 1, 2 \
], [ 1, 3 ], [ 1, 4 ], [ 2, 1 ], [ 2, 5 ], [ 2, 6 ], \n  [ 3, 8 ], [ 3, 4 ], [\
 3, 7 ], [ 4, 6 ], [ 4, 7 ], [ 4, 1 ], \n  [ 5, 7 ], [ 5, 6 ], [ 5, 8 ], [ 6, \
4 ], [ 6, 8 ], [ 6, 2 ], \n  [ 7, 5 ], [ 7, 1 ], [ 7, 3 ], [ 8, 3 ], [ 8, 2 ],\
 [ 8, 5 ] ]\ngap> DigraphEdges(gr2);\n[ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 8 ]\
, [ 2, 1 ], [ 2, 5 ], \n  [ 2, 6 ], [ 2, 7 ], [ 3, 8 ], [ 3, 4 ], [ 3, 7 ], [ \
3, 6 ], \n  [ 4, 6 ], [ 4, 7 ], [ 4, 1 ], [ 4, 5 ], [ 5, 7 ], [ 5, 6 ], \n  [ \
5, 8 ], [ 5, 4 ], [ 6, 4 ], [ 6, 8 ], [ 6, 2 ], [ 6, 3 ], \n  [ 7, 5 ], [ 7, 1\
 ], [ 7, 3 ], [ 7, 2 ], [ 8, 3 ], [ 8, 2 ], \n  [ 8, 5 ], [ 8, 1 ] ]\ngap> gr3\
 := DigraphRemoveEdgeOrbit(gr2, [1, 8]);\n<immutable digraph with 8 vertices, \
24 edges>\ngap> gr3 = gr1;\ntrue\n]]></Example>\n  </Description>\n</ManSectio\
n>\n\n    <ManSection>\n  <Oper Name=\"DigraphAddEdges\" Arg=\"digraph, edges\
\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If <A>edges</A> is\
 a (possibly empty) list of pairs of vertices of\n    <A>digraph</A>, then thi\
s operation returns a digraph constructed from\n    <A>digraph</A> by adding t\
he edges specified by <A>edges</A>.  More\n    precisely, for every <C>edge</C\
> in <A>edges</A>, a new edge\n    will be added with source <C>edge[1]</C> an\
d range <C>edges[2]</C>.\n    <P/>\n\n    If an edge is included in <A>edges</\
A> with multiplicity <C>k</C>,\n    then it will be added <C>k</C> times.\n\n \
   If <A>digraph</A> belongs to <Ref Filt=\"IsMutableDigraph\"/>, then the edg\
es\n    are added directly to <A>digraph</A>. If <A>digraph</A> belongs to <Re\
f\n      Filt=\"IsImmutableDigraph\"/>, then the result is returned as an immu\
table\n    digraph.\n    <P/>\n\n    <Example><![CDATA[\ngap> func := function\
(n)\n>  local source, range, i;\n>  source := [];\n>  range  := [];\n>  for i \
in [1 .. n - 2] do\n>    Add(source, i);\n>    Add(range, i + 1);\n>  od;\n>  \
return Digraph(n, source, range);\n> end;;\ngap> D := func(1024);\n<immutable \
digraph with 1024 vertices, 1022 edges>\ngap> new := DigraphAddEdges(D,\n> [[1\
023, 1024], [1, 1024], [1023, 1024], [1024, 1]]);\n<immutable multidigraph wit\
h 1024 vertices, 1026 edges>\ngap> D = new;\nfalse\ngap> D2 := DigraphMutableC\
opy(func(1024));\n<mutable digraph with 1024 vertices, 1022 edges>\ngap> new :\
= DigraphAddEdges(D2,\n> [[1023, 1024], [1, 1024], [1023, 1024], [1024, 1]]);\
\n<mutable multidigraph with 1024 vertices, 1026 edges>\ngap> D2 = new;\ntrue\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper \
Name=\"DigraphRemoveVertex\" Arg=\"digraph, v\"/>\n  <Returns>A digraph.</Retu\
rns>\n  <Description>\n    If <A>v</A> is a vertex of <A>digraph</A>, then thi\
s operation returns a\n    digraph constructed from <A>digraph</A> by removing\
 vertex <A>v</A>,\n    along with any edge whose source or range vertex is <A>\
v</A>.<P/>\n\n    If <A>digraph</A> has <C>n</C> vertices, then the vertices o\
f the returned\n    digraph are <C>[1..n-1]</C>, but the original labels can b\
e\n    accessed via <Ref Oper=\"DigraphVertexLabels\"/>. <P/>\n\n    If <A>dig\
raph</A> belongs to <Ref Filt=\"IsMutableDigraph\"/>, then the\n    vertex is \
removed directly from <A>digraph</A>. If <A>digraph</A> belongs\n    to <Ref F\
ilt=\"IsImmutableDigraph\"/>, an immutable copy of <A>digraph</A>\n    without\
 the vertex is returned.<P/>\n\n    <Example><![CDATA[\ngap> D := Digraph([\"a\
\", \"b\", \"c\"],\n>                  [\"a\", \"a\", \"b\", \"c\", \"c\"],\n>\
                  [\"b\", \"c\", \"a\", \"a\", \"c\"]);\n<immutable digraph wi\
th 3 vertices, 5 edges>\ngap> DigraphVertexLabels(D);\n[ \"a\", \"b\", \"c\" ]\
\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 3 ], [ 2, 1 ], [ 3, 1 ], [ 3, 3 ] ]\
\ngap> new := DigraphRemoveVertex(D, 2);\n<immutable digraph with 2 vertices, \
3 edges>\ngap> DigraphVertexLabels(new);\n[ \"a\", \"c\" ]\ngap> D := CycleDig\
raph(IsMutableDigraph, 5);\n<mutable digraph with 5 vertices, 5 edges>\ngap> n\
ew := DigraphRemoveVertex(D, 1);\n<mutable digraph with 4 vertices, 3 edges>\n\
gap> DigraphVertexLabels(D);\n[ 2, 3, 4, 5 ]\ngap> D = new;\ntrue\n]]></Exampl\
e>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"Digrap\
hRemoveVertices\" Arg=\"digraph, verts\"/>\n  <Returns>A digraph.</Returns>\n \
 <Description>\n    If <A>verts</A> is a (possibly empty) duplicate-free list \
of vertices of\n    <A>digraph</A>, then this operation returns a digraph cons\
tructed from\n    <A>digraph</A> by removing every vertex in <A>verts</A>, alo\
ng with any edge\n    whose source or range vertex is in <A>verts</A>.<P/>\n\n\
    If <A>digraph</A> has <C>n</C> vertices, then the vertices of the new\n   \
 digraph are <C>[1 .. n-Length(<A>verts</A>)]</C>, but the\n    original label\
s can be accessed via <Ref Oper=\"DigraphVertexLabels\"/>. <P/>\n\n    If <A>d\
igraph</A> belongs to <Ref Filt=\"IsMutableDigraph\"/>, then the\n    vertices\
 are removed directly from <A>digraph</A>. If <A>digraph</A> belongs\n    to <\
Ref Filt=\"IsImmutableDigraph\"/>, an immutable copy of <A>digraph</A>\n    wi\
thout the vertices is returned.<P/>\n\n    <Example><![CDATA[\ngap> D := Digra\
ph([[3], [1, 3, 5], [1], [1, 2, 4], [2, 3, 5]]);\n<immutable digraph with 5 ve\
rtices, 11 edges>\ngap> SetDigraphVertexLabels(D, [\"a\", \"b\", \"c\", \"d\",\
 \"e\"]);\ngap> new := DigraphRemoveVertices(D, [2, 4]);\n<immutable digraph w\
ith 3 vertices, 4 edges>\ngap> DigraphVertexLabels(new);\n[ \"a\", \"c\", \"e\
\" ]\ngap> D := CycleDigraph(IsMutableDigraph, 5);\n<mutable digraph with 5 ve\
rtices, 5 edges>\ngap> new := DigraphRemoveVertices(D, [1, 3]);\n<mutable digr\
aph with 3 vertices, 1 edge>\ngap> DigraphVertexLabels(D);\n[ 2, 4, 5 ]\ngap> \
D = new;\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSect\
ion>\n  <Oper Name=\"DigraphRemoveEdge\" Arg=\"digraph, edge\"\n    Label=\"fo\
r a digraph and an edge\"/>\n  <Oper Name=\"DigraphRemoveEdge\" Arg=\"digraph,\
 src, ran\"\n    Label=\"for a digraph, source, and range\"/>\n  <Returns>A di\
graph.</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph with no \
multiple edges and <A>edge</A> is a\n    pair of vertices of <A>digraph</A>, o\
r <A>src</A> and <A>ran</A> are\n    vertices of <A>digraph</A>, then this ope\
ration returns a digraph\n    constructed from <A>digraph</A> by removing the \
edge specified by\n    <A>edge</A> or <A>[src, ran]</A>. <P/>  \n\n    If <A>d\
igraph</A> belongs to <Ref\n      Filt=\"IsMutableDigraph\"/>, then the edge i\
s removed directly from\n    <A>digraph</A>. If <A>digraph</A> belongs to <Ref\
\n      Filt=\"IsImmutableDigraph\"/>, an immutable copy of <A>digraph</A> wit\
hout\n    the edge is returned.\n    <P/>\n\n    Note that if <A>digraph</A> b\
elongs to <Ref Filt=\"IsImmutableDigraph\"/>,\n    then a new copy of <A>digra\
ph</A> will be returned even if <A>edge</A> or \n    <A>[src, ran]</A> does no\
t define an edge of <A>digraph</A>.<P/>\n\n    <Example><![CDATA[\ngap> D := C\
ycleDigraph(250000);\n<immutable cycle digraph with 250000 vertices>\ngap> D :\
= DigraphRemoveEdge(D, [250000, 1]);\n<immutable digraph with 250000 vertices,\
 249999 edges>\ngap> new := DigraphRemoveEdge(D, [25000, 2]);;\ngap> new = D;\
\ntrue\ngap> IsIdenticalObj(new, D);\nfalse\ngap> D := DigraphMutableCopy(D);;\
\ngap> new := DigraphRemoveEdge(D, 2500, 2);;\ngap> IsIdenticalObj(new, D);\nt\
rue]]>\n</Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Op\
er Name=\"DigraphRemoveEdgeOrbit\" Arg=\"digraph, edge\"/>\n  <Returns>\n    A\
 new digraph.\n  </Returns>\n  <Description>\n    This operation returns a new\
 digraph with the same vertices as\n    <A>digraph</A> and with the orbit of t\
he edge <A>edge</A> (under the action\n    of the <Ref Attr=\"DigraphGroup\"/>\
 of <A>digraph</A>) removed.\n    If <A>edge</A> is not an edge in <A>digraph<\
/A>, then <A>digraph</A> is\n    returned unchanged. The argument <A>digraph</\
A> must be an immutable\n    digraph.\n    <P/>\n\n    An edge is simply a pai\
r of vertices of <A>digraph</A>.\n    <Example><![CDATA[\ngap> gr1 := CayleyDi\
graph(DihedralGroup(8));\n<immutable digraph with 8 vertices, 24 edges>\ngap> \
gr2 := DigraphAddEdgeOrbit(gr1, [1, 8]);\n<immutable digraph with 8 vertices, \
32 edges>\ngap> DigraphEdges(gr1);\n[ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 2, 1 ], \
[ 2, 5 ], [ 2, 6 ], \n  [ 3, 8 ], [ 3, 4 ], [ 3, 7 ], [ 4, 6 ], [ 4, 7 ], [ 4,\
 1 ], \n  [ 5, 7 ], [ 5, 6 ], [ 5, 8 ], [ 6, 4 ], [ 6, 8 ], [ 6, 2 ], \n  [ 7,\
 5 ], [ 7, 1 ], [ 7, 3 ], [ 8, 3 ], [ 8, 2 ], [ 8, 5 ] ]\ngap> DigraphEdges(gr\
2);\n[ [ 1, 2 ], [ 1, 3 ], [ 1, 4 ], [ 1, 8 ], [ 2, 1 ], [ 2, 5 ], \n  [ 2, 6 \
], [ 2, 7 ], [ 3, 8 ], [ 3, 4 ], [ 3, 7 ], [ 3, 6 ], \n  [ 4, 6 ], [ 4, 7 ], [\
 4, 1 ], [ 4, 5 ], [ 5, 7 ], [ 5, 6 ], \n  [ 5, 8 ], [ 5, 4 ], [ 6, 4 ], [ 6, \
8 ], [ 6, 2 ], [ 6, 3 ], \n  [ 7, 5 ], [ 7, 1 ], [ 7, 3 ], [ 7, 2 ], [ 8, 3 ],\
 [ 8, 2 ], \n  [ 8, 5 ], [ 8, 1 ] ]\ngap> gr3 := DigraphRemoveEdgeOrbit(gr2, [\
1, 8]);\n<immutable digraph with 8 vertices, 24 edges>\ngap> gr3 = gr1;\ntrue\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper \
Name=\"DigraphRemoveEdges\" Arg=\"digraph, edges\"/>\n  <Returns>A digraph.</R\
eturns>\n  <Description>\n    If one of the following holds:\n    <List>\n    \
  <Item>\n        <A>digraph</A> is a digraph with no multiple edges, and\n   \
     <A>edges</A> is a list of pairs of vertices of <A>digraph</A>, or\n      \
</Item>\n      <Item> <A>digraph</A> is a digraph and <A>edges</A> is an empty\
 list </Item>\n    </List>\n\n    then this operation returns a digraph constr\
ucted from <A>digraph</A>\n    by removing all of the edges specified by <A>ed\
ges</A>\n    (see <Ref Oper=\"DigraphRemoveEdge\" Label=\"for a digraph and an\
 edge\"/>).\n    <P/>\n\n    If <A>digraph</A> belongs to <Ref Filt=\"IsMutabl\
eDigraph\"/>, then the edge\n    is removed directly from <A>digraph</A>. If <\
A>digraph</A> belongs to <Ref\n      Filt=\"IsImmutableDigraph\"/>, the edge i\
s removed from an immutable copy of\n    <A>digraph</A> and this new digraph i\
s returned.<P/>\n\n    Note that if <A>edges</A> is empty, then this operation\
\n    will always return <A>digraph</A> rather than a copy. Also, if any eleme\
nt\n    of <A>edges</A> is invalid (i.e. does not define an edge of <A>digraph\
</A>)\n    then that element will simply be ignored.\n\n    <Example><![CDATA[\
\ngap> D := CycleDigraph(250000);\n<immutable cycle digraph with 250000 vertic\
es>\ngap> D := DigraphRemoveEdges(D, [[250000, 1]]);\n<immutable digraph with \
250000 vertices, 249999 edges>\ngap> D := DigraphMutableCopy(D);\n<mutable dig\
raph with 250000 vertices, 249999 edges>\ngap> new := DigraphRemoveEdges(D, [[\
1, 2], [2, 3], [3, 100]]);\n<mutable digraph with 250000 vertices, 249997 edge\
s>\ngap> new = D;\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\n   \
 <ManSection>\n  <Oper Name=\"DigraphRemoveLoops\" Arg=\"digraph\"/>\n  <Attr \
Name=\"DigraphRemoveLoopsAttr\" Arg=\"digraph\"/>\n  <Returns>A digraph.</Retu\
rns>\n  <Description>\n    If <A>digraph</A> is a digraph, then this operation\
 returns a\n    digraph  constructed from <A>digraph</A> by removing every loo\
p. A loop\n    is an edge with equal source and range.<P/>\n\n    If <A>digrap\
h</A> is immutable, then a new immutable digraph is returned.\n    Otherwise, \
the loops are removed from the mutable digraph <A>digraph</A>\n    in-place.\n\
    <Example><![CDATA[\ngap> D := Digraph([[1, 2, 4], [1, 4], [3, 4], [1, 4, 5\
], [1, 5]]);\n<immutable digraph with 5 vertices, 12 edges>\ngap> DigraphRemov\
eLoops(D);\n<immutable digraph with 5 vertices, 8 edges>\ngap> D := Digraph(Is\
MutableDigraph, [[1, 2], [1]]);\n<mutable digraph with 2 vertices, 3 edges>\ng\
ap> DigraphRemoveLoops(D);\n<mutable digraph with 2 vertices, 2 edges>\ngap> D\
;\n<mutable digraph with 2 vertices, 2 edges>\n]]></Example>\n  </Description>\
\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphRemoveAllMultipleEd\
ges\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphRemoveAllMultipleEdgesAttr\" Ar\
g=\"digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If <A>d\
igraph</A> is a digraph, then this operation returns a\n    digraph  construct\
ed from <A>digraph</A> by removing all multiple edges.\n    The result is the \
largest subdigraph of <A>digraph</A> which does not\n    contain multiple edge\
s.<P/>\n\n    If <A>digraph</A> is immutable, then a new immutable digraph is \
returned.\n    Otherwise, the multiple edges of the mutable digraph <A>digraph\
</A> are\n    removed in-place.\n    <Example><![CDATA[\ngap> D1 := Digraph([[\
1, 2, 3, 2], [1, 1, 3], [2, 2, 2]]);\n<immutable multidigraph with 3 vertices,\
 10 edges>\ngap> D2 := DigraphRemoveAllMultipleEdges(D1);\n<immutable digraph \
with 3 vertices, 6 edges>\ngap> OutNeighbours(D2);\n[ [ 1, 2, 3 ], [ 1, 3 ], [\
 2 ] ]\ngap> D := Digraph(IsMutableDigraph, [[2, 2], [1]]);\n<mutable multidig\
raph with 2 vertices, 3 edges>\ngap> DigraphRemoveAllMultipleEdges(D);\n<mutab\
le digraph with 2 vertices, 2 edges>\ngap> D;\n<mutable digraph with 2 vertice\
s, 2 edges>\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection\
>\n  <Oper Name=\"DigraphReverseEdges\" Arg=\"digraph, edges\"\n    Label=\"fo\
r a digraph and a list of edges\"/>\n  <Oper Name=\"DigraphReverseEdge\" Arg=\
\"digraph, edge\"\n    Label=\"for a digraph and an edge\"/>\n  <Oper Name=\"D\
igraphReverseEdge\" Arg=\"digraph, src, ran\"\n    Label=\"for a digraph, sour\
ce, and range\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If <A\
>digraph</A> is a digraph without multiple edges, and <A>edges</A> is a\n    l\
ist of pairs of vertices of <A>digraph</A> (the entries of each pair\n    corr\
esponding to the source and the range of an edge, respectively),\n    then <C>\
DigraphReverseEdges</C> returns a digraph constructed from\n    <A>digraph</A>\
 by reversing the orientation of every edge specified by\n    <A>edges</A>. If\
 only one edge is to be reversed, then\n    <C>DigraphReverseEdge</C> can be u\
sed instead. In this case, the second\n    argument should just be a single ve\
rtex-pair, or the second and third\n    arguments should be the source and ran\
ge of an edge respectively. <P/>\n\n    Note that even though <A>digraph</A> c\
annot have multiple edges, the\n    output may have multiple edges. <P/>\n\n  \
  If <A>digraph</A> belongs to <Ref Filt=\"IsMutableDigraph\"/>, then the edge\
s\n    are reversed in <A>digraph</A>. If <A>digraph</A> belongs to <Ref\n    \
  Filt=\"IsImmutableDigraph\"/>, an immutable copy of <A>digraph</A> with the\
\n    specified edges reversed is returned.<P/>\n    <Example><![CDATA[\ngap> \
D := DigraphFromDiSparse6String(\".Tg?i@s?t_e?_qEsC\");\n<immutable digraph wi\
th 21 vertices, 8 edges>\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 7 ], [ 1, 8 \
], [ 5, 21 ], [ 7, 19 ], [ 9, 1 ], \n  [ 11, 2 ], [ 21, 1 ] ]\ngap> new := Dig\
raphReverseEdge(D, [7, 19]);\n<immutable digraph with 21 vertices, 8 edges>\ng\
ap> DigraphEdges(new);\n[ [ 1, 2 ], [ 1, 7 ], [ 1, 8 ], [ 5, 21 ], [ 9, 1 ], [\
 11, 2 ], \n  [ 19, 7 ], [ 21, 1 ] ]\ngap> D2 := DigraphMutableCopy(new);;\nga\
p> new := DigraphReverseEdges(D2, [[19, 7]]);;\ngap> D2 = new;\ntrue\ngap> D =\
 new;\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection\
>\n  <Func Name=\"DigraphDisjointUnion\" Arg=\"D1, D2, ...\" Label=\"for an\n \
   arbitrary number of digraphs\"/>\n  <Func Name=\"DigraphDisjointUnion\" Arg\
=\"list\" Label=\"for a list of digraphs\"/>\n  <Returns>A digraph.</Returns>\
\n  <Description>\n    In the first form, if <A>D1</A>, <A>D2</A>, etc. are di\
graphs, then\n    <C>DigraphDisjointUnion</C> returns their disjoint union.\n\
\n    In the second form, if <A>list</A> is a non-empty list of digraphs, then\
\n    <C>DigraphDisjointUnion</C> returns the disjoint union of the digraphs\n\
    contained in the list.  <P/>\n\n    For a disjoint union of digraphs, the \
vertex set is the disjoint union of\n    the vertex sets, and the edge list is\
 the disjoint union of the edge lists.\n    <P/>\n\n    More specifically, for\
 a collection of digraphs <A>D1</A>, <A>D2</A>,\n    <C>...</C>, the disjoint \
union with have\n    <C>DigraphNrVertices(</C><A>D1</A><C>)</C> <C>+</C>\n    \
<C>DigraphNrVertices(</C><A>D2</A><C>)</C> <C>+</C> <C>...</C> vertices.\n    \
The edges of <A>D1</A> will remain unchanged, whilst the edges of the\n    <C>\
i</C>th digraph, <A>D</A><C>[i]</C>, will be changed so that they\n    belong \
to the vertices of the disjoint union corresponding to\n    <A>D</A><C>[i]</C>\
.  In particular, the edges of <A>D</A><C>[i]</C> will\n    have their source \
and range increased by\n    <C>DigraphNrVertices(</C><A>D1</A><C>)</C> <C>+</C\
> <C>...</C> <C>+</C>\n    <C>DigraphNrVertices(</C><A>D</A><C>[i-1])</C>.\n\n\
    <P/>\n\n    Note that previously set <Ref Oper=\"DigraphVertexLabels\"/> w\
ill be lost.<P/>\n\n    If the first digraph <A>D1</A> [<A>list[1]</A>] belong\
s to <Ref\n    Filt=\"IsMutableDigraph\"/>, then <A>D1</A> [<A>list[1]</A>] is\
 modified in\n    place to contain the appropriate vertices and edges. If <A>d\
igraph</A> belongs\n    to <Ref Filt=\"IsImmutableDigraph\"/>, a new immutable\
 digraph containing the\n    appropriate vertices and edges is returned.\n<Exa\
mple><![CDATA[\ngap> D1 := CycleDigraph(3);\n<immutable cycle digraph with 3 v\
ertices>\ngap> OutNeighbours(D1);\n[ [ 2 ], [ 3 ], [ 1 ] ]\ngap> D2 := Complet\
eDigraph(3);\n<immutable complete digraph with 3 vertices>\ngap> OutNeighbours\
(D2);\n[ [ 2, 3 ], [ 1, 3 ], [ 1, 2 ] ]\ngap> union := DigraphDisjointUnion(D1\
, D2);\n<immutable digraph with 6 vertices, 9 edges>\ngap> OutNeighbours(union\
);\n[ [ 2 ], [ 3 ], [ 1 ], [ 5, 6 ], [ 4, 6 ], [ 4, 5 ] ]\n]]></Example>\n  </\
Description>\n</ManSection>\n\n    <ManSection>\n  <Func Name=\"DigraphEdgeUni\
on\" Arg=\"D1, D2, ...\"\n    Label=\"for a positive number of digraphs\"/>\n \
 <Func Name=\"DigraphEdgeUnion\" Arg=\"list\" Label=\"for a list of digraphs\"\
/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    In the first form, i\
f <A>D1</A>, <A>D2</A>, etc. are digraphs, then\n    <C>DigraphEdgeUnion</C> r\
eturns their edge union.\n\n    In the second form, if <A>list</A> is a non-em\
pty list of digraphs, then\n    <C>DigraphEdgeUnion</C> returns the edge union\
 of the digraphs contained\n    in the list.  <P/>\n\n    The vertex set of th\
e edge union of a collection of digraphs is the\n    <E>union</E> of the verte\
x sets, whilst the edge list of the edge union is\n    the <E>concatenation</E\
> of the edge lists.  The number of vertices of the\n    edge union is equal t\
o the <E>maximum</E> number of vertices of one of the\n    digraphs, whilst th\
e number of edges of the edge union will equal the\n    <E>sum</E> of the numb\
er of edges of each digraph. <P/>\n\n    Note that previously set <Ref Oper=\"\
DigraphVertexLabels\"/> will be lost.\n    <P/>\n\n    If the first digraph <A\
>D1</A> [<A>list[1]</A>] belongs to <Ref\n    Filt=\"IsMutableDigraph\"/>, the\
n <A>D1</A> [<A>list[1]</A>] is modified in\n    place to contain the appropri\
ate vertices and edges. If <A>digraph</A> belongs\n    to <Ref Filt=\"IsImmuta\
bleDigraph\"/>, a new immutable digraph containing the\n    appropriate vertic\
es and edges is returned.\n<Example><![CDATA[\ngap> D := CycleDigraph(10);\n<i\
mmutable cycle digraph with 10 vertices>\ngap> DigraphEdgeUnion(D, D);\n<immut\
able multidigraph with 10 vertices, 20 edges>\ngap> D1 := Digraph([[2], [1]]);\
\n<immutable digraph with 2 vertices, 2 edges>\ngap> D2 := Digraph([[2, 3], [2\
], [1]]);\n<immutable digraph with 3 vertices, 4 edges>\ngap> union := Digraph\
EdgeUnion(D1, D2);\n<immutable multidigraph with 3 vertices, 6 edges>\ngap> Ou\
tNeighbours(union);\n[ [ 2, 2, 3 ], [ 1, 2 ], [ 1 ] ]\ngap> union = DigraphByE\
dges(\n> Concatenation(DigraphEdges(D1), DigraphEdges(D2)));\ntrue\n]]></Examp\
le>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Func Name=\"Digra\
phJoin\" Arg=\"D1, D2, ...\"\n    Label=\"for a positive number of digraphs\"/\
>\n  <Func Name=\"DigraphJoin\" Arg=\"list\" Label=\"for a list of digraphs\"/\
>\n  <Returns>A digraph.</Returns>\n  <Description>\n    In the first form, if\
 <A>D1</A>, <A>D2</A>, etc. are digraphs, then\n    <C>DigraphJoin</C> returns\
 their join.\n\n    In the second form, if <A>list</A> is a non-empty list of \
digraphs,\n    then <C>DigraphJoin</C> returns the join of the digraphs contai\
ned in the\n    list. <P/>\n\n    The join of a collection of digraphs <A>D1</\
A>, <A>D2</A>, <C>...</C> is\n    formed by first taking the <Ref Func=\"Digra\
phDisjointUnion\"\n      Label=\"for a list of digraphs\"/> of the collection.\
\n\n    In the disjoint union, if <M>i \\neq j</M> then there are no edges bet\
ween\n    vertices corresponding to digraphs <A>D</A><C>[i]</C> and\n    <A>D<\
/A><C>[j]</C> in the collection; the join is created by including\n    all suc\
h edges.<P/>\n\n    For example, the join of two empty digraphs is a complete \
bipartite\n    digraph.<P/>\n\n    Note that previously set <Ref Oper=\"Digrap\
hVertexLabels\"/> will be lost.\n    <P/>\n\n    If the first digraph <A>D1</A\
> [<A>list[1]</A>] belongs to <Ref\n    Filt=\"IsMutableDigraph\"/>, then <A>D\
1</A> [<A>list[1]</A>] is modified in\n    place to contain the appropriate ve\
rtices and edges. If <A>digraph</A> belongs\n    to <Ref Filt=\"IsImmutableDig\
raph\"/>, a new immutable digraph containing the\n    appropriate vertices and\
 edges is returned.\n<Example><![CDATA[\ngap> D := CompleteDigraph(3);\n<immut\
able complete digraph with 3 vertices>\ngap> IsCompleteDigraph(DigraphJoin(D, \
D));\ntrue\ngap> D2 := CycleDigraph(3);\n<immutable cycle digraph with 3 verti\
ces>\ngap> DigraphJoin(D, D2);\n<immutable digraph with 6 vertices, 27 edges>\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Func \
Name=\"DigraphCartesianProduct\" Arg=\"gr1, gr2, ...\"\n    Label=\"for a posi\
tive number of digraphs\"/>\n  <Func Name=\"DigraphCartesianProduct\" Arg=\"li\
st\"\n    Label=\"for a list of digraphs\"/>\n  <Returns>A digraph.</Returns>\
\n  <Description>\n    In the first form, if <A>gr1</A>, <A>gr2</A>, etc. are \
digraphs, then\n    <C>DigraphCartesianProduct</C> returns a digraph isomorphi\
c to their\n    Cartesian product.\n    <P/>\n\n    In the second form, if <A>\
list</A> is a non-empty list of digraphs,\n    then <C>DigraphCartesianProduct\
</C> returns a digraph isomorphic to the \n    Cartesian product of the digrap\
hs contained in the list.\n    <P/>\n \n    Mathematically, the Cartesian prod\
uct of two digraphs <C>G</C>, <C>H</C>\n    is a digraph with vertex set <C>Ca\
rtesian(DigraphVertices(G),\n    DigraphVertices(H))</C> such that there is an\
 edge from <C>[u, u']</C> to\n    <C>[v, v']</C> iff <C> u = v </C> and there \
is an edge from <C>u'</C> to\n    <C>v'</C> in <C>H</C> or <C> u' = v'</C> and\
 there is an edge from\n    <C>u</C> to <C>v</C> in <C>G</C>.\n    <P/>\n\n   \
 Due to technical reasons, the digraph <C>D</C> returned by\n    <C>DigraphCar\
tesianProduct</C> has vertex set\n    <C>[1 ..  DigraphNrVertices(G)*DigraphNr\
Vertices(H)]</C> instead, and the\n     exact\n    method of encoding pairs of\
 vertices into integers is implementation\n    specific.  The original vertex \
pair can be somewhat regained by using\n    <Ref Attr=\"DigraphCartesianProduc\
tProjections\"/>. In addition,\n    <Ref Oper=\"DigraphVertexLabels\"/> are pr\
eserved: if vertex pair\n    <C>[u,u']</C> was encoded as <C>i</C> then the ve\
rtex label of <C>i</C>\n    will be the pair of vertex labels of <C>u</C> and \
<C>u'</C> i.e.\n    <C>DigraphVertexLabel(D,i) = [DigraphVertexLabel(G,u),\n  \
    DigraphVertexLabel(H,u')]</C>.\n    <P/>\n\n    As the Cartesian product i\
s associative, the Cartesian product of a collection \n    of digraphs <A>gr1<\
/A>, <A>gr2</A>, <C>...</C> is computed in the obvious \n    fashion. \n    <P\
/>\n\n<Example><![CDATA[\ngap> gr := ChainDigraph(4);\n<immutable chain digrap\
h with 4 vertices>\ngap> gr2 := CycleDigraph(3);\n<immutable cycle digraph wit\
h 3 vertices>\ngap> gr3 := DigraphCartesianProduct(gr, gr2);\n<immutable digra\
ph with 12 vertices, 21 edges>\ngap> IsIsomorphicDigraph(gr3, \n> Digraph([[2,\
 5], [3, 6], [4, 7], [8], \n>          [6, 9], [7, 10], [8, 11], [12],\n>     \
     [10, 1], [11, 2], [12, 3], [4]]));\ntrue\n]]></Example>\n  </Description>\
\n</ManSection>\n\n    <ManSection>\n  <Func Name=\"DigraphDirectProduct\" Arg\
=\"gr1, gr2, ...\"\n    Label=\"for a positive number of digraphs\"/>\n  <Func\
 Name=\"DigraphDirectProduct\" Arg=\"list\"\n    Label=\"for a list of digraph\
s\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    In the first form\
, if <A>gr1</A>, <A>gr2</A>, etc. are digraphs, then\n    <C>DigraphDirectProd\
uct</C> returns a digraph isomorphic to their direct\n    product.\n    <P/>\n\
\n    In the second form, if <A>list</A> is a non-empty list of digraphs, then\
\n    <C>DigraphDirectProduct</C> returns a digraph isomorphic to the direct\n\
    product of the digraphs contained in the list.\n    <P/>\n\n    Mathematic\
ally, the direct product of two digraphs <C>G</C>, <C>H</C> is a\n    digraph \
with vertex set <C>Cartesian(DigraphVertices(G),\n    DigraphVertices(H))</C> \
such that there is an edge from <C>[u, u']</C>\n    to <C>[v, v']</C> iff ther\
e is an edge from <C>u</C> to <C>v</C> in\n    <C>G</C> and an edge from <C>u'\
</C> to <C>v'</C> in <C>H</C>. \n    <P/> \n\n    Due to technical reasons, th\
e digraph <C>D</C> returned by\n    <C>DigraphDirectProduct</C> has vertex set\
\n    <C>[1 ..  DigraphNrVertices(G)*DigraphNrVertices(H)]</C> instead, and th\
e\n    exact method of encoding pairs of vertices into integers is implementat\
ion\n    specific.  The original vertex pair can be somewhat regained by using\
\n    <Ref Attr=\"DigraphDirectProductProjections\"/>. In addition\n    <Ref O\
per=\"DigraphVertexLabels\"/> are preserved: if vertex pair\n    <C>[u,u']</C>\
 was encoded as <C>i</C> then the vertex label of <C>i</C>\n    will be the pa\
ir of vertex labels of <C>u</C> and <C>u'</C> i.e.\n    <C>DigraphVertexLabel(\
D,i) = [DigraphVertexLabel(G,u),\n    DigraphVertexLabel(H,u')]</C>.\n    <P/>\
\n\n    As the direct product is associative, the direct product of a collecti\
on \n    of digraphs <A>gr1</A>, <A>gr2</A>, <C>...</C> is computed in the obv\
ious \n    fashion. \n    <P/>\n\n<Example><![CDATA[\ngap> gr := ChainDigraph(\
4);\n<immutable chain digraph with 4 vertices>\ngap> gr2 := CycleDigraph(3);\n\
<immutable cycle digraph with 3 vertices>\ngap> gr3 := DigraphDirectProduct(gr\
, gr2);\n<immutable digraph with 12 vertices, 9 edges>\ngap> IsIsomorphicDigra\
ph(gr3, \n> Digraph([[6], [7], [8], [], \n>          [10], [11], [12], [],\n> \
         [2], [3], [4], []]));\ntrue\n]]></Example>\n  </Description>\n</ManSe\
ction>\n\n    <ManSection>\n  <Attr Name=\"DigraphCartesianProductProjections\
\" Arg=\"digraph\"/>\n  <Returns>A list of transformations.</Returns>\n  <Desc\
ription>\n    If <A>digraph</A> is a Cartesian product digraph, \n    <C>digra\
ph = DigraphCartesianProduct(gr_1, gr_2, ... )</C>, then\n    <C>DigraphCartes\
ianProductProjections</C> returns a list <C>proj</C>\n    such that <C>proj[i]\
</C> is the projection onto the <C>i</C>-th\n    coordinate of the product.\n \
   <P/>\n\n    A projection is an idempotent endomorphism of <A>digraph</A>. I\
f\n    <C>gr1, gr2, ...</C> are all loopless digraphs, then the induced \n    \
subdigraph of <A>digraph</A> on the image of <C>proj[i]</C> is \n    isomorphi\
c to <C>gr_i</C>.\n    <P/>\n\n    Currently this attribute is only set upon c\
reating an immutable \n    digraph via <C>DigraphCartesianProduct</C> and ther\
e is no way \n    of calculating it for other digraphs.\n    <P/>\n\n    For m\
ore information see\n    <Ref Func=\"DigraphCartesianProduct\" Label=\"for a l\
ist of digraphs\"/> \n\n    <Example><![CDATA[\ngap> D := DigraphCartesianProd\
uct(ChainDigraph(3), CycleDigraph(4),\n> Digraph([[2], [2]]));;\ngap> HasDigra\
phCartesianProductProjections(D);\ntrue\ngap> proj := DigraphCartesianProductP\
rojections(D);; Length(proj);\n3\ngap> IsIdempotent(proj[2]);\ntrue\ngap> Rank\
OfTransformation(proj[3]);\n2\ngap> S := ImageSetOfTransformation(proj[2]);;\n\
gap> IsIsomorphicDigraph(CycleDigraph(4), InducedSubdigraph(D, S));\ntrue\n]]>\
</Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\
\"DigraphDirectProductProjections\" Arg=\"digraph\"/>\n  <Returns>A list of tr\
ansformations.</Returns>\n  <Description>\n    If <A>digraph</A> is a direct p\
roduct digraph, \n    <C>digraph = DigraphDirectProduct(gr_1, gr_2, ... )</C>,\
 then\n    <C>DigraphDirectProductProjections</C> returns a list <C>proj</C>\n\
    such that <C>proj[i]</C> is the projection onto the <C>i</C>-th\n    coord\
inate of the product.\n    <P/>\n\n    A projection is an idempotent endomorph\
ism of <A>digraph</A>. If\n    <C>gr1, gr2, ...</C> are all loopless digraphs,\
 then the image \n    of <A>digraph</A> under <C>proj[i]</C> is isomorphic to \
<C>gr_i</C>.\n    <P/>\n\n    Currently this attribute is only set upon creati\
ng an immutable\n    digraph via <C>DigraphDirectProduct</C> and there is no w\
ay of \n    calculating it for other digraphs.\n    <P/>\n\n    For more infor\
mation, see\n    <Ref Func=\"DigraphDirectProduct\" Label=\"for a list of digr\
aphs\"/> \n\n    <Example><![CDATA[\ngap> D := DigraphDirectProduct(ChainDigra\
ph(3), CycleDigraph(4),\n> Digraph([[2], [2]]));;\ngap> HasDigraphDirectProduc\
tProjections(D);\ntrue\ngap> proj := DigraphDirectProductProjections(D);; Leng\
th(proj);\n3\ngap> IsIdempotent(proj[2]);\ntrue\ngap> RankOfTransformation(pro\
j[3]);\n2\ngap> P := DigraphRemoveAllMultipleEdges(\n> ReducedDigraph(OnDigrap\
hs(D, proj[2])));; \ngap> IsIsomorphicDigraph(CycleDigraph(4), P);\ntrue\n]]><\
/Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\
\"LineDigraph\" Arg=\"digraph\"/>\n  <Oper Name=\"EdgeDigraph\" Arg=\"digraph\
\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    Given a digraph <A\
>digraph</A>, the operation returns the digraph\n    obtained by associating a\
 vertex with each edge of <A>digraph</A>, and\n    creating an edge from a ver\
tex <K>v</K> to a vertex <K>u</K> if and only\n    if the terminal vertex of t\
he edge associated with <K>v</K> is the start\n    vertex of the edge associat\
ed with <K>u</K>.<P/>\n\n    Note that the returned digraph is always a new im\
mutable digraph, and the\n    argument <A>digraph</A> is never modified.\n    \
<Example><![CDATA[\ngap> LineDigraph(CompleteDigraph(3));\n<immutable digraph \
with 6 vertices, 12 edges>\ngap> LineDigraph(ChainDigraph(3));\n<immutable dig\
raph with 2 vertices, 1 edge>\n]]></Example>\n  </Description>\n</ManSection>\
\n\n    <ManSection>\n  <Oper Name=\"LineUndirectedDigraph\" Arg=\"digraph\"/>\
\n  <Oper Name=\"EdgeUndirectedDigraph\" Arg=\"digraph\"/>\n  <Returns>A digra\
ph.</Returns>\n  <Description>\n    Given a symmetric digraph <A>digraph</A>, \
the operation returns the\n    symmetric digraph obtained by associating a ver\
tex with each edge of\n    <A>digraph</A>, ignoring directions and multiplicit\
es, and adding an edge\n    between two vertices if and only if the correspond\
ing edges have a vertex in\n    common.<P/>\n\n    Note that the returned digr\
aph is always a new immutable digraph, and the\n    argument <A>digraph</A> is\
 never modified.\n    <Example><![CDATA[\ngap> LineUndirectedDigraph(CompleteD\
igraph(3));\n<immutable digraph with 3 vertices, 6 edges>\ngap> LineUndirected\
Digraph(DigraphSymmetricClosure(ChainDigraph(3)));\n<immutable digraph with 2 \
vertices, 2 edges>\n]]></Example>\n  </Description>\n</ManSection>\n\n    <Man\
Section>\n  <Oper Name=\"DoubleDigraph\" Arg=\"digraph\"/>\n  <Returns>A digra\
ph.</Returns>\n  <Description>\n    Let <A>digraph</A> be a digraph with verte\
x set <C>V</C>. This function\n    returns the double digraph of <A>digraph</A\
>. The vertex set of the double\n    digraph is the orginal vertex set togethe\
r with a duplicate. The edges are\n    <C>[u_1, v_2]</C> and <C>[u_2, v_1]</C>\
 if and only if <C>[u, v]</C> is an\n    edge in <A>digraph</A>, together with\
 the original edges and their\n    duplicates.<P/>\n\n    If <A>digraph</A> is\
 mutable, then <A>digraph</A> is modified in-place. If\n    <A>digraph</A> is \
immutable, then a new immutable digraph constructed as\n    described above is\
 returned.\n    <Example><![CDATA[\ngap> gamma := Digraph([[2], [3], [1]]);\n<\
immutable digraph with 3 vertices, 3 edges>\ngap> DoubleDigraph(gamma);\n<immu\
table digraph with 6 vertices, 12 edges>\n]]></Example>\n  </Description>\n</M\
anSection>\n\n    <ManSection>\n  <Oper Name=\"BipartiteDoubleDigraph\" Arg=\"\
digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    Let <A>digr\
aph</A> be a digraph with vertex set <C>V</C>. This function\n    returns the \
bipartite double digraph of <A>digraph</A>. The vertex set of\n    the double \
digraph is the original vertex set together with a duplicate. The\n    edges a\
re <C>[u_1, v_2]</C> and <C>[u_2, v_1]</C> if and only if <C>[u,\n      v]</C>\
 is an edge in <A>digraph</A>. The resulting graph is bipartite,\n    since th\
e orignal edges are not included in the resulting digraph.<P/>\n\n    If <A>di\
graph</A> is mutable, then <A>digraph</A> is modified in-place. If\n    <A>dig\
raph</A> is immutable, then a new immutable digraph constructed as\n    descri\
bed above is returned.\n    <Example><![CDATA[\ngap> gamma := Digraph([[2], [3\
], [1]]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> BipartiteDoubleD\
igraph(gamma);\n<immutable digraph with 6 vertices, 6 edges>\n]]></Example>\n \
 </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphAddA\
llLoops\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphAddAllLoopsAttr\" Arg=\"dig\
raph\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    For a digraph \
<A>digraph</A> this operation returns a new digraph constructed\n    from <A>d\
igraph</A>, such that a loop is added for every vertex which did not\n    have\
 a loop in <A>digraph</A>.<P/>\n\n    If <A>digraph</A> is immutable, then a n\
ew immutable digraph is returned.\n    Otherwise, the loops are added to the l\
oopless vertices of the mutable digraph\n    <A>digraph</A> in-place.\n    <Ex\
ample><![CDATA[\ngap> D := EmptyDigraph(13);\n<immutable empty digraph with 13\
 vertices>\ngap> D := DigraphAddAllLoops(D);\n<immutable reflexive digraph wit\
h 13 vertices, 13 edges>\ngap> OutNeighbours(D);\n[ [ 1 ], [ 2 ], [ 3 ], [ 4 ]\
, [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9 ], \n  [ 10 ], [ 11 ], [ 12 ], [ 13 ] ]\ngap\
> D := Digraph([[1, 2, 3], [1, 3], [1]]);\n<immutable digraph with 3 vertices,\
 6 edges>\ngap> D := DigraphAddAllLoops(D);\n<immutable reflexive digraph with\
 3 vertices, 8 edges>\ngap> OutNeighbours(D);\n[ [ 1, 2, 3 ], [ 1, 3, 2 ], [ 1\
, 3 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3\
 vertices, 3 edges>\ngap> DigraphAddAllLoops(D);\n<mutable digraph with 3 vert\
ices, 6 edges>\ngap> D;\n<mutable digraph with 3 vertices, 6 edges>\n]]></Exam\
ple>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"Dist\
anceDigraph\" Arg=\"digraph, i\"\n        Label=\"for digraph and int\"/>\n  <\
Oper Name=\"DistanceDigraph\" Arg=\"digraph, list\"\n        Label=\"for digra\
ph and list\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    The fir\
st argument is a digraph, the second argument is a non-negative\n    integer o\
r a list of positive integers. This operation returns a digraph on\n    the sa\
me set of vertices as <A>digraph</A>, with two vertices being adjacent\n    if\
 and only if the distance between them in <A>digraph</A> equals <A>i</A>\n    \
or is a number in <A>list</A>.  See <Ref Oper=\"DigraphShortestDistance\"\n   \
 Label=\"for a digraph and two vertices\"/>. <P/>\n\n    If <A>digraph</A> is \
mutable, then <A>digraph</A> is modified in-place. If\n    <A>digraph</A> is i\
mmutable, then a new immutable digraph constructed as\n    described above is \
returned.\n    <Example><![CDATA[\ngap> digraph := DigraphFromSparse6String(\n\
> \":]n?AL`BC_DEbEF`GIaGHdIJeGKcKL_@McDHfILaBJfHMjKM\");\n<immutable digraph w\
ith 30 vertices, 90 edges>\ngap> DistanceDigraph(digraph, 1);\n<immutable digr\
aph with 30 vertices, 90 edges>\ngap> DistanceDigraph(digraph, [1, 2]);\n<immu\
table digraph with 30 vertices, 270 edges>\n]]></Example>\n  </Description>\n<\
/ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphClosure\" Arg=\"digrap\
h, k\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    Given a symmet\
ric loopless digraph with no multiple edges <A>digraph</A>,\n    the <E><A>k</\
A>-closure of <A>digraph</A></E> is defined to be the unique\n    smallest sym\
metric loopless digraph <C>C</C> with no multiple edges on the\n    vertices o\
f <A>digraph</A> that contains all the edges of <A>digraph</A>\n    and satsif\
ies the property that the sum of the degrees of every two\n    non-adjacenct v\
ertices in <C>C</C> is less than <A>k</A>. See <Ref\n    Prop=\"IsSymmetricDig\
raph\"/>, <Ref Prop=\"DigraphHasLoops\"/>, <Ref\n    Prop=\"IsMultiDigraph\"/>\
, and <Ref Oper=\"OutDegreeOfVertex\"/>. <P/>\n\n    The operation <C>DigraphC\
losure</C> returns the <A>k</A>-closure of\n    <A>digraph</A>.\n    <Example>\
<![CDATA[\ngap> D := CompleteDigraph(6);\n<immutable complete digraph with 6 v\
ertices>\ngap> D := DigraphRemoveEdges(D, [[1, 2], [2, 1]]);\n<immutable digra\
ph with 6 vertices, 28 edges>\ngap> closure := DigraphClosure(D, 6);\n<immutab\
le digraph with 6 vertices, 30 edges>\ngap> IsCompleteDigraph(closure);\ntrue\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper \
Name=\"DigraphMycielskian\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphMycielski\
anAttr\" Arg=\"digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n\
    If <A>digraph</A> is a symmetric digraph, then\n    <C>DigraphMycielskian<\
/C> returns the Mycielskian of <A>digraph</A>.<P/>\n    \n    The Mycielskian \
of a symmetric digraph is a larger symmetric digraph\n    constructed from it,\
 which has a larger chromatic number. For further\n    information, see <URL>h\
ttps://en.wikipedia.org/wiki/Mycielskian</URL>.<P/>\n\n    If <A>digraph</A> i\
s immutable, then a new immutable digraph is returned.\n    Otherwise, the mut\
able digraph <A>digraph</A> is changed in-place into\n    its Mycielskian.<P/>\
\n\n    <Example><![CDATA[\ngap> D := CycleDigraph(2);\n<immutable cycle digra\
ph with 2 vertices>\ngap> ChromaticNumber(D);\n2\ngap> D := DigraphMycielskian\
(D);\n<immutable digraph with 5 vertices, 10 edges>\ngap> ChromaticNumber(D);\
\n3\ngap> D := DigraphMycielskian(D);\n<immutable digraph with 11 vertices, 40\
 edges>\ngap> ChromaticNumber(D);\n4\ngap> D := CompleteBipartiteDigraph(IsMut\
able, 2, 3);\n<mutable digraph with 5 vertices, 12 edges>\ngap> DigraphMyciels\
kian(D);\n<mutable digraph with 11 vertices, 46 edges>\ngap> D;\n<mutable digr\
aph with 11 vertices, 46 edges>\n]]></Example>\n  </Description>\n</ManSection\
>\n\n  </Section>\n\n  <Section><Heading>Random digraphs</Heading>\n    <ManSe\
ction>\n  <Oper Name=\"RandomDigraph\" Arg=\"[filt, ]n[, p]\"/>\n  <Returns>A \
digraph.</Returns>\n  <Description>\n    If the optional first argument <A>fil\
t</A> is present, then this should\n    specify the category or representation\
 the digraph being created will\n    belong to. For example, if <A>filt</A> is\
 <Ref Filt=\"IsMutableDigraph\"/>,\n    then the digraph being created will be\
 mutable, if <A>filt</A> is <Ref\n    Filt=\"IsImmutableDigraph\"/>, then the \
digraph will be immutable. \n    If the optional first argument <A>filt</A> is\
 not present, then <Ref\n      Filt=\"IsImmutableDigraph\"/> is used by defaul\
t.<P/>\n\n    If <A>n</A> is a positive integer, then this function returns a \
random\n    digraph with <A>n</A> vertices and without multiple edges. The res\
ult\n    may or may not have loops.<P/>\n\n    If the optional second argument\
 <A>p</A> is a float with value\n    <M>0 \\leq </M> <A> p </A> <M> \\leq 1</M\
>, then an edge will exist between each\n    pair of vertices with probability\
 approximately <A>p</A>.\n    If <A>p</A> is not specified, then a random prob\
ability will be assumed\n    (chosen with uniform probability).\n    <Log><![C\
DATA[\ngap> RandomDigraph(1000);\n<immutable digraph with 1000 vertices, 36444\
4 edges>\ngap> RandomDigraph(10000, 0.023);\n<immutable digraph with 10000 ver\
tices, 2300438 edges>\ngap> RandomDigraph(IsMutableDigraph, 1000, 1 / 2);\n<mu\
table digraph with 1000 vertices, 499739 edges>\n]]></Log>\n  </Description>\n\
</ManSection>\n\n    <ManSection>\n  <Oper Name=\"RandomMultiDigraph\" Arg=\"n\
[, m]\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If <A>n</A> i\
s a positive integer, then this function returns a random\n    digraph with <A\
>n</A> vertices. If the optional second argument\n    <A>m</A> is a positive i\
nteger, then the digraph will have <A>m</A>\n    edges. If <A>m</A> is not spe\
cified, then the number of edges will be\n    chosen randomly (with uniform pr\
obability) from the range\n    <C>[1 .. </C><M>{n \\choose 2}</M><C>]</C>.\n  \
  <P/>\n\n    The method used by this function chooses each edge from the set \
of\n    all possible edges with uniform probability. No effort is made to avoi\
d\n    creating multiple edges, so it is possible (but not guaranteed) that th\
e\n    result will have multiple edges. The result may or may not have loops.<\
P/>\n    <Log><![CDATA[\ngap> RandomMultiDigraph(1000);\n<immutable multidigra\
ph with 1000 vertices, 216659 edges>\ngap> RandomMultiDigraph(1000, 950);\n<im\
mutable multidigraph with 1000 vertices, 950 edges>\n]]></Log>\n  </Descriptio\
n>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"RandomTournament\" Arg=\
\"[filt, ]n\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If the \
optional first argument <A>filt</A> is present, then this should\n    specify \
the category or representation the digraph being created will\n    belong to. \
For example, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then the\
 digraph being created will be mutable, if <A>filt</A> is <Ref\n    Filt=\"IsI\
mmutableDigraph\"/>, then the digraph will be immutable. \n    If the optional\
 first argument <A>filt</A> is not present, then <Ref\n      Filt=\"IsImmutabl\
eDigraph\"/> is used by default.<P/>\n\n    If <A>n</A> is a non-negative inte\
ger, this function returns a random\n    tournament with <A>n</A> vertices. Se\
e <Ref Prop=\"IsTournament\"/>. <P/>\n    <Log><![CDATA[\ngap> RandomTournamen\
t(10);\n<immutable tournament with 10 vertices>\ngap> RandomTournament(IsMutab\
leDigraph, 10);\n<mutable digraph with 1000 vertices, 500601 edges>\n]]></Log>\
\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"RandomLa\
ttice\" Arg=\"n\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If \
the optional first argument <A>filt</A> is present, then this should\n    spec\
ify the category or representation the digraph being created will\n    belong \
to. For example, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then\
 the digraph being created will be mutable, if <A>filt</A> is <Ref\n    Filt=\
\"IsImmutableDigraph\"/>, then the digraph will be immutable. \n    If the opt\
ional first argument <A>filt</A> is not present, then <Ref\n      Filt=\"IsImm\
utableDigraph\"/> is used by default.<P/>\n\n    If <A>n</A> is a positive int\
eger, this function return a random lattice\n    with <C>m</C> vertices, where\
 it is guaranteed that <C>m</C> is between\n    <A>n</A> and <C>2 * <A>n</A></\
C>. See <Ref Prop=\"IsLatticeDigraph\"/>. <P/>\n    <Log><![CDATA[\ngap> Rando\
mLattice(10);\n<immutable lattice digraph with 10 vertices, 39 edges>\ngap> Ra\
ndomLattice(IsMutableDigraph, 10);\n<mutable digraph with 12 vertices, 52 edge\
s>\n]]></Log>\n  </Description>\n</ManSection>\n\n  </Section>\n\n  <Section><\
Heading>Standard examples</Heading>\n    <ManSection>\n  <Oper Name=\"ChainDig\
raph\" Arg=\"[filt, ]n\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n\
    If <A>n</A> is a positive integer, this function returns a chain\n    with\
 <A>n</A> vertices and <C><A>n</A> - 1</C> edges.\n    Specifically,\n    for \
each vertex <C>i</C> (with <C>i</C> &lt; <C>n</C>), there is a directed\n    e\
dge with source <C>i</C> and range <C>i + 1</C>. <P/>\n\n    If the optional f\
irst argument <A>filt</A> is present, then this should\n    specify the catego\
ry or representation the digraph being created will\n    belong to. For exampl\
e, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then the digraph b\
eing created will be mutable, if <A>filt</A> is <Ref\n    Filt=\"IsImmutableDi\
graph\"/>, then the digraph will be immutable. \n    If the optional first arg\
ument <A>filt</A> is not present, then <Ref\n      Filt=\"IsImmutableDigraph\"\
/> is used by default.<P/>\n\n    The <Ref Oper=\"DigraphReflexiveTransitiveCl\
osure\"/> of a chain represents a\n    total order.\n    <Example><![CDATA[\ng\
ap> ChainDigraph(42);\n<immutable chain digraph with 42 vertices>\ngap> ChainD\
igraph(IsMutableDigraph, 10);\n<mutable digraph with 10 vertices, 9 edges>\n]]\
></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name\
=\"CompleteDigraph\" Arg=\"[filt, ]n\"/>\n  <Returns>A digraph.</Returns>\n  <\
Description>\n    If <A>n</A> is a non-negative integer, this function returns\
 the complete\n    digraph with <A>n</A> vertices. See <Ref Prop=\"IsCompleteD\
igraph\"/>. <P/>\n\n    If the optional first argument <A>filt</A> is present,\
 then this should\n    specify the category or representation the digraph bein\
g created will\n    belong to. For example, if <A>filt</A> is <Ref Filt=\"IsMu\
tableDigraph\"/>,\n    then the digraph being created will be mutable, if <A>f\
ilt</A> is <Ref\n    Filt=\"IsImmutableDigraph\"/>, then the digraph will be i\
mmutable. \n    If the optional first argument <A>filt</A> is not present, the\
n <Ref\n      Filt=\"IsImmutableDigraph\"/> is used by default.\n    <Example>\
<![CDATA[\ngap> CompleteDigraph(20);\n<immutable complete digraph with 20 vert\
ices>\ngap> CompleteDigraph(IsMutableDigraph, 10);\n<mutable digraph with 10 v\
ertices, 90 edges>\n]]></Example>\n  </Description>\n</ManSection>\n\n    <Man\
Section>\n  <Oper Name=\"CompleteBipartiteDigraph\" Arg=\"[filt, ]m, n\"/>\n  \
<Returns>A digraph.</Returns>\n  <Description>\n    A complete bipartite digra\
ph is a digraph whose vertices\n    can be partitioned into two non-empty vert\
ex sets, such there exists\n    a unique edge with source <C>i</C> and range <\
C>j</C> if and only if\n    <C>i</C> and <C>j</C> lie in different vertex sets\
. <P/>\n\n    If <A>m</A> and <A>n</A> are positive integers, this function\n \
   returns the complete bipartite digraph with vertex sets of sizes\n    <A>m<\
/A> (containing the vertices <C>[1 .. m]</C>) and\n    <A>n</A> (containing th\
e vertices <C>[m + 1 .. m + n]</C>).\n    <P/>\n\n    If the optional first ar\
gument <A>filt</A> is present, then this should\n    specify the category or r\
epresentation the digraph being created will\n    belong to. For example, if <\
A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then the digraph being cr\
eated will be mutable, if <A>filt</A> is <Ref\n    Filt=\"IsImmutableDigraph\"\
/>, then the digraph will be immutable. \n    If the optional first argument <\
A>filt</A> is not present, then <Ref\n      Filt=\"IsImmutableDigraph\"/> is u\
sed by default.\n\n    <Example><![CDATA[\ngap> CompleteBipartiteDigraph(2, 3)\
;\n<immutable complete bipartite digraph with bicomponent sizes 2 and 3>\ngap>\
 CompleteBipartiteDigraph(IsMutableDigraph, 3, 2);\n<mutable digraph with 5 ve\
rtices, 12 edges>\n]]></Example>\n  </Description>\n</ManSection>\n\n      <Ma\
nSection>\n    <Oper Name=\"CompleteMultipartiteDigraph\" Arg = \"[filt, ]orde\
rs\"/>\n    <Returns>A digraph.</Returns>\n    <Description>\n      For a list\
 <A>orders</A> of <C>n</C> positive integers,\n      this function returns the\
 digraph containing <C>n</C> independent sets\n      of vertices of orders <C>\
[<A>l</A>[1] .. <A>l</A>[n]]</C>. Moreover,\n      each vertex is adjacent to \
every other not contained in the\n      same independent set.\n      <P/>\n\n \
     If the optional first argument <A>filt</A> is present, then this should\n\
      specify the category or representation the digraph being created will\n \
     belong to. For example, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/\
>,\n      then the digraph being created will be mutable, if <A>filt</A> is <R\
ef\n      Filt=\"IsImmutableDigraph\"/>, then the digraph will be immutable. \
\n      If the optional first argument <A>filt</A> is not present, then <Ref\n\
        Filt=\"IsImmutableDigraph\"/> is used by default.\n      <Example><![C\
DATA[\ngap> CompleteMultipartiteDigraph([5, 4, 2]);\n<immutable complete multi\
partite digraph with 11 vertices, 76 edges>\ngap> CompleteMultipartiteDigraph(\
IsMutableDigraph, [5, 4, 2]);\n<mutable digraph with 11 vertices, 76 edges>\n]\
]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Nam\
e=\"CycleDigraph\" Arg=\"[filt, ]n\"/>\n  <Returns>A digraph.</Returns>\n  <De\
scription>\n    If <A>n</A> is a positive integer, this function returns a <E>\
cycle</E>\n    digraph with <A>n</A> vertices and <A>n</A> edges. Specifically\
,\n    for each vertex <C>i</C> (with <C>i</C> &lt; <C>n</C>), there is a dire\
cted\n    edge with source <C>i</C> and range <C>i + 1</C>. In addition, there\
 is\n    an edge with source <C>n</C> and range <C>1</C>. <P/>\n\n    If the o\
ptional first argument <A>filt</A> is present, then this should\n    specify t\
he category or representation the digraph being created will\n    belong to. F\
or example, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then the \
digraph being created will be mutable, if <A>filt</A> is <Ref\n    Filt=\"IsIm\
mutableDigraph\"/>, then the digraph will be immutable. \n    If the optional \
first argument <A>filt</A> is not present, then <Ref\n    Filt=\"IsImmutableDi\
graph\"/> is used by default.\n  <Example><![CDATA[\ngap> CycleDigraph(1);\n<i\
mmutable digraph with 1 vertex, 1 edge>\ngap> CycleDigraph(123);\n<immutable c\
ycle digraph with 123 vertices>\ngap> CycleDigraph(IsMutableDigraph, 10);\n<mu\
table digraph with 10 vertices, 10 edges>\n]]></Example>\n  </Description>\n</\
ManSection>\n\n    <ManSection>\n  <Oper Name=\"EmptyDigraph\" Arg=\"[filt, ]n\
\"/>\n  <Oper Name=\"NullDigraph\" Arg=\"[filt, ]n\"/>\n  <Returns>A digraph.<\
/Returns>\n  <Description>\n    If <A>n</A> is a non-negative integer, this fu\
nction returns the\n    <E>empty</E> or <E>null</E> digraph with <A>n</A> vert\
ices. An empty\n    digraph is one with no edges.\n    <P/>\n      \n    If th\
e optional first argument <A>filt</A> is present, then this should\n    specif\
y the category or representation the digraph being created will\n    belong to\
. For example, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then t\
he digraph being created will be mutable, if <A>filt</A> is <Ref\n    Filt=\"I\
sImmutableDigraph\"/>, then the digraph will be immutable. \n    If the option\
al first argument <A>filt</A> is not present, then <Ref\n      Filt=\"IsImmuta\
bleDigraph\"/> is used by default.<P/>\n\n    <C>NullDigraph</C> is a synonym \
for <C>EmptyDigraph</C>.\n\n    <Example><![CDATA[\ngap> EmptyDigraph(20);\n<i\
mmutable empty digraph with 20 vertices>\ngap> NullDigraph(10);\n<immutable em\
pty digraph with 10 vertices>\ngap> EmptyDigraph(IsMutableDigraph, 10);\n<muta\
ble empty digraph with 10 vertices>]]></Example>\n  </Description>\n</ManSecti\
on>\n\n    <ManSection>\n  <Oper Name=\"JohnsonDigraph\" Arg=\"[filt, ]n, k\"/\
>\n  <Returns>A digraph.</Returns>\n  <Description>\n    If <A>n</A> and <A>k<\
/A> are non-negative integers, then this operation\n    returns a symmetric di\
graph which corresponds to the undirected <E>Johnson\n    graph</E> <M>J(n, k)\
</M>. <P/>\n\n    If the optional first argument <A>filt</A> is present, then \
this should\n    specify the category or representation the digraph being crea\
ted will\n    belong to. For example, if <A>filt</A> is <Ref Filt=\"IsMutableD\
igraph\"/>,\n    then the digraph being created will be mutable, if <A>filt</A\
> is <Ref\n    Filt=\"IsImmutableDigraph\"/>, then the digraph will be immutab\
le. \n    If the optional first argument <A>filt</A> is not present, then <Ref\
\n      Filt=\"IsImmutableDigraph\"/> is used by default.<P/>\n\n    The <E>Jo\
hnson graph</E> <M>J(n, k)</M> has vertices given by all the\n    <A>k</A>-sub\
sets of the range <C>[1 .. <A>n</A>]</C>, and two vertices are\n      connecte\
d by an edge iff their intersection has size <M><A>k</A> - 1</M>.\n\n    <Exam\
ple><![CDATA[\ngap> gr := JohnsonDigraph(3, 1);\n<immutable symmetric digraph \
with 3 vertices, 6 edges>\ngap> OutNeighbours(gr);\n[ [ 2, 3 ], [ 1, 3 ], [ 1,\
 2 ] ]\ngap> gr := JohnsonDigraph(4, 2);\n<immutable symmetric digraph with 6 \
vertices, 24 edges>\ngap> OutNeighbours(gr);\n[ [ 2, 3, 4, 5 ], [ 1, 3, 4, 6 ]\
, [ 1, 2, 5, 6 ], [ 1, 2, 5, 6 ], \n  [ 1, 3, 4, 6 ], [ 2, 3, 4, 5 ] ]\ngap> J\
ohnsonDigraph(1, 0);\n<immutable empty digraph with 1 vertex>\ngap> JohnsonDig\
raph(IsMutableDigraph, 1, 0);\n<mutable empty digraph with 1 vertex>\n]]></Exa\
mple>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"Pet\
ersenGraph\" Arg=\"[filt]\"/>\n  <Returns>A digraph.</Returns>\n  <Description\
>\n\n    From <URL>https://en.wikipedia.org/wiki/Petersen_graph</URL>:<P/>\n\n\
    <Q>The Petersen graph is an undirected graph with 10 vertices and 15 edges\
.\n    It is a small graph that serves as a useful example and counterexample \
for\n    many problems in graph theory. The Petersen graph is named after Juli\
us\n    Petersen, who in 1898 constructed it to be the smallest bridgeless cub\
ic\n    graph with no three-edge-coloring.</Q><P/>\n    \n    If the optional \
first argument <A>filt</A> is present, then this should\n    specify the categ\
ory or representation the digraph being created will\n    belong to. For examp\
le, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\"/>,\n    then the digraph \
being created will be mutable, if <A>filt</A> is <Ref\n    Filt=\"IsImmutableD\
igraph\"/>, then the digraph will be immutable. \n    If the optional first ar\
gument <A>filt</A> is not present, then <Ref\n      Filt=\"IsImmutableDigraph\
\"/> is used by default.<P/>\n\n    See also <Ref Oper=\"GeneralisedPetersenGr\
aph\"/>.\n\n<Example><![CDATA[\ngap> ChromaticNumber(PetersenGraph());\n3\ngap\
> PetersenGraph(IsMutableDigraph);\n<mutable digraph with 10 vertices, 30 edge\
s>\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Ope\
r Name=\"GeneralisedPetersenGraph\" Arg=\"[filt, ]n, k\"/>\n  <Returns>A digra\
ph.</Returns>\n  <Description>\n    If <A>n</A> is a positive integer and <A>k\
</A> is a non-negative\n    integer less than <C><A>n</A> / 2</C>, then this o\
peration returns\n    the <E>generalised Petersen graph</E> <M>GPG(<A>n</A>, k\
)</M>. <P/>\n\n    From\n    <URL>https://en.wikipedia.org/wiki/Generalized_Pe\
tersen_graph</URL>:\n    <P/>\n\n    <Q>The generalized Petersen graphs are a \
family of cubic\n    graphs formed by connecting the vertices of a regular pol\
ygon to the\n    corresponding vertices of a star polygon. They include the Pe\
tersen graph\n    and generalize one of the ways of constructing the Petersen \
graph. The\n    generalized Petersen graph family was introduced in 1950 by H.\
 S. M.\n    Coxeter and was given its name in 1969 by Mark Watkins.</Q>\n    <\
P/>\n\n    If the optional first argument <A>filt</A> is present, then this sh\
ould\n    specify the category or representation the digraph being created wil\
l\n    belong to. For example, if <A>filt</A> is <Ref Filt=\"IsMutableDigraph\
\"/>,\n    then the digraph being created will be mutable, if <A>filt</A> is <\
Ref\n    Filt=\"IsImmutableDigraph\"/>, then the digraph will be immutable. \n\
    If the optional first argument <A>filt</A> is not present, then <Ref\n    \
  Filt=\"IsImmutableDigraph\"/> is used by default.<P/>\n\n    See also <Ref O\
per=\"PetersenGraph\"/>.\n\n<Example><![CDATA[\ngap> GeneralisedPetersenGraph(\
7, 2);\n<immutable symmetric digraph with 14 vertices, 42 edges>\ngap> General\
isedPetersenGraph(40, 1);\n<immutable symmetric digraph with 80 vertices, 240 \
edges>\ngap> D := GeneralisedPetersenGraph(5, 2);\n<immutable symmetric digrap\
h with 10 vertices, 30 edges>\ngap> IsIsomorphicDigraph(D, PetersenGraph());\n\
true\ngap> GeneralisedPetersenGraph(IsMutableDigraph, 9, 4);\n<mutable digraph\
 with 18 vertices, 54 edges>\n]]></Example>\n  </Description>\n</ManSection>\n\
\n  </Section>\n\n</Chapter>\n <!-- creating -->\n  <Chapter Label=\"Operators\
\"><Heading>Operators</Heading>\n\n  <Section><Heading>Operators for digraphs<\
/Heading>\n    <List>\n     <Mark><C><A>digraph1</A> = <A>digraph2</A></C></Ma\
rk>\n     <Item>\n       <Index Key=\"=\"><C>=</C> (for digraphs)</Index>\n   \
    returns <K>true</K> if <A>digraph1</A> and <A>digraph2</A> have the same\n\
       vertices, and <C>DigraphEdges(<A>digraph1</A>) =\n         DigraphEdges\
(<A>digraph2</A>)</C>, up to some re-ordering of the edge\n       lists. <P/>\
\n\n       Note that this operator does not compare the vertex labels\n       \
of <A>digraph1</A> and <A>digraph2</A>.\n     </Item>\n\n     <Mark><C><A>digr\
aph1</A> &lt; <A>digraph2</A></C></Mark>\n     <Item>\n       <Index Key=\"&lt\
;\"><C>&lt;</C> (for digraphs)</Index>\n\n       This operator returns <K>true\
</K> if one of the following holds:\n\n       <List>\n         <Item>\n       \
    The number <M>n_1</M> of vertices in <A>digraph1</A> is less than\n       \
    the number <M>n_2</M> of vertices in <A>digraph2</A>;\n         </Item>\n \
        <Item>\n           <M>n_1 = n_2</M>, and the number <M>m_1</M> of edge\
s in\n           <A>digraph1</A> is less than the number <M>m_2</M> of edges i\
n\n           <A>digraph2</A>;\n         </Item>\n         <Item>\n           \
<M>n_1 = n_2</M>, <M>m_1 = m_2</M>, and\n           <C>DigraphEdges(<A>digraph\
1</A>)</C> is less than\n           <C>DigraphEdges(<A>digraph2</A>)</C> after\
 having both of these sets\n           have been sorted with respect to the le\
xicographical order.\n         </Item>\n       </List>\n     </Item>\n   </Lis\
t>\n\n   <ManSection>\n  <Oper Name=\"IsSubdigraph\" Arg=\"super, sub\"/>\n  <\
Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    If <A>sup\
er</A> and <A>sub</A> are digraphs, then this operation returns\n    <K>true</\
K> if <A>sub</A> is a subdigraph of <A>super</A>, and <K>false</K>\n    if it \
is not. <P/>\n\n    A digraph <A>sub</A> is a <E>subdigraph</E> of a digraph <\
A>super</A> if\n    <A>sub</A> and <A>super</A> share the same number of verti\
ces, and the\n    collection of edges of <A>super</A> (including repeats) cont\
ains the\n    collection of edges of <A>sub</A> (including repeats).  <P/>\n\n\
    In other words, <A>sub</A> is a subdigraph of <A>super</A> if and only if\
\n    <C>DigraphNrVertices(<A>sub</A>) = DigraphNrVertices(<A>super</A>)</C>, \
and\n    for each pair of vertices <C>i</C> and <C>j</C>, there are at least a\
s many\n    edges of the form <C>[i, j]</C> in <A>super</A> as there are in <A\
>sub</A>.\n    <P/>\n\n    <Example><![CDATA[\ngap> g := Digraph([[2, 3], [1],\
 [2, 3]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> h := Digraph([[\
2, 3], [], [2]]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> IsSubdig\
raph(g, h);\ntrue\ngap> IsSubdigraph(h, g);\nfalse\ngap> IsSubdigraph(Complete\
Digraph(4), CycleDigraph(4));\ntrue\ngap> IsSubdigraph(CycleDigraph(4), ChainD\
igraph(4));\ntrue\ngap> g := Digraph([[2, 2], [1]]);\n<immutable multidigraph \
with 2 vertices, 3 edges>\ngap> h := Digraph([[2], [1]]);\n<immutable digraph \
with 2 vertices, 2 edges>\ngap> IsSubdigraph(g, h);\ntrue\ngap> IsSubdigraph(h\
, g);\nfalse]]></Example>\n  </Description>\n</ManSection>\n\n   <ManSection>\
\n  <Oper Name=\"IsUndirectedSpanningTree\" Arg=\"super, sub\"/>\n  <Oper Name\
=\"IsUndirectedSpanningForest\" Arg=\"super, sub\"/>\n  <Returns><K>true</K> o\
r <K>false</K>.</Returns>\n  <Description>\n    The operation <C>IsUndirectedS\
panningTree</C> returns <K>true</K> if the\n    digraph <A>sub</A> is an undir\
ected spanning tree of the digraph\n    <A>super</A>, and the operation <C>IsU\
ndirectedSpanningForest</C> returns\n    <K>true</K> if the digraph <A>sub</A>\
 is an undirected spanning forest of\n    the digraph <A>super</A>. <P/>\n\n  \
  An <E>undirected spanning tree</E> of a digraph <A>super</A> is a subdigraph\
\n    of <A>super</A> that is an undirected tree (see <Ref Oper=\"IsSubdigraph\
\" />\n    and <Ref Prop=\"IsUndirectedTree\" />). Note that a digraph whose <\
Ref\n      Oper=\"MaximalSymmetricSubdigraph\"/> is not connected has no undir\
ected\n    spanning trees (see <Ref Prop=\"IsConnectedDigraph\"/>). <P/>\n\n  \
  An <E>undirected spanning forest</E> of a digraph <A>super</A> is a\n    sub\
digraph of <A>super</A> that is an undirected forest (see <Ref\n      Oper=\"I\
sSubdigraph\"/> and <Ref Prop=\"IsUndirectedForest\"/>), and is not\n    conta\
ined in any larger such subdigraph of <A>super</A>.  Equivalently, an\n    und\
irected spanning forest is a subdigraph of <A>super</A> whose connected\n    c\
omponents coincide with those of the <Ref\n      Oper=\"MaximalSymmetricSubdig\
raph\"/> of <A>super</A> (see <Ref\n      Attr=\"DigraphConnectedComponents\"/\
>). <P/>\n\n    Note that an undirected spanning tree is an undirected spannin\
g forest that\n    is connected.\n\n    <Example><![CDATA[\ngap> D := Complete\
Digraph(4);\n<immutable complete digraph with 4 vertices>\ngap> tree := Digrap\
h([[3], [4], [1, 4], [2, 3]]);\n<immutable digraph with 4 vertices, 6 edges>\n\
gap> IsSubdigraph(D, tree) and IsUndirectedTree(tree);\ntrue\ngap> IsUndirecte\
dSpanningTree(D, tree);\ntrue\ngap> forest := EmptyDigraph(4);\n<immutable emp\
ty digraph with 4 vertices>\ngap> IsSubdigraph(D, forest) and IsUndirectedFore\
st(forest);\ntrue\ngap> IsUndirectedSpanningForest(D, forest);\nfalse\ngap> Is\
Subdigraph(tree, forest);\ntrue\ngap> D := DigraphDisjointUnion(CycleDigraph(2\
), CycleDigraph(2));\n<immutable digraph with 4 vertices, 4 edges>\ngap> IsUnd\
irectedTree(D);\nfalse\ngap> IsUndirectedForest(D) and IsUndirectedSpanningFor\
est(D, D);\ntrue]]></Example>\n  </Description>\n</ManSection>\n\n  </Section>\
\n</Chapter>\n <!-- operators/hashs -->\n  <Chapter Label=\"Attributes and ope\
rations\"><Heading>Attributes and operations</Heading>\n  <Section><Heading>Ve\
rtices and edges</Heading>\n    <ManSection>\n  <Attr Name=\"DigraphVertices\"\
 Arg=\"digraph\"/>\n  <Returns>A list of integers.</Returns>\n  <Description>\
\n    Returns the vertices of the digraph <A>digraph</A>. <P/>\n\n    Note tha\
t the vertices of a digraph are always a range of\n    positive integers from \
<C>1</C> to the number of vertices of the graph.\n    <Example><![CDATA[\ngap>\
 gr := Digraph([\"a\", \"b\", \"c\"],\n>                  [\"a\", \"b\", \"b\"\
],\n>                  [\"b\", \"c\", \"a\"]);\n<immutable digraph with 3 vert\
ices, 3 edges>\ngap> DigraphVertices(gr);\n[ 1 .. 3 ]\ngap> gr := Digraph([1, \
2, 3, 4, 5, 7],\n>                  [1, 2, 2, 4, 4],\n>                  [2, 7\
, 5, 3, 7]);\n<immutable digraph with 6 vertices, 5 edges>\ngap> DigraphVertic\
es(gr);\n[ 1 .. 6 ]\ngap> DigraphVertices(RandomDigraph(100));\n[ 1 .. 100 ]\n\
gap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices\
, 3 edges>\ngap> DigraphVertices(D);\n[ 1 .. 3 ]\n]]></Example>\n  </Descripti\
on>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphNrVertices\" Arg\
=\"digraph\"/>\n  <Returns>An integer.</Returns>\n  <Description>\n    Returns\
 the number of vertices of the digraph <A>digraph</A>. <P/>\n\n    <Example><!\
[CDATA[\ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n>                  [\"a\",\
 \"b\", \"b\"],\n>                  [\"b\", \"c\", \"a\"]);\n<immutable digrap\
h with 3 vertices, 3 edges>\ngap> DigraphNrVertices(gr);\n3\ngap> gr := Digrap\
h([1, 2, 3, 4, 5, 7],\n>                  [1, 2, 2, 4, 4],\n>                 \
 [2, 7, 5, 3, 7]);\n<immutable digraph with 6 vertices, 5 edges>\ngap> Digraph\
NrVertices(gr);\n6\ngap> DigraphNrVertices(RandomDigraph(100));\n100\ngap> D :\
= CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edge\
s>\ngap> DigraphNrVertices(D);\n3\n]]></Example>\n  </Description>\n</ManSecti\
on>\n\n    <ManSection>\n  <Attr Name=\"DigraphEdges\" Arg=\"digraph\"/>\n  <R\
eturns>A list of lists.</Returns>\n  <Description>\n    <C>DigraphEdges</C> re\
turns a list of edges of the digraph <A>digraph</A>,\n    where each edge is a\
 pair of elements of <Ref Attr=\"DigraphVertices\"/> of\n    the form <C>[sour\
ce,range]</C>.\n    <P/>\n\n    The entries of <C>DigraphEdges(</C><A>digraph<\
/A><C>)</C> are in one-to-one\n    corresponence with the edges of <A>digraph<\
/A>.  Hence\n    <C>DigraphEdges(</C><A>digraph</A><C>)</C> is duplicate-free \
if and only if\n    <A>digraph</A> contains no multiple edges. <P/>\n\n    The\
 entries of <C>DigraphEdges</C> are guaranteed to be sorted by their\n    firs\
t component (i.e. by the source of each edge), but they are not\n    necessari\
ly then sorted by the second component.\n    <Example><![CDATA[\ngap> gr := Di\
graphFromDiSparse6String(\".DaXbOe?EAM@G~\");\n<immutable multidigraph with 5 \
vertices, 16 edges>\ngap> edges := ShallowCopy(DigraphEdges(gr));; Sort(edges)\
;\ngap> edges;\n[ [ 1, 1 ], [ 1, 3 ], [ 1, 3 ], [ 1, 4 ], [ 1, 5 ], [ 2, 1 ], \
\n  [ 2, 2 ], [ 2, 3 ], [ 2, 5 ], [ 3, 2 ], [ 3, 4 ], [ 3, 5 ], \n  [ 4, 2 ], \
[ 4, 4 ], [ 4, 5 ], [ 5, 1 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n\
<mutable digraph with 3 vertices, 3 edges>\ngap> DigraphEdges(D);\n[ [ 1, 2 ],\
 [ 2, 3 ], [ 3, 1 ] ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <\
ManSection>\n  <Attr Name=\"DigraphNrEdges\" Arg=\"digraph\"/>\n  <Returns>An \
integer.</Returns>\n  <Description>\n    This function returns the number of e\
dges of the digraph <A>digraph</A>.\n    <Example><![CDATA[\ngap> gr := Digrap\
h([\n> [1, 3, 4, 5], [1, 2, 3, 5], [2, 4, 5], [2, 4, 5], [1]]);;\ngap> Digraph\
NrEdges(gr);\n15\ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n>                \
  [\"a\", \"b\", \"b\"],\n>                  [\"b\", \"a\", \"a\"]);\n<immutab\
le multidigraph with 3 vertices, 3 edges>\ngap> DigraphNrEdges(gr);\n3\ngap> D\
 := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 ed\
ges>\ngap> DigraphNrEdges(D);\n3\n]]></Example>\n  </Description>\n</ManSectio\
n>\n\n    <ManSection>\n  <Attr Name=\"DigraphNrLoops\" Arg=\"digraph\"/>\n  <\
Returns>An integer.</Returns>\n  <Description>\n    This function returns the \
number of loops of the digraph <A>digraph</A>. See <Ref Prop=\"DigraphHasLoops\
\"/>. <P/>\n    <Example><![CDATA[\ngap> D := Digraph([[2, 3], [1, 4], [3, 3, \
5], [], [2, 5]]);\n<immutable multidigraph with 5 vertices, 9 edges>\ngap> Dig\
raphNrLoops(D);\n3\ngap> D := EmptyDigraph(5);\n<immutable empty digraph with \
5 vertices>\ngap> DigraphNrLoops(D);\n0\ngap> D := CompleteDigraph(5);\n<immut\
able complete digraph with 5 vertices>\ngap> DigraphNrLoops(D);\n0\n]]></Examp\
le>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"Digra\
phSinks\" Arg=\"digraph\"/>\n  <Returns>A list of vertices.</Returns>\n  <Desc\
ription>\n    This function returns a list of the sinks of the digraph\n    <A\
>digraph</A>.\n    A sink of a digraph is a vertex with out-degree zero.\n    \
See <Ref Oper=\"OutDegreeOfVertex\"/>.\n    <Example><![CDATA[\ngap> gr := Dig\
raph([[3, 5, 2, 2], [3], [], [5, 2, 5, 3], []]);\n<immutable multidigraph with\
 5 vertices, 9 edges>\ngap> DigraphSinks(gr);\n[ 3, 5 ]\ngap> D := CycleDigrap\
h(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> Digr\
aphSinks(D);\n[  ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <Man\
Section>\n  <Attr Name=\"DigraphSources\" Arg=\"digraph\"/>\n  <Returns>A list\
 of vertices.</Returns>\n  <Description>\n    This function returns an immutab\
le list of the sources of the digraph\n    <A>digraph</A>.\n    A source of a \
digraph is a vertex with in-degree zero.\n    See <Ref Oper=\"InDegreeOfVertex\
\"/>.\n    <Example><![CDATA[\ngap> gr := Digraph([[3, 5, 2, 2], [3], [], [5, \
2, 5, 3], []]);\n<immutable multidigraph with 5 vertices, 9 edges>\ngap> Digra\
phSources(gr);\n[ 1, 4 ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutab\
le digraph with 3 vertices, 3 edges>\ngap> DigraphSources(D);\n[  ]\n]]></Exam\
ple>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"Digr\
aphTopologicalSort\" Arg=\"digraph\"/>\n  <Returns>A list of positive integers\
, or <K>fail</K>.</Returns>\n  <Description>\n    If <A>digraph</A> is a digra\
ph whose only directed cycles are loops, then\n    <C>DigraphTopologicalSort</\
C> returns the vertices of <A>digraph</A> ordered\n    so that every edge's so\
urce appears no earlier in the list than its range.\n    If the digraph <A>dig\
raph</A> contains directed cycles of length greater\n    than <M>1</M>, then t\
his operation returns <K>fail</K>.\n    <P/>\n\n    See Section <Ref Subsect=\
\"Definitions\" Style=\"Number\" /> for the definition\n    of a directed cycl\
e, and the definition of a loop.\n\n    <P/>\n\n    The method used for this a\
ttribute has complexity <M>O(m+n)</M> where\n    <M>m</M> is the number of edg\
es (counting multiple edges as one) and\n    <M>n</M> is the number of vertice\
s in the digraph. <P/>\n    <Example><![CDATA[\ngap> D := Digraph([\n> [2, 3],\
 [], [4, 6], [5], [], [7, 8, 9], [], [], []]);\n<immutable digraph with 9 vert\
ices, 8 edges>\ngap> DigraphTopologicalSort(D);\n[ 2, 5, 4, 7, 8, 9, 6, 3, 1 ]\
\ngap> D := Digraph(IsMutableDigraph, [[2, 3], [3], [4], []]);\n<mutable digra\
ph with 4 vertices, 4 edges>\ngap> DigraphTopologicalSort(D);\n[ 4, 3, 2, 1 ]\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper \
Name = \"DigraphVertexLabel\" Arg=\"digraph, i\"/>\n  <Oper Name =\"SetDigraph\
VertexLabel\" Arg=\"digraph, i, obj\"/>\n  <Description>\n    If <A>digraph</A\
> is a digraph, then the first operation returns the label\n    of the vertex \
<A>i</A>. The second operation can be used to set the label\n    of the vertex\
 <A>i</A> in <A>digraph</A> to the arbitrary &GAP; object\n    <A>obj</A>.  <P\
/>\n\n    The label of a vertex can be changed an arbitrary number of times. I\
f no\n    label has been set for the vertex <A>i</A>, then the default value i\
s\n    <A>i</A>. <P/>\n\n    If <A>digraph</A> is a digraph created from a rec\
ord with a component\n    <C>vertices</C>, then the labels of the vertices are\
 set to the value of\n    this component.<P/>\n\n    Induced subdigraphs, and \
some other operations which create new digraphs from\n    old ones, inherit th\
eir labels from their parents.\n\n    <Example><![CDATA[\ngap> D := DigraphFro\
mDigraph6String(\"&DHUEe_\");\n<immutable digraph with 5 vertices, 11 edges>\n\
gap> DigraphVertexLabel(D, 3);\n3\ngap> D := Digraph([\"a\", \"b\", \"c\"], []\
, []);\n<immutable empty digraph with 3 vertices>\ngap> DigraphVertexLabel(D, \
2);\n\"b\"\ngap> SetDigraphVertexLabel(D, 2, \"d\");\ngap> DigraphVertexLabel(\
D, 2);\n\"d\"\ngap> D := InducedSubdigraph(D, [1, 2]);\n<immutable empty digra\
ph with 2 vertices>\ngap> DigraphVertexLabel(D, 2);\n\"d\"\ngap> D := Digraph(\
IsMutableDigraph, [\"e\", \"f\", \"g\"], [], []);\n<mutable empty digraph with\
 3 vertices>\ngap> DigraphVertexLabel(D, 1);\n\"e\"\ngap> SetDigraphVertexLabe\
l(D, 1, \"h\");\ngap> DigraphVertexLabel(D, 1);\n\"h\"\ngap> InducedSubdigraph\
(D, [1, 2]);\n<mutable empty digraph with 2 vertices>\ngap> DigraphVertexLabel\
(D, 1);\n\"h\"\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSect\
ion>\n  <Oper Name=\"DigraphVertexLabels\" Arg=\"digraph\"/>\n  <Oper Name=\"S\
etDigraphVertexLabels\" Arg=\"digraph, list\"/>\n  <Description>\n    If <A>di\
graph</A> is a digraph, then <C>DigraphVertexLabels</C> returns a\n    copy of\
 the labels of the vertices in <A>digraph</A>.\n    <C>SetDigraphVertexLabels<\
/C> can be used to set the labels of the vertices\n    in <A>digraph</A> to th\
e list of\n    arbitrary &GAP; objects <A>list</A>. <P/>\n\n    The label of a\
 vertex can be changed an arbitrary number of times. If no\n    label has been\
 set for the vertex <A>i</A>, then the default value is\n    <A>i</A>. <P/>\n\
\n    If <A>digraph</A> is a digraph created from a record with a component\n \
   <C>vertices</C>, then the labels of the vertices are set to the value of\n \
   this component.<P/>\n\n    Induced subdigraphs, and other operations which \
create new digraphs from\n    old ones, inherit their labels from their parent\
s.\n\n    <Example><![CDATA[\ngap> D := DigraphFromDigraph6String(\"&DHUEe_\")\
;\n<immutable digraph with 5 vertices, 11 edges>\ngap> DigraphVertexLabels(D);\
\n[ 1 .. 5 ]\ngap> D := Digraph([\"a\", \"b\", \"c\"], [], []);\n<immutable em\
pty digraph with 3 vertices>\ngap> DigraphVertexLabels(D);\n[ \"a\", \"b\", \"\
c\" ]\ngap> SetDigraphVertexLabel(D, 2, \"d\");\ngap> DigraphVertexLabels(D);\
\n[ \"a\", \"d\", \"c\" ]\ngap> D := InducedSubdigraph(D, [1, 3]);\n<immutable\
 empty digraph with 2 vertices>\ngap> DigraphVertexLabels(D);\n[ \"a\", \"c\" \
]\ngap> D := Digraph(IsMutableDigraph, [\"e\", \"f\", \"g\"], [], []);\n<mutab\
le empty digraph with 3 vertices>\ngap> SetDigraphVertexLabels(D, [\"h\", \"i\
\", \"j\"]);\ngap> DigraphVertexLabels(D);\n[ \"h\", \"i\", \"j\" ]\ngap> Indu\
cedSubdigraph(D, [1, 3]);\n<mutable empty digraph with 2 vertices>\ngap> Digra\
phVertexLabels(D);\n[ \"h\", \"j\" ]\n]]></Example>\n  </Description>\n</ManSe\
ction>\n\n    <ManSection>\n  <Oper Name = \"DigraphEdgeLabel\" Arg=\"digraph,\
 i, j\"/>\n  <Oper Name = \"SetDigraphEdgeLabel\" Arg=\"digraph, i, j, obj\"/>\
\n  <Description>\n    If <A>digraph</A> is a digraph without multiple edges, \
then the first\n    operation returns the label of the edge from vertex <A>i</\
A> to vertex\n    <A>j</A>.  The second operation can be used to set the label\
 of the edge\n    between vertex <A>i</A> and vertex <A>j</A> to the arbitrary\
 &GAP; object\n    <A>obj</A>. <P/>\n\n    The label of an edge can be changed\
 an arbitrary number of times. If no\n    label has been set for the edge, the\
n the default value is <A>1</A>. <P/>\n\n    Induced subdigraphs, and some oth\
er operations which create new digraphs from\n    old ones, inherit their edge\
 labels from their parents.\n\n    See also <Ref Oper=\"DigraphEdgeLabels\"/>.\
\n\n    <Example><![CDATA[\ngap> D := DigraphFromDigraph6String(\"&DHUEe_\");\
\n<immutable digraph with 5 vertices, 11 edges>\ngap> DigraphEdgeLabel(D, 3, 1\
);\n1\ngap> SetDigraphEdgeLabel(D, 2, 5, [42]);\ngap> DigraphEdgeLabel(D, 2, 5\
);\n[ 42 ]\ngap> D := InducedSubdigraph(D, [2, 5]);\n<immutable digraph with 2\
 vertices, 3 edges>\ngap> DigraphEdgeLabel(D, 1, 2);\n[ 42 ]\ngap> D := ChainD\
igraph(IsMutableDigraph, 5);\n<mutable digraph with 5 vertices, 4 edges>\ngap>\
 DigraphEdgeLabel(D, 2, 3);\n1\ngap> SetDigraphEdgeLabel(D, 4, 5, [1729]);\nga\
p> DigraphEdgeLabel(D, 4, 5);\n[ 1729 ]\ngap> InducedSubdigraph(D, [4, 5]);\n<\
mutable digraph with 2 vertices, 1 edge>\ngap> DigraphEdgeLabel(D, 1, 2);\n[ 1\
729 ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <\
Oper Name=\"DigraphEdgeLabels\" Arg=\"digraph\"/>\n  <Oper Name=\"SetDigraphEd\
geLabels\" Arg=\"digraph, labels\"\n    Label=\"for a digraph and a list of li\
sts\"/>\n  <Oper Name=\"SetDigraphEdgeLabels\" Arg=\"digraph, func\"\n    Labe\
l=\"for a digraph and a function\"/>\n  <Description>\n    If <A>digraph</A> i\
s a digraph without multiple edges, then\n    <C>DigraphEdgeLabels</C> returns\
 a copy of the labels of the edges\n    in <A>digraph</A> as a list of lists <\
C>labels</C> such that\n    <C>labels[i][j]</C> is the label on the edge from \
vertex <C>i</C>\n    to vertex <C>OutNeighbours(digraph)[i][j]</C>.\n\n    <C>\
SetDigraphEdgeLabels</C> can be used to set the labels of the edges in\n    <A\
>digraph</A> without multiple edges to the list <A>labels</A> of lists of\n   \
 arbitrary &GAP; objects such that <C>list[i][j]</C> is the label on the edge\
\n    from vertex <C>i</C> to the vertex <C>OutNeighbours(digraph>[i][j]</C>.\
\n\n    Alternatively <C>SetDigraphEdgeLabels</C> can be called with binary fu\
nction\n    <A>func</A> that as its second argument that when passed two verti\
ces <C>i</C>\n    and <C>j</C> returns the label for the edge between vertex <\
C>i</C> and vertex\n    <C>j</C>. <P/>\n\n    The label of an edge can be chan\
ged an arbitrary number of times. If no\n    label has been set for an edge, t\
hen the default value is <C>1</C>. <P/>\n\n    Induced subdigraphs, and some o\
ther operations which create new digraphs\n    from old ones, inherit their la\
bels from their parents.\n\n    <Example><![CDATA[\ngap> D := DigraphFromDigra\
ph6String(\"&DHUEe_\");\n<immutable digraph with 5 vertices, 11 edges>\ngap> D\
igraphEdgeLabels(D);\n[ [ 1 ], [ 1, 1, 1 ], [ 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ] ]\
\ngap> SetDigraphEdgeLabel(D, 2, 1, \"d\");\ngap> DigraphEdgeLabels(D);\n[ [ 1\
 ], [ \"d\", 1, 1 ], [ 1 ], [ 1, 1, 1 ], [ 1, 1, 1 ] ]\ngap> D := InducedSubdi\
graph(D, [1, 2, 3]);\n<immutable digraph with 3 vertices, 4 edges>\ngap> Digra\
phEdgeLabels(D);\n[ [ 1 ], [ \"d\", 1 ], [ 1 ] ]\ngap> OutNeighbours(D);\n[ [ \
3 ], [ 1, 3 ], [ 1 ] ]\ngap> D := CompleteBipartiteDigraph(IsMutableDigraph, 2\
, 3);\n<mutable digraph with 5 vertices, 12 edges>\ngap> DigraphEdgeLabels(D);\
\n[ [ 1, 1, 1 ], [ 1, 1, 1 ], [ 1, 1 ], [ 1, 1 ], [ 1, 1 ] ]\ngap> SetDigraphE\
dgeLabel(D, 2, 4, \"a\");\ngap> DigraphEdgeLabels(D);\n[ [ 1, 1, 1 ], [ 1, \"a\
\", 1 ], [ 1, 1 ], [ 1, 1 ], [ 1, 1 ] ]\ngap> InducedSubdigraph(D, [1, 2, 3, 4\
]);\n<mutable digraph with 4 vertices, 8 edges>\ngap> DigraphEdgeLabels(D);\n[\
 [ 1, 1 ], [ 1, \"a\" ], [ 1, 1 ], [ 1, 1 ] ]\ngap> OutNeighbors(D);\n[ [ 3, 4\
 ], [ 3, 4 ], [ 1, 2 ], [ 1, 2 ] ]\n]]></Example>\n  </Description>\n</ManSect\
ion>\n\n    <ManSection>\n  <Oper Name=\"DigraphInEdges\" Arg=\"digraph, verte\
x\"/>\n  <Returns>A list of edges.</Returns>\n  <Description>\n    <C>DigraphI\
nEdges</C> returns the list of all edges of <A>digraph</A>\n    which have <A>\
vertex</A> as their range.\n    <Example><![CDATA[\ngap> D := Digraph([[2, 2],\
 [3, 3], [4, 4], [1, 1]]);\n<immutable multidigraph with 4 vertices, 8 edges>\
\ngap> DigraphInEdges(D, 2);\n[ [ 1, 2 ], [ 1, 2 ] ]\n]]></Example>\n  </Descr\
iption>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphOutEdges\" A\
rg=\"digraph, vertex\"/>\n  <Returns>A list of edges.</Returns>\n  <Descriptio\
n>\n    <C>DigraphOutEdges</C> returns the list of all edges of <A>digraph</A>\
\n    which have <A>vertex</A> as their source.\n    <Example><![CDATA[\ngap> \
D := Digraph([[2, 2], [3, 3], [4, 4], [1, 1]]);\n<immutable multidigraph with \
4 vertices, 8 edges>\ngap> DigraphOutEdges(D, 2);\n[ [ 2, 3 ], [ 2, 3 ] ]\n]]>\
</Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\
\"IsDigraphEdge\" Arg=\"digraph, list\"\n        Label=\"for digraph and list\
\"/>\n  <Oper Name=\"IsDigraphEdge\" Arg=\"digraph, u, v\"\n        Label=\"fo\
r digraph and two pos ints\"/>\n  <Returns><K>true</K> or <K>false</K>.</Retur\
ns>\n  <Description>\n    In the first form, this function returns <K>true</K>\
 if and only if the list\n    <A>list</A> specifies an edge in the digraph <A>\
digraph</A>.  Specifically,\n    this operation returns <K>true</K> if <A>list\
</A> is a pair of positive\n    integers where <A>list</A><C>[1]</C> is the so\
urce and <A>list</A><C>[2]</C>\n    is the range of an edge in <A>digraph</A>,\
 and <K>false</K> otherwise. <P/>\n\n    The second form simply returns <K>tru\
e</K> if <C>[<A>u</A>, <A>v</A>]</C> is\n    an edge in <A>digraph</A>, and <K\
>false</K> otherwise.\n\n<Example><![CDATA[\ngap> D := Digraph([[2, 2], [6], [\
], [3], [], [1]]);\n<immutable multidigraph with 6 vertices, 5 edges>\ngap> Is\
DigraphEdge(D, [1, 1]);\nfalse\ngap> IsDigraphEdge(D, [1, 2]);\ntrue\ngap> IsD\
igraphEdge(D, [1, 8]);\nfalse\n]]></Example>\n  </Description>\n</ManSection>\
\n\n    <ManSection>\n  <Oper Name=\"IsMatching\" Arg=\"digraph, list\"/>\n  <\
Oper Name=\"IsMaximalMatching\" Arg=\"digraph, list\"/>\n  <Oper Name=\"IsMaxi\
mumMatching\" Arg=\"digraph, list\"/>\n  <Oper Name=\"IsPerfectMatching\" Arg=\
\"digraph, list\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Des\
cription>\n    If <A>digraph</A> is a digraph and <A>list</A> is a list of pai\
rs of\n    vertices of <A>digraph</A>, then <C>IsMatching</C> returns <K>true<\
/K> if\n    <A>list</A> is a matching of <A>digraph</A>.  The operation\n    <\
C>IsMaximalMatching</C> returns <K>true</K> if <A>list</A> is a maximal \n    \
matching, <C>IsMaximumMatching</C> returns <K>true</K> if <A>list</A> is a\n  \
  maximum matching and <C>IsPerfectMatching</C> returns <K>true</K> if \n    <\
A>list</A> is a perfect, matching of <A>digraph</A>, respectively.  \n    Othe\
rwise, each of these operations return <K>false</K>.\n    <P/>\n\n    A <E>mat\
ching</E> <C>M</C> of a digraph <A>digraph</A> is a subset of the\n    edges o\
f <A>digraph</A>, i.e. <C>DigraphEdges(<A>digraph</A>)</C>, such\n    that no \
pair of distinct edges in <C>M</C> are incident to the same vertex\n    of <A>\
digraph</A>.  Note that this definition allows a matching to contain\n    loop\
s.  See <Ref Prop=\"DigraphHasLoops\" />.  The matching <C>M</C> is\n    <E>ma\
ximal</E> if it is contained in no larger matching of the digraph,\n    is <E>\
maximum</E> if it has the greatest cardinality among all matchings and\n    is\
 <E>perfect</E> if every vertex of the digraph is incident to an edge in\n    \
the matching.  Every maximum or perfect matching is maximal. Note, however,\n \
   that not every perfect matching of digraphs with loops is maximum.\n\n    <\
Example><![CDATA[\ngap> D := Digraph([[1, 2], [1, 2], [2, 3, 4], [3, 5], [1]])\
;\n<immutable digraph with 5 vertices, 10 edges>\ngap> IsMatching(D, [[2, 1], \
[3, 2]]);\nfalse\ngap> edges := [[3, 2]];;\ngap> IsMatching(D, edges);\ntrue\n\
gap> IsMaximalMatching(D, edges);\nfalse\ngap> edges := [[2, 1], [3, 4]];;\nga\
p> IsMaximalMatching(D, edges);\ntrue\ngap> IsPerfectMatching(D, edges);\nfals\
e\ngap> edges := [[1, 2], [3, 3], [4, 5]];;\ngap> IsPerfectMatching(D, edges);\
\ntrue\ngap> IsMaximumMatching(D, edges);\nfalse\ngap> edges := [[1, 1], [2, 2\
], [3, 3], [4, 5]];;\ngap> IsMaximumMatching(D, edges);\ntrue\n]]></Example>\n\
  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphMax\
imalMatching\" Arg=\"digraph\"/>\n  <Returns>A list of pairs of vertices.</Ret\
urns>\n  <Description>\n    This function returns a maximal matching of the di\
graph <A>digraph</A>.\n    <P/>\n\n    For the definition of a maximal matchin\
g, see <Ref Oper=\"IsMaximalMatching\"/>. \n\n    <Example><![CDATA[\ngap> D :\
= DigraphFromDiSparse6String(\".IeAoXCJU@|SHAe?d\");\n<immutable digraph with \
10 vertices, 13 edges>\ngap> M := DigraphMaximalMatching(D);; IsMaximalMatchin\
g(D, M);\ntrue\ngap> D := RandomDigraph(100);;\ngap> IsMaximalMatching(D, Digr\
aphMaximalMatching(D));\ntrue\ngap> D := GeneralisedPetersenGraph(IsMutableDig\
raph, 9, 2);\n<mutable digraph with 18 vertices, 54 edges>\ngap> IsMaximalMatc\
hing(D, DigraphMaximalMatching(D));\ntrue\n]]></Example>\n  </Description>\n</\
ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphMaximumMatching\" Arg=\
\"digraph\"/>\n  <Returns>A list of pairs of vertices.</Returns>\n  <Descripti\
on>\n    This function returns a maximum matching of the digraph <A>digraph</A\
>.\n    <P/>\n\n    For the definition of a maximum matching, see <Ref Oper=\"\
IsMaximumMatching\"/>.\n    If <A>digraph</A> is bipartite (see <Ref Oper=\"Is\
BipartiteDigraph\"/>), then \n    the algorithm used has complexity <C>O(m*sqr\
t(n))</C>. Otherwise for general \n    graphs the complexity is <C>O(m*n*log(n\
))</C>. Here <C>n</C> is the number of vertices \n    and <C>m</C> is the numb\
er of edges.\n\n    <Example><![CDATA[\ngap> D := DigraphFromDigraph6String(\"\
&I@EA_A?AdDp[_c??OO\");\n<immutable digraph with 10 vertices, 23 edges>\ngap> \
M := DigraphMaximumMatching(D);; IsMaximalMatching(D, M);\ntrue\ngap> Length(M\
);\n5\ngap> D := Digraph([[5, 6, 7, 8], [6, 7, 8], [7, 8], [8], \n>           \
       [], [], [], []]);;\ngap> M := DigraphMaximumMatching(D);\n[ [ 1, 5 ], [\
 2, 6 ], [ 3, 7 ], [ 4, 8 ] ]\ngap> D := GeneralisedPetersenGraph(IsMutableDig\
raph, 9, 2);\n<mutable digraph with 18 vertices, 54 edges>\ngap> M := DigraphM\
aximumMatching(D);;\ngap> IsMaximalMatching(D, M);\ntrue\ngap> Length(M);\n9\n\
]]></Example>\n  </Description>\n</ManSection>\n\n  </Section>\n\n  <Section><\
Heading>Neighbours and degree</Heading>\n    <ManSection>\n  <Attr Name=\"Adja\
cencyMatrix\" Arg=\"digraph\"/>\n  <Oper Name=\"AdjacencyMatrixMutableCopy\" A\
rg=\"digraph\"/>\n  <Returns>A square matrix of non-negative integers.</Return\
s>\n  <Description>\n    This function returns the adjacency matrix <C>mat</C>\
 of the digraph\n    <A>digraph</A>.\n    The value of the matrix entry <C>mat\
[i][j]</C> is the number of edges\n    in <A>digraph</A> with source <C>i</C> \
and range <C>j</C>. If <A>digraph</A>\n    has no vertices, then the empty lis\
t is returned. <P/>\n\n    The function <C>AdjacencyMatrix</C> returns an immu\
table list of\n    lists, whereas the function <C>AdjacencyMatrixMutableCopy</\
C> returns a copy\n    of <C>AdjacencyMatrix</C> that is a mutable list of mut\
able lists. <P/>\n\n    <Example><![CDATA[\ngap> gr := Digraph([\n> [2, 2, 2],\
 [1, 3, 6, 8, 9, 10], [4, 6, 8],\n> [1, 2, 3, 9], [3, 3], [3, 5, 6, 10], [1, 2\
, 7],\n> [1, 2, 3, 10, 5, 6, 10], [1, 3, 4, 5, 8, 10],\n> [2, 3, 4, 6, 7, 10]]\
);\n<immutable multidigraph with 10 vertices, 44 edges>\ngap> mat := Adjacency\
Matrix(gr);;\ngap> Display(mat);\n[ [  0,  3,  0,  0,  0,  0,  0,  0,  0,  0 ]\
,\n  [  1,  0,  1,  0,  0,  1,  0,  1,  1,  1 ],\n  [  0,  0,  0,  1,  0,  1, \
 0,  1,  0,  0 ],\n  [  1,  1,  1,  0,  0,  0,  0,  0,  1,  0 ],\n  [  0,  0, \
 2,  0,  0,  0,  0,  0,  0,  0 ],\n  [  0,  0,  1,  0,  1,  1,  0,  0,  0,  1 \
],\n  [  1,  1,  0,  0,  0,  0,  1,  0,  0,  0 ],\n  [  1,  1,  1,  0,  1,  1,\
  0,  0,  0,  2 ],\n  [  1,  0,  1,  1,  1,  0,  0,  1,  0,  1 ],\n  [  0,  1,\
  1,  1,  0,  1,  1,  0,  0,  1 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, \
3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> Display(AdjacencyMatrix(\
D));\n[ [  0,  1,  0 ],\n  [  0,  0,  1 ],\n  [  1,  0,  0 ] ]\n]]></Example>\
\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"Characte\
risticPolynomial\" Arg=\"digraph\"/>\n  <Returns>A polynomial with integer coe\
fficients.</Returns>\n  <Description>\n    This function returns the character\
istic polynomial of the digraph\n     <A>digraph</A>. That is it returns the c\
haracteristic polynomial\n      of the adjacency matrix of the digraph <A>digr\
aph</A>\n    <Example><![CDATA[\ngap> D := Digraph([\n> [2, 2, 2], [1, 3, 6, 8\
, 9, 10], [4, 6, 8],\n> [1, 2, 3, 9], [3, 3], [3, 5, 6, 10], [1, 2, 7],\n> [1,\
 2, 3, 10, 5, 6, 10], [1, 3, 4, 5, 8, 10],\n> [2, 3, 4, 6, 7, 10]]);\n<immutab\
le multidigraph with 10 vertices, 44 edges>\ngap> CharacteristicPolynomial(D);\
\nx_1^10-3*x_1^9-7*x_1^8-x_1^7+14*x_1^6+x_1^5-26*x_1^4+51*x_1^3-10*x_1^2\\\n+1\
8*x_1-30\ngap> D := CompleteDigraph(5);\n<immutable complete digraph with 5 ve\
rtices>\ngap> CharacteristicPolynomial(D);\nx_1^5-10*x_1^3-20*x_1^2-15*x_1-4\n\
gap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices\
, 3 edges>\ngap> CharacteristicPolynomial(D);\nx_1^3-1\n]]></Example>\n  </Des\
cription>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"BooleanAdjacencyM\
atrix\" Arg=\"digraph\"/>\n  <Oper Name=\"BooleanAdjacencyMatrixMutableCopy\" \
Arg=\"digraph\"/>\n  <Returns>A square matrix of booleans.</Returns>\n  <Descr\
iption>\n    If <A>digraph</A> is a digraph with a positive number of vertices\
\n    <C>n</C>, then <C>BooleanAdjacencyMatrix(</C><A>digraph</A><C>)</C>\n   \
 returns the boolean adjacency matrix <C>mat</C> of <A>digraph</A>.  The\n    \
value of the matrix entry <C>mat[j][i]</C> is <K>true</K> if and only if\n    \
there exists an edge in <A>digraph</A> with source <C>j</C> and range\n    <C>\
i</C>.  If <A>digraph</A> has no vertices, then the empty list is\n    returne\
d. <P/>\n\n    Note that the boolean adjacency matrix loses information about \
multiple\n    edges.  <P/>\n\n    The attribute <C>BooleanAdjacencyMatrix</C> \
returns an immutable list of\n    immutable lists, whereas the function\n    <\
C>BooleanAdjacencyMatrixMutableCopy</C> returns a copy of the\n    <C>BooleanA\
djacencyMatrix</C> that is a mutable list of mutable lists. <P/>\n    <Example\
><![CDATA[\ngap> gr := Digraph([[3, 4], [2, 3], [1, 2, 4], [4]]);\n<immutable \
digraph with 4 vertices, 8 edges>\ngap> PrintArray(BooleanAdjacencyMatrix(gr))\
;\n[ [  false,  false,   true,   true ],\n  [  false,   true,   true,  false ]\
,\n  [   true,   true,  false,   true ],\n  [  false,  false,  false,   true ]\
 ]\ngap> gr := CycleDigraph(4);;\ngap> PrintArray(BooleanAdjacencyMatrix(gr));\
\n[ [  false,   true,  false,  false ],\n  [  false,  false,   true,  false ],\
\n  [  false,  false,  false,   true ],\n  [   true,  false,  false,  false ] \
]\ngap> BooleanAdjacencyMatrix(EmptyDigraph(0));\n[  ]\ngap> D := CycleDigraph\
(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> Print\
Array(BooleanAdjacencyMatrix(D));\n[ [  false,   true,  false ],\n  [  false, \
 false,   true ],\n  [   true,  false,  false ] ]\n]]></Example>\n  </Descript\
ion>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphAdjacencyFuncti\
on\" Arg=\"digraph\"/>\n  <Returns>A function.</Returns>\n  <Description>\n   \
 If <A>digraph</A> is a digraph, then <C>DigraphAdjacencyFunction</C> returns\
\n    a function which takes two integer parameters <C>x, y</C> and returns\n \
   <K>true</K> if there exists an edge from vertex <C>x</C> to vertex <C>y</C>\
\n    in <A>digraph</A> and <K>false</K> if not.\n\n    <Example><![CDATA[\nga\
p> digraph := Digraph([[1, 2], [3], []]);\n<immutable digraph with 3 vertices,\
 3 edges>\ngap> foo := DigraphAdjacencyFunction(digraph);\nfunction( u, v ) ..\
. end\ngap> foo(1, 1);\ntrue\ngap> foo(1, 2);\ntrue\ngap> foo(1, 3);\nfalse\ng\
ap> foo(3, 1);\nfalse\ngap> gr := Digraph([\"a\", \"b\", \"c\"],\n>           \
       [\"a\", \"b\", \"b\"],\n>                  [\"b\", \"a\", \"a\"]);\n<im\
mutable multidigraph with 3 vertices, 3 edges>\ngap> foo := DigraphAdjacencyFu\
nction(gr);\nfunction( u, v ) ... end\ngap> foo(1, 2);\ntrue\ngap> foo(3, 2);\
\nfalse\ngap> foo(3, 1);\nfalse\ngap> D := CycleDigraph(IsMutableDigraph, 3);\
\n<mutable digraph with 3 vertices, 3 edges>\ngap> foo := DigraphAdjacencyFunc\
tion(D);\nfunction( u, v ) ... end\ngap> foo(1, 2);\ntrue\ngap> foo(2, 1);\nfa\
lse\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <At\
tr Name=\"DigraphRange\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphSource\" Arg\
=\"digraph\"/>\n  <Returns>A list of positive integers.</Returns>\n  <Descript\
ion>\n    <C>DigraphRange</C> and <C>DigraphSource</C> return the range and so\
urce of\n    the digraph <A>digraph</A>. More precisely, position <C>i</C> in\
\n    <C>DigraphRange(<A>digraph</A>)</C> is the range of the <C>i</C>th edge \
of\n    <A>digraph</A>.\n\n    <Example><![CDATA[\ngap> gr := Digraph([\n> [2,\
 1, 3, 5], [1, 3, 4], [2, 3], [2], [1, 2, 3, 4]]);\n<immutable digraph with 5 \
vertices, 14 edges>\ngap> DigraphRange(gr);\n[ 2, 1, 3, 5, 1, 3, 4, 2, 3, 2, 1\
, 2, 3, 4 ]\ngap> DigraphSource(gr);\n[ 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5,\
 5 ]\ngap> DigraphEdges(gr);\n[ [ 1, 2 ], [ 1, 1 ], [ 1, 3 ], [ 1, 5 ], [ 2, 1\
 ], [ 2, 3 ], \n  [ 2, 4 ], [ 3, 2 ], [ 3, 3 ], [ 4, 2 ], [ 5, 1 ], [ 5, 2 ], \
\n  [ 5, 3 ], [ 5, 4 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutab\
le digraph with 3 vertices, 3 edges>\ngap> DigraphRange(D);\n[ 2, 3, 1 ]\ngap>\
 DigraphSource(D);\n[ 1, 2, 3 ]\n]]></Example>\n  </Description>\n</ManSection\
>\n\n    <ManSection>\n  <Attr Name=\"OutNeighbours\" Arg=\"digraph\"/>\n  <At\
tr Name=\"OutNeighbors\" Arg=\"digraph\"/>\n  <Oper Name=\"OutNeighboursMutabl\
eCopy\" Arg=\"digraph\"/>\n  <Oper Name=\"OutNeighborsMutableCopy\" Arg=\"digr\
aph\"/>\n  <Returns>The adjacencies of a digraph.</Returns>\n  <Description>\n\
    This function returns the list <C>out</C> of out-neighbours of each vertex\
\n    of the digraph <A>digraph</A>.\n    More specifically, a vertex <C>j</C>\
 appears in <C>out[i]</C> each time\n    there exists an edge with source <C>i\
</C> and range <C>j</C> in\n    <A>digraph</A>. <P/>\n\n    The function <C>Ou\
tNeighbours</C> returns an immutable list of\n    lists, whereas the function \
<C>OutNeighboursMutableCopy</C> returns a copy\n    of <C>OutNeighbours</C> wh\
ich is a mutable list of mutable lists. <P/>\n\n    <Example><![CDATA[\ngap> g\
r := Digraph([\"a\", \"b\", \"c\"],\n>                  [\"a\", \"b\", \"b\"],\
\n>                  [\"b\", \"a\", \"c\"]);\n<immutable digraph with 3 vertic\
es, 3 edges>\ngap> OutNeighbours(gr);\n[ [ 2 ], [ 1, 3 ], [  ] ]\ngap> gr := D\
igraph([[1, 2, 3], [2, 1], [3]]);\n<immutable digraph with 3 vertices, 6 edges\
>\ngap> OutNeighbours(gr);\n[ [ 1, 2, 3 ], [ 2, 1 ], [ 3 ] ]\ngap> gr := Digra\
phByAdjacencyMatrix([\n>  [1, 2, 1],\n>  [1, 1, 0],\n>  [0, 0, 1]]);\n<immutab\
le multidigraph with 3 vertices, 7 edges>\ngap> OutNeighbours(gr);\n[ [ 1, 2, \
2, 3 ], [ 1, 2 ], [ 3 ] ]\ngap> OutNeighboursMutableCopy(gr);\n[ [ 1, 2, 2, 3 \
], [ 1, 2 ], [ 3 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable d\
igraph with 3 vertices, 3 edges>\ngap> OutNeighbours(D);\n[ [ 2 ], [ 3 ], [ 1 \
] ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <At\
tr Name=\"InNeighbours\" Arg=\"digraph\"/>\n  <Attr Name=\"InNeighbors\" Arg=\
\"digraph\"/>\n  <Oper Name=\"InNeighboursMutableCopy\" Arg=\"digraph\"/>\n  <\
Oper Name=\"InNeighborsMutableCopy\" Arg=\"digraph\"/>\n  <Returns>A list of l\
ists of vertices.</Returns>\n  <Description>\n    This function returns the li\
st <C>inn</C> of in-neighbours of each vertex\n    of the digraph <A>digraph</\
A>.\n    More specifically, a vertex <C>j</C> appears in <C>inn[i]</C> each ti\
me\n    there exists an edge with source <C>j</C> and range <C>i</C> in\n    <\
A>digraph</A>. <P/>\n\n    The function <C>InNeighbours</C> returns an immutab\
le list of\n    lists, whereas the function <C>InNeighboursMutableCopy</C> ret\
urns a copy\n    of <C>InNeighbours</C> which is a mutable list of mutable lis\
ts. <P/>\n\n    Note that each entry of <C>inn</C> is sorted into ascending or\
der. <P/>\n\n    <Example><![CDATA[\ngap> gr := Digraph([\"a\", \"b\", \"c\"],\
\n>                  [\"a\", \"b\", \"b\"],\n>                  [\"b\", \"a\",\
 \"c\"]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> InNeighbours(gr)\
;\n[ [ 2 ], [ 1 ], [ 2 ] ]\ngap> gr := Digraph([[1, 2, 3], [2, 1], [3]]);\n<im\
mutable digraph with 3 vertices, 6 edges>\ngap> InNeighbours(gr);\n[ [ 1, 2 ],\
 [ 1, 2 ], [ 1, 3 ] ]\ngap> gr := DigraphByAdjacencyMatrix([\n>  [1, 2, 1],\n>\
  [1, 1, 0],\n>  [0, 0, 1]]);\n<immutable multidigraph with 3 vertices, 7 edge\
s>\ngap> InNeighbours(gr);\n[ [ 1, 2 ], [ 1, 1, 2 ], [ 1, 3 ] ]\ngap> InNeighb\
oursMutableCopy(gr);\n[ [ 1, 2 ], [ 1, 1, 2 ], [ 1, 3 ] ]\ngap> D := CycleDigr\
aph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> In\
Neighbours(D);\n[ [ 3 ], [ 1 ], [ 2 ] ]\n]]></Example>\n  </Description>\n</Ma\
nSection>\n\n    <ManSection>\n  <Attr Name=\"OutDegrees\" Arg=\"digraph\"/>\n\
  <Attr Name=\"OutDegreeSequence\" Arg=\"digraph\"/>\n  <Attr Name=\"OutDegree\
Set\" Arg=\"digraph\"/>\n  <Returns>A list of non-negative integers.</Returns>\
\n  <Description>\n\n    Given a digraph <A>digraph</A> with <M>n</M> vertices\
, the function\n    <C>OutDegrees</C> returns an immutable list <C>out</C> of \
length <M>n</M>, such that\n    for a vertex <C>i</C> in <A>digraph</A>, the v\
alue of <C>out[i]</C> is the\n    out-degree of vertex <C>i</C>.\n    See <Ref\
 Oper=\"OutDegreeOfVertex\"/>. <P/>\n\n    The function <C>OutDegreeSequence</\
C> returns the same list,\n    after it has been sorted into non-increasing or\
der. <P/>\n\n    The function <C>OutDegreeSet</C> returns the same list, sorte\
d into\n    increasing order with duplicate entries removed. <P/>\n\n    <Exam\
ple><![CDATA[\ngap> D := Digraph([[1, 3, 2, 2], [], [2, 1], []]);\n<immutable \
multidigraph with 4 vertices, 6 edges>\ngap> OutDegrees(D);\n[ 4, 0, 2, 0 ]\ng\
ap> OutDegreeSequence(D);\n[ 4, 2, 0, 0 ]\ngap> OutDegreeSet(D);\n[ 0, 2, 4 ]\
\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertic\
es, 3 edges>\ngap> OutDegrees(D);\n[ 1, 1, 1 ]\n]]></Example>\n  </Description\
>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"InDegrees\" Arg=\"digraph\
\"/>\n  <Attr Name=\"InDegreeSequence\" Arg=\"digraph\"/>\n  <Attr Name=\"InDe\
greeSet\" Arg=\"digraph\"/>\n  <Returns>A list of non-negative integers.</Retu\
rns>\n  <Description>\n\n    Given a digraph <A>digraph</A> with <M>n</M> vert\
ices, the function\n    <C>InDegrees</C> returns an immutable list <C>inn</C> \
of length <M>n</M>, such that\n    for a vertex <C>i</C> in <A>digraph</A>, th\
e value of <C>inn[i]</C> is\n    the in-degree of vertex <C>i</C>.\n    See <R\
ef Oper=\"InDegreeOfVertex\"/>. <P/>\n\n    The function <C>InDegreeSequence</\
C> returns the same list,\n    after it has been sorted into non-increasing or\
der. <P/>\n\n    The function <C>InDegreeSet</C> returns the same list, sorted\
 into\n    increasing order with duplicate entries removed. <P/>\n\n    <Examp\
le><![CDATA[\ngap> D := Digraph([[1, 3, 2, 2, 4], [], [2, 1, 4], []]);\n<immut\
able multidigraph with 4 vertices, 8 edges>\ngap> InDegrees(D);\n[ 2, 3, 1, 2 \
]\ngap> InDegreeSequence(D);\n[ 3, 2, 2, 1 ]\ngap> InDegreeSet(D);\n[ 1, 2, 3 \
]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 verti\
ces, 3 edges>\ngap> InDegrees(D);\n[ 1, 1, 1 ]\n]]></Example>\n  </Description\
>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"OutDegreeOfVertex\" Arg=\
\"digraph, vertex\"/>\n  <Returns>The non-negative integer.</Returns>\n  <Desc\
ription>\n    This operation returns the out-degree of the vertex <A>vertex</A\
> in the\n    digraph <A>digraph</A>.\n    The out-degree of <A>vertex</A> is \
the number of edges in <A>digraph</A>\n    whose source is <A>vertex</A>.\n   \
 <P/>\n    <Example><![CDATA[\ngap> D := Digraph([\n> [2, 2, 1], [1, 4], [2, 2\
, 4, 2], [1, 1, 2, 2, 1, 2, 2]]);\n<immutable multidigraph with 4 vertices, 16\
 edges>\ngap> OutDegreeOfVertex(D, 1);\n3\ngap> OutDegreeOfVertex(D, 2);\n2\ng\
ap> OutDegreeOfVertex(D, 3);\n4\ngap> OutDegreeOfVertex(D, 4);\n7\n]]></Exampl\
e>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"OutNei\
ghboursOfVertex\" Arg=\"digraph, vertex\"/>\n  <Oper Name=\"OutNeighborsOfVert\
ex\" Arg=\"digraph, vertex\"/>\n  <Returns>A list of vertices.</Returns>\n  <D\
escription>\n\n    This operation returns the list <C>out</C> of vertices of t\
he digraph\n    <A>digraph</A>.\n    A vertex <C>i</C> appears in the list <C>\
out</C> each time there exists an\n    edge  with source <A>vertex</A> and ran\
ge <C>i</C> in <A>digraph</A>; in\n    particular, this means that <C>out</C> \
may contain duplicates.<P/>\n    <Example><![CDATA[\ngap> D := Digraph([\n> [2\
, 2, 3], [1, 3, 4], [2, 2, 3], [1, 1, 2, 2, 1, 2, 2]]);\n<immutable multidigra\
ph with 4 vertices, 16 edges>\ngap> OutNeighboursOfVertex(D, 1);\n[ 2, 2, 3 ]\
\ngap> OutNeighboursOfVertex(D, 3);\n[ 2, 2, 3 ]\n]]></Example>\n  </Descripti\
on>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"InDegreeOfVertex\" Arg=\
\"digraph, vertex\"/>\n  <Returns>A non-negative integer.</Returns>\n  <Descri\
ption>\n    This operation returns the in-degree of the vertex <A>vertex</A> i\
n the\n    digraph <A>digraph</A>.\n    The in-degree of <A>vertex</A> is the \
number of edges in <A>digraph</A>\n    whose range is <A>vertex</A>.\n    <Exa\
mple><![CDATA[\ngap> D := Digraph([\n> [2, 2, 1], [1, 4], [2, 2, 4, 2], [1, 1,\
 2, 2, 1, 2, 2]]);\n<immutable multidigraph with 4 vertices, 16 edges>\ngap> I\
nDegreeOfVertex(D, 1);\n5\ngap> InDegreeOfVertex(D, 2);\n9\ngap> InDegreeOfVer\
tex(D, 3);\n0\ngap> InDegreeOfVertex(D, 4);\n2\n]]></Example>\n  </Description\
>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"InNeighboursOfVertex\" Ar\
g=\"digraph, vertex\"/>\n  <Oper Name=\"InNeighborsOfVertex\" Arg=\"digraph, v\
ertex\"/>\n  <Returns>A list of postitive vertices.</Returns>\n  <Description>\
\n\n    This operation returns the list <C>inn</C> of vertices of the digraph\
\n    <A>digraph</A>.\n    A vertex <C>i</C> appears in the list <C>inn</C> ea\
ch time there exists an\n    edge  with source <C>i</C> and range <A>vertex</A\
> in <A>digraph</A>; in\n    particular, this means that <C>inn</C> may contai\
n duplicates. <P/>\n\n    <Example><![CDATA[\ngap> D := Digraph([\n> [2, 2, 3]\
, [1, 3, 4], [2, 2, 3], [1, 1, 2, 2, 1, 2, 2]]);\n<immutable multidigraph with\
 4 vertices, 16 edges>\ngap> InNeighboursOfVertex(D, 1);\n[ 2, 4, 4, 4 ]\ngap>\
 InNeighboursOfVertex(D, 2);\n[ 1, 1, 3, 3, 4, 4, 4, 4 ]\n]]></Example>\n  </D\
escription>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphLoops\" \
Arg=\"digraph\"/>\n  <Returns>A list of vertices.</Returns>\n  <Description>\n\
    If <A>digraph</A> is a digraph, then <C>DigraphLoops</C> returns the list\
\n    consisting of the <Ref Attr=\"DigraphVertices\"/> of <A>digraph</A>\n   \
 at which there is a loop. See <Ref Prop=\"DigraphHasLoops\"/>. <P/>\n\n    <E\
xample><![CDATA[\ngap> D := Digraph([[2], [3], []]);\n<immutable digraph with \
3 vertices, 2 edges>\ngap> DigraphHasLoops(D);\nfalse\ngap> DigraphLoops(D);\n\
[  ]\ngap> D := Digraph([[3, 5], [1], [2, 4, 3], [4], [2, 1]]);\n<immutable di\
graph with 5 vertices, 9 edges>\ngap> DigraphLoops(D);\n[ 3, 4 ]\ngap> D := Di\
graph(IsMutableDigraph, [[1], [1]]);\n<mutable digraph with 2 vertices, 2 edge\
s>\ngap> DigraphLoops(D);\n[ 1 ]\n]]></Example>\n  </Description>\n</ManSectio\
n>\n\n    <ManSection>\n  <Oper Name=\"PartialOrderDigraphMeetOfVertices\"\n  \
  Arg=\"digraph, u, v\"/>\n  <Oper Name=\"PartialOrderDigraphJoinOfVertices\"\
\n    Arg=\"digraph, u, v\"/>\n  <Returns>A positive integer or <K>fail</K></R\
eturns>\n    <Description>\n    If the first argument is a partial order digra\
ph <Ref\n    Prop=\"IsPartialOrderDigraph\"/> then these operations return the\
 meet, or\n    the join, of the two input vertices. If the meet (or join) is d\
oes not\n    exist then <K>fail</K> is returned. The meet (or join) is guarant\
eed to\n    exist when the first argument satisfies\n    <Ref Prop=\"IsMeetSem\
ilatticeDigraph\"/>  (or\n    <Ref Prop=\"IsJoinSemilatticeDigraph\"/>) - see \
the documentation for these\n    properties for the definition of the meet (or\
 the join).\n\n    <Example><![CDATA[\ngap> D := Digraph([[1], [1, 2], [1, 3],\
 [1, 2, 3, 4]]);\n<immutable digraph with 4 vertices, 9 edges>\ngap> PartialOr\
derDigraphMeetOfVertices(D, 2, 3);\n4\ngap> PartialOrderDigraphJoinOfVertices(\
D, 2, 3);\n1\ngap> PartialOrderDigraphMeetOfVertices(D, 1, 2);\n2\ngap> Partia\
lOrderDigraphJoinOfVertices(D, 3, 4);\n3\ngap> D := Digraph([[1], [2], [1, 2, \
3], [1, 2, 4]]);\n<immutable digraph with 4 vertices, 8 edges>\ngap> PartialOr\
derDigraphMeetOfVertices(D, 3, 4);\nfail\ngap> PartialOrderDigraphJoinOfVertic\
es(D, 3, 4);\nfail\ngap> PartialOrderDigraphMeetOfVertices(D, 1, 2);\nfail\nga\
p> PartialOrderDigraphJoinOfVertices(D, 1, 2);\nfail\n]]></Example>\n  </Descr\
iption>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DegreeMatrix\" Arg=\
\"digraph\"/>\n  <Returns>A square matrix of non-negative integers.</Returns>\
\n  <Description>\n    This function returns the outdegree matrix <C>mat</C> o\
f the digraph\n    <A>digraph</A>. The value of the <C>i</C>th diagonal matrix\
 entry is the\n    outdegree of the vertex <C>i</C> in <A>digraph</A>. All off\
-diagonal entries \n    are <C>0</C>.\n    If <A>digraph</A> has no vertices, \
then the empty list is returned. <P/>\n\n    See <Ref Attr=\"OutDegrees\"/> fo\
r more information.\n    <Example><![CDATA[\ngap> D := Digraph([[1, 2, 3], [4]\
, [1, 3, 4], []]);\n<immutable digraph with 4 vertices, 7 edges>\ngap> PrintAr\
ray(DegreeMatrix(D));\n[ [  3,  0,  0,  0 ],\n  [  0,  1,  0,  0 ],\n  [  0,  \
0,  3,  0 ],\n  [  0,  0,  0,  0 ] ]\ngap> D := CycleDigraph(5);;\ngap> PrintA\
rray(DegreeMatrix(D));\n[ [  1,  0,  0,  0,  0 ],\n  [  0,  1,  0,  0,  0 ],\n\
  [  0,  0,  1,  0,  0 ],\n  [  0,  0,  0,  1,  0 ],\n  [  0,  0,  0,  0,  1 ]\
 ]\ngap> DegreeMatrix(EmptyDigraph(0));\n[  ]\ngap> D := CycleDigraph(IsMutabl\
eDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> Display(Degree\
Matrix(D));\n[ [  1,  0,  0 ],\n  [  0,  1,  0 ],\n  [  0,  0,  1 ] ]\n]]></Ex\
ample>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"La\
placianMatrix\" Arg=\"digraph\"/>\n  <Returns>A square matrix of integers.</Re\
turns>\n  <Description>\n    This function returns the outdegree Laplacian mat\
rix <C>mat</C> of the\n    digraph <A>digraph</A>. The outdegree Laplacian mat\
rix is defined as\n    <C>DegreeMatrix(digraph) - AdjacencyMatrix(digraph)</C>\
.  If\n    <A>digraph</A> has no vertices, then the empty list is returned. <P\
/>\n\n    See <Ref Attr=\"DegreeMatrix\"/> and <Ref Attr=\"AdjacencyMatrix\"/>\
 for more\n    information.\n    <Example><![CDATA[\ngap> gr := Digraph([[1, 2\
, 3], [4], [1, 3, 4], []]);\n<immutable digraph with 4 vertices, 7 edges>\ngap\
> PrintArray(LaplacianMatrix(gr));\n[ [   2,  -1,  -1,   0 ],\n  [   0,   1,  \
 0,  -1 ],\n  [  -1,   0,   2,  -1 ],\n  [   0,   0,   0,   0 ] ]\ngap> Laplac\
ianMatrix(EmptyDigraph(0));\n[  ]\ngap> D := CycleDigraph(IsMutableDigraph, 3)\
;\n<mutable digraph with 3 vertices, 3 edges>\ngap> Display(LaplacianMatrix(D)\
);\n[ [   1,  -1,   0 ],\n  [   0,   1,  -1 ],\n  [  -1,   0,   1 ] ]\n]]></Ex\
ample>\n  </Description>\n</ManSection>\n\n  </Section>\n\n  <Section><Heading\
>Reachability and connectivity</Heading>\n    <ManSection>\n  <Attr Name=\"Dig\
raphDiameter\" Arg=\"digraph\"/>\n  <Returns>An integer or <C>fail</C>.</Retur\
ns>\n  <Description>\n    This function returns the diameter of the digraph <A\
>digraph</A>.\n    <P/>\n\n    If a digraph <A>digraph</A> is strongly connect\
ed and has at least 1\n    vertex, then the <E>diameter</E> is the maximum sho\
rtest distance between\n    any pair of distinct vertices. Otherwise then the \
diameter of\n    <A>digraph</A> is undefined, and this function returns the va\
lue\n    <C>fail</C>. <P/>\n\n    See <Ref Attr=\"DigraphShortestDistances\"/>\
. <P/>\n    <Example><![CDATA[\ngap> D := Digraph([[2], [3], [4, 5], [5], [1, \
2, 3, 4, 5]]);\n<immutable digraph with 5 vertices, 10 edges>\ngap> DigraphDia\
meter(D);\n3\ngap> D := ChainDigraph(2);\n<immutable chain digraph with 2 vert\
ices>\ngap> DigraphDiameter(D);\nfail\ngap> IsStronglyConnectedDigraph(D);\nfa\
lse\ngap> D := GeneralisedPetersenGraph(IsMutableDigraph, 6, 2);\n<mutable dig\
raph with 12 vertices, 36 edges>\ngap> DigraphDiameter(D);\n4\n]]></Example>\n\
  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphSho\
rtestDistance\" Label=\"for a digraph and two vertices\"\n        Arg=\"digrap\
h, u, v\"/>\n  <Oper Name=\"DigraphShortestDistance\" Label=\"for a digraph an\
d a list\"\n        Arg=\"digraph, list\"/>\n  <Oper Name=\"DigraphShortestDis\
tance\" Label=\"for a digraph, a list, and a list\"\n        Arg=\"digraph, li\
st1, list2\"/>\n  <Returns>An integer or <K>fail</K></Returns>\n  <Description\
>\n    If there is a directed path in the digraph <A>digraph</A> between verte\
x\n    <A>u</A> and vertex <A>v</A>, then this operation returns the length of\
 the\n    shortest such directed path.  If no such directed path exists, then \
this\n    operation returns <K>fail</K>. See Section <Ref Subsect=\"Definition\
s\"\n      Style=\"Number\" /> for the definition of a directed path. <P/>\n\n\
    If the second form is used, then <A>list</A> should be a list of length tw\
o,\n    containing two positive integers which correspond to the vertices <A>u\
</A>\n    and <A>v</A>. <P/>\n\n    Note that as usual, a vertex is considered\
 to be at distance 0 from\n    itself .<P/>\n\n    If the third form is used, \
then <A>list1</A> and <A>list2</A> are both lists\n    of vertices. The shorte\
st directed path between <A>list1</A> and\n    <A>list2</A> is then the length\
 of the shortest directed path which starts\n    with a vertex in <A>list1</A>\
 and terminates at a vertex in <A>list2</A>, if\n    such directed path exists\
. If <A>list1</A> and <A>list2</A> have non-empty\n    intersection, the opera\
tion returns <C>0</C>.<P/>\n    <Example><![CDATA[\ngap> D := Digraph([[2], [3\
], [1, 4], [1, 3], [5]]);\n<immutable digraph with 5 vertices, 7 edges>\ngap> \
DigraphShortestDistance(D, 1, 3);\n2\ngap> DigraphShortestDistance(D, [3, 3]);\
\n0\ngap> DigraphShortestDistance(D, 5, 2);\nfail\ngap> DigraphShortestDistanc\
e(D, [1, 2], [4, 5]);\n2\ngap> DigraphShortestDistance(D, [1, 3], [3, 5]);\n0\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr \
Name=\"DigraphShortestDistances\" Arg=\"digraph\"/>\n  <Returns>A square matri\
x.</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph with <M>n</M\
> vertices, then this\n    function returns an <M>n \\times n</M> matrix <C>ma\
t</C>, where each entry is\n    either a non-negative integer, or <K>fail</K>.\
  If <M>n = 0</M>, then an\n    empty list is returned. <P/>\n\n    If there i\
s a directed path from vertex <C>i</C> to vertex <C>j</C>, then\n    the value\
 of <C>mat[i][j]</C> is the length of the shortest such directed\n    path. If\
 no such directed path exists, then the value of <C>mat[i][j]</C> is\n    <C>f\
ail</C>.  We use the convention that the distance from every vertex to\n    it\
self is <C>0</C>, i.e. <C>mat[i][i] = 0</C> for all vertices <C>i</C>.\n    <P\
/>\n\n    The method used in this function is a version of the Floyd-Warshall\
\n    algorithm, and has complexity <M>O(n^3)</M>.\n\n    <Example><![CDATA[\n\
gap> D := Digraph([[1, 2], [3], [1, 2], [4]]);\n<immutable digraph with 4 vert\
ices, 6 edges>\ngap> mat := DigraphShortestDistances(D);;\ngap> PrintArray(mat\
);\n[ [     0,     1,     2,  fail ],\n  [     2,     0,     1,  fail ],\n  [ \
    1,     1,     0,  fail ],\n  [  fail,  fail,  fail,     0 ] ]\ngap> D := C\
ycleDigraph(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\
\ngap> DigraphShortestDistances(D);\n[ [ 0, 1, 2 ], [ 2, 0, 1 ], [ 1, 2, 0 ] ]\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper \
Name=\"DigraphLongestDistanceFromVertex\" Arg=\"digraph, v\"/>\n  <Returns>An \
integer, or <K>infinity</K>.</Returns>\n  <Description>\n    If <A>digraph</A>\
 is a digraph and <A>v</A> is a vertex in <A>digraph</A>,\n    then this opera\
tion returns the length of the longest directed walk in\n    <A>digraph</A> wh\
ich begins at vertex <A>v</A>.  See Section <Ref\n      Subsect=\"Definitions\
\" Style=\"Number\" /> for the definitions of directed\n    walk, directed cyc\
le, and loop.\n    <P/>\n\n    <List>\n      <Item>\n        If there exists a\
 directed walk starting at vertex <A>v</A>\n        which traverses a loop or \
a directed cycle,\n        then we consider there to be a walk of infinite len\
gth from <A>v</A>\n        (realised by repeatedly traversing the loop/directe\
d cycle),\n        and so the result is <K>infinity</K>.\n        To disallow \
walks using loops, try using\n        <Ref Oper=\"DigraphRemoveLoops\"/>:<P/>\
\n\n        <C>DigraphLongestDistanceFromVertex(DigraphRemoveLoops(<A>digraph<\
/A>,<A>v</A>))</C>.\n      </Item>\n\n      <Item>\n        Otherwise, if all \
directed walks\n        starting at vertex <A>v</A> have finite length,\n     \
   then the length of the longest such walk is returned.\n      </Item>\n    <\
/List>\n\n    Note that the result is <C>0</C> if and only if <A>v</A> is a si\
nk of\n    <A>digraph</A>.  See <Ref Attr=\"DigraphSinks\"/>.\n\n<Example><![C\
DATA[\ngap> D := Digraph([[2], [3, 4], [], [5], [], [6]]);\n<immutable digraph\
 with 6 vertices, 5 edges>\ngap> DigraphLongestDistanceFromVertex(D, 1);\n3\ng\
ap> DigraphLongestDistanceFromVertex(D, 3);\n0\ngap> 3 in DigraphSinks(D);\ntr\
ue\ngap> DigraphLongestDistanceFromVertex(D, 6);\ninfinity\n]]></Example>\n  <\
/Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphDistan\
ceSet\" Label=\"for a digraph, a pos int, and an int\" Arg=\"digraph, vertex, \
distance\"/>\n  <Oper Name=\"DigraphDistanceSet\" Label=\"for a digraph, a pos\
 int, and a list\" Arg=\"digraph, vertex, distances\"/>\n  <Returns>A list of \
vertices</Returns>\n  <Description>\n    This operation returns the list of al\
l vertices in digraph <A>digraph</A>\n    such that the shortest distance to a\
 vertex <A>vertex</A> is\n    <A>distance</A> or is in the list <A>distances</\
A>. <P/>\n\n    <A>digraph</A> should be a digraph, <A>vertex</A> should be a \
positive\n    integer, <A>distance</A> should be a non-negative integer, and\n\
    <A>distances</A> should be a list of non-negative integers.\n\n    <Exampl\
e><![CDATA[\ngap> D := Digraph([[2], [3], [1, 4], [1, 3]]);\n<immutable digrap\
h with 4 vertices, 6 edges>\ngap> DigraphDistanceSet(D, 2, [1, 2]);\n[ 3, 1, 4\
 ]\ngap> DigraphDistanceSet(D, 3, 1);\n[ 1, 4 ]\ngap> DigraphDistanceSet(D, 2,\
 0);\n[ 2 ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection\
>\n  <Attr Name=\"DigraphGirth\" Arg=\"digraph\"/>\n  <Returns>An integer, or \
<K>infinity</K>.</Returns>\n  <Description>\n    This attribute returns the <E\
>girth</E> of the digraph <A>digraph</A>.\n    The <E>girth</E> of a digraph i\
s the length of its shortest simple circuit.\n    See Section <Ref Subsect=\"D\
efinitions\" Style=\"Number\" /> for the definitions\n    of simple circuit, d\
irected cycle, and loop.\n    <P/>\n\n    If <A>digraph</A> has no directed cy\
cles, then this function will return\n    <K>infinity</K>.  If <A>digraph</A> \
contains a loop, then this function will\n    return <C>1</C>.\n    <P/>\n\n  \
  In the worst case, the method used in this function is a version of the\n   \
 Floyd-Warshall algorithm, and has complexity <C>O(<A>n</A> ^ 3)</C>, where\n \
   <A>n</A> is the number of vertices in <A>digraph</A>.  If the digraph has\n\
    known automorphisms [see <Ref Attr=\"DigraphGroup\"/>], then the performan\
ce\n    is likely to be better.\n    <P/>\n\n    For symmetric digraphs, see a\
lso <Ref Attr=\"DigraphUndirectedGirth\"/>. <P/>\n    <Example><![CDATA[\ngap>\
 D := Digraph([[1], [1]]);\n<immutable digraph with 2 vertices, 2 edges>\ngap>\
 DigraphGirth(D);\n1\ngap> D := Digraph([[2, 3], [3], [4], []]);\n<immutable d\
igraph with 4 vertices, 4 edges>\ngap> DigraphGirth(D);\ninfinity\ngap> D := D\
igraph([[2, 3], [3], [4], [1]]);\n<immutable digraph with 4 vertices, 5 edges>\
\ngap> DigraphGirth(D);\n3\ngap> D := GeneralisedPetersenGraph(IsMutableDigrap\
h, 6, 2);\n<mutable digraph with 12 vertices, 36 edges>\ngap> DigraphGirth(D);\
\n2\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <At\
tr Name=\"DigraphOddGirth\" Arg=\"digraph\"/>\n  <Returns>An integer, or <K>in\
finity</K>.</Returns>\n  <Description>\n    This attribute returns the <E>odd \
girth</E> of the digraph <A>digraph</A>.\n    The <E>odd girth</E> of a digrap\
h is the length of its shortest simple\n    circuit of odd length.  See Sectio\
n <Ref Subsect=\"Definitions\"\n    Style=\"Number\" /> for the definitions of\
 simple circuit, directed\n    cycle, and loop.\n    <P/>\n\n    If <A>digraph\
</A> has no directed cycles of odd length, then this function\n    will return\
 <K>infinity</K>, even if <A>digraph</A> has a directed cycle\n    of even len\
gth.  If <A>digraph</A> contains a loop, then this function\n    will return <\
C>1</C>.\n    <P/>\n\n    See also <Ref Attr=\"DigraphGirth\"/>. <P/>\n    <Ex\
ample><![CDATA[\ngap> D := Digraph([[2], [3, 1], [1]]);\n<immutable digraph wi\
th 3 vertices, 4 edges>\ngap> DigraphOddGirth(D);\n3\ngap> D := CycleDigraph(4\
);\n<immutable cycle digraph with 4 vertices>\ngap> DigraphOddGirth(D);\ninfin\
ity\ngap> D := Digraph([[2], [3], [], [3], [4]]);\n<immutable digraph with 5 v\
ertices, 4 edges>\ngap> DigraphOddGirth(D);\ninfinity\ngap> D := CycleDigraph(\
IsMutableDigraph, 4);\n<mutable digraph with 4 vertices, 4 edges>\ngap> Digrap\
hDisjointUnion(D, CycleDigraph(5));\n<mutable digraph with 9 vertices, 9 edges\
>\ngap> DigraphOddGirth(D);\n5\n]]></Example>\n  </Description>\n</ManSection>\
\n\n    <ManSection>\n  <Attr Name=\"DigraphUndirectedGirth\" Arg=\"digraph\"/\
>\n  <Returns>An integer or <K>infinity</K>.</Returns>\n  <Description>\n    I\
f <A>digraph</A> is a symmetric digraph, then this function returns the\n    g\
irth of <A>digraph</A> when treated as an undirected graph (i.e. each pair\n  \
  of edges <M>[i, j]</M> and <M>[j, i]</M> is treated as a single edge between\
\n    <M>i</M> and <M>j</M>). <P/>\n\n    The <E>girth</E> of an undirected gr\
aph is the length of its shortest simple\n    cycle, i.e. the shortest non-tri\
vial path starting and ending at the same\n    vertex and passing through no v\
ertex or edge more than once. <P/>\n\n    If <A>digraph</A> has no cycles, the\
n this function will return\n    <K>infinity</K>. <P/>\n    <Example><![CDATA[\
\ngap> D := Digraph([[2, 4], [1, 3], [2, 4], [1, 3]]);\n<immutable digraph wit\
h 4 vertices, 8 edges>\ngap> DigraphUndirectedGirth(D);\n4\ngap> D := Digraph(\
[[2], [1, 3], [2]]);\n<immutable digraph with 3 vertices, 4 edges>\ngap> Digra\
phUndirectedGirth(D);\ninfinity\ngap> D := Digraph([[1], [], [4], [3]]);\n<imm\
utable digraph with 4 vertices, 3 edges>\ngap> DigraphUndirectedGirth(D);\n1\n\
gap> D := GeneralisedPetersenGraph(IsMutableDigraph, 9, 2);\n<mutable digraph \
with 18 vertices, 54 edges>\ngap> DigraphUndirectedGirth(D);\n5\n]]></Example>\
\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphC\
onnectedComponents\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphNrConnectedCompo\
nents\" Arg=\"digraph\"/>\n  <Returns>A record.</Returns>\n  <Description>\n  \
  This function returns the record <C>wcc</C> corresponding to the weakly\n   \
 connected components of the digraph <A>digraph</A>.  Two vertices of\n    <A>\
digraph</A> are in the same weakly connected component whenever they are\n    \
equal, or there exists a directed path (ignoring the orientation of edges)\n  \
  between them.  More formally, two vertices are in the same weakly connected\
\n    component of <A>digraph</A> if and only if they are in the same strongly\
\n    connected component (see <Ref Attr=\"DigraphStronglyConnectedComponents\
\"/>)\n    of the <Ref Oper=\"DigraphSymmetricClosure\"/> of <A>digraph</A>.  \
<P/>\n\n    The set of weakly connected components is a partition of\n    the \
vertex set of <A>digraph</A>. <P/>\n\n    The record <C>wcc</C> has 2 componen\
ts: <C>comps</C> and <C>id</C>.\n    The component <C>comps</C> is a list of t\
he weakly connected components\n    of  <A>digraph</A> (each of which is a lis\
t of vertices).\n    The component <C>id</C> is a list such that the vertex <C\
>i</C> is an\n    element of the weakly connected component <C>comps[id[i]]</C\
>. <P/>\n\n    The method used in this function has complexity  <M>O(m+n)</M>,\
 where\n    <M>m</M> is the number of edges and\n    <M>n</M> is the number of\
 vertices in the digraph. <P/>\n\n    <C>DigraphNrConnectedComponents(<A>digra\
ph</A>)</C> is simply a shortcut\n    for <C>Length(DigraphConnectedComponents\
(<A>digraph</A>).comps)</C>,\n    and is no more efficient.\n\n    <Example><!\
[CDATA[\ngap> gr := Digraph([[2], [3, 1], []]);\n<immutable digraph with 3 ver\
tices, 3 edges>\ngap> DigraphConnectedComponents(gr);\nrec( comps := [ [ 1, 2,\
 3 ] ], id := [ 1, 1, 1 ] )\ngap> gr := Digraph([[1], [1, 2], []]);\n<immutabl\
e digraph with 3 vertices, 3 edges>\ngap> DigraphConnectedComponents(gr);\nrec\
( comps := [ [ 1, 2 ], [ 3 ] ], id := [ 1, 1, 2 ] )\ngap> DigraphNrConnectedCo\
mponents(gr);\n2\ngap> gr := EmptyDigraph(0);\n<immutable empty digraph with 0\
 vertices>\ngap> DigraphConnectedComponents(gr);\nrec( comps := [  ], id := [ \
 ] )\ngap> D := CycleDigraph(IsMutableDigraph, 2);\n<mutable digraph with 2 ve\
rtices, 2 edges>\ngap> G := CycleDigraph(3);\n<immutable cycle digraph with 3 \
vertices>\ngap> DigraphDisjointUnion(D, G);\n<mutable digraph with 5 vertices,\
 5 edges>\ngap> DigraphConnectedComponents(D);\nrec( comps := [ [ 1, 2 ], [ 3,\
 4, 5 ] ], id := [ 1, 1, 2, 2, 2 ] )\n]]></Example>\n  </Description>\n</ManSe\
ction>\n\n    <ManSection>\n  <Oper Name=\"DigraphConnectedComponent\" Arg=\"d\
igraph, vertex\"/>\n  <Returns>A list of vertices.</Returns>\n  <Description>\
\n    If <A>vertex</A> is a vertex in the digraph <A>digraph</A>, then\n    th\
is operation returns the connected component of <A>vertex</A>\n    in <A>digra\
ph</A>.\n    See <Ref Attr=\"DigraphConnectedComponents\"/> for more informati\
on.\n    <Example><![CDATA[\ngap> D := Digraph([[3], [2], [1, 2], [4]]);\n<imm\
utable digraph with 4 vertices, 5 edges>\ngap> DigraphConnectedComponent(D, 3)\
;\n[ 1, 2, 3 ]\ngap> DigraphConnectedComponent(D, 2);\n[ 1, 2, 3 ]\ngap> Digra\
phConnectedComponent(D, 4);\n[ 4 ]\n]]></Example>\n  </Description>\n</ManSect\
ion>\n\n    <ManSection>\n  <Attr Name=\"DigraphStronglyConnectedComponents\" \
Arg=\"digraph\"/>\n  <Attr Name=\"DigraphNrStronglyConnectedComponents\" Arg=\
\"digraph\"/>\n  <Returns>A record.</Returns>\n  <Description>\n    This funct\
ion returns the record <C>scc</C> corresponding to the strongly\n    connected\
 components of the digraph <A>digraph</A>.  Two vertices of\n    <A>digraph</A\
> are in the same strongly connected component whenever they\n    are equal, o\
r there is a directed path from each vertex to the other.  The\n    set of str\
ongly connected components is a partition of the vertex set of\n    <A>digraph\
</A>.\n    <P/>\n\n    The record <C>scc</C> has 2 components: <C>comps</C> an\
d <C>id</C>.\n    The component <C>comps</C> is a list of the strongly connect\
ed components\n    of <A>digraph</A> (each of which is a list of vertices).\n \
   The component <C>id</C> is a list such that the vertex <C>i</C> is an\n    \
element of the strongly connected component <C>comps[id[i]]</C>. <P/>\n\n    T\
he method used in this function is a non-recursive version of Gabow's\n    Alg\
orithm <Cite Key=\"Gab00\"/> and has complexity <M>O(m+n)</M> where\n    <M>m<\
/M> is the number of edges (counting multiple edges as one) and\n    <M>n</M> \
is the number of vertices in the digraph. <P/>\n\n    <C>DigraphNrStronglyConn\
ectedComponents(<A>digraph</A>)</C> is simply a\n    shortcut for\n    <C>Leng\
th(DigraphStronglyConnectedComponents(<A>digraph</A>).comps)</C>,\n    and is \
no more efficient.\n\n    <Example><![CDATA[\ngap> gr := Digraph([[2], [3, 1],\
 []]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> DigraphStronglyConn\
ectedComponents(gr);\nrec( comps := [ [ 3 ], [ 1, 2 ] ], id := [ 2, 2, 1 ] )\n\
gap> DigraphNrStronglyConnectedComponents(gr);\n2\ngap> D := DigraphDisjointUn\
ion(CycleDigraph(4), CycleDigraph(5));\n<immutable digraph with 9 vertices, 9 \
edges>\ngap> DigraphStronglyConnectedComponents(D);\nrec( comps := [ [ 1, 2, 3\
, 4 ], [ 5, 6, 7, 8, 9 ] ], \n  id := [ 1, 1, 1, 1, 2, 2, 2, 2, 2 ] )\ngap> Di\
graphNrStronglyConnectedComponents(D);\n2\ngap> D := CycleDigraph(IsMutableDig\
raph, 2);\n<mutable digraph with 2 vertices, 2 edges>\ngap> G := CycleDigraph(\
3);\n<immutable cycle digraph with 3 vertices>\ngap> DigraphDisjointUnion(D, G\
);\n<mutable digraph with 5 vertices, 5 edges>\ngap> DigraphStronglyConnectedC\
omponents(D);\nrec( comps := [ [ 1, 2 ], [ 3, 4, 5 ] ], id := [ 1, 1, 2, 2, 2 \
] )\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Op\
er Name=\"DigraphStronglyConnectedComponent\" Arg=\"digraph, vertex\"/>\n  <Re\
turns>A list of vertices.</Returns>\n  <Description>\n    If <A>vertex</A> is \
a vertex in the digraph <A>digraph</A>, then\n    this operation returns the s\
trongly connected component of <A>vertex</A>\n    in <A>digraph</A>.\n    See \
<Ref Attr=\"DigraphStronglyConnectedComponents\"/> for more information.\n    \
<Example><![CDATA[\ngap> D := Digraph([[3], [2], [1, 2], [3]]);\n<immutable di\
graph with 4 vertices, 5 edges>\ngap> DigraphStronglyConnectedComponent(D, 3);\
\n[ 1, 3 ]\ngap> DigraphStronglyConnectedComponent(D, 2);\n[ 2 ]\ngap> Digraph\
StronglyConnectedComponent(D, 4);\n[ 4 ]\n]]></Example>\n  </Description>\n</M\
anSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphBicomponents\" Arg=\"dig\
raph\"/>\n  <Returns>A pair of lists of vertices, or <K>fail</K>.</Returns>\n \
 <Description>\n    If <A>digraph</A> is a bipartite digraph, i.e. if it satis\
fies <Ref\n      Prop=\"IsBipartiteDigraph\"/>, then <C>DigraphBicomponents</C\
> returns a\n    pair of bicomponents of <A>digraph</A>. Otherwise,\n    <C>Di\
graphBicomponents</C> returns <K>fail</K>.<P/>\n\n    For a bipartite digraph,\
 the vertices can be partitioned into two non-empty\n    sets such that the so\
urce and range of any edge are in distinct sets. The\n    parts of this partit\
ion are called <E>bicomponents</E> of <A>digraph</A>.\n    Equivalently, a pai\
r of bicomponents of <A>digraph</A> consists of the\n    color-classes of a 2-\
coloring of <A>digraph</A>. <P/>\n\n    For a bipartite digraph with at least \
3 vertices, there is a unique pair of\n    bicomponents of bipartite if and on\
ly if the digraph is connected. See <Ref\n      Prop=\"IsConnectedDigraph\"/> \
for more information.\n    <Example><![CDATA[\ngap> D := CycleDigraph(3);\n<im\
mutable cycle digraph with 3 vertices>\ngap> DigraphBicomponents(D);\nfail\nga\
p> D := ChainDigraph(5);\n<immutable chain digraph with 5 vertices>\ngap> Digr\
aphBicomponents(D);\n[ [ 1, 3, 5 ], [ 2, 4 ] ]\ngap> D := Digraph([[5], [1, 4]\
, [5], [5], []]);\n<immutable digraph with 5 vertices, 5 edges>\ngap> DigraphB\
icomponents(D);\n[ [ 1, 3, 4 ], [ 2, 5 ] ]\ngap> D := CompleteBipartiteDigraph\
(IsMutableDigraph, 2, 3);\n<mutable digraph with 5 vertices, 12 edges>\ngap> D\
igraphBicomponents(D);\n[ [ 1, 2 ], [ 3, 4, 5 ] ]\n]]></Example>\n  </Descript\
ion>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"ArticulationPoints\" A\
rg=\"digraph\"/>\n  <Returns>A list of vertices.</Returns>\n  <Description>\n \
   A connected digraph is <E>biconnected</E> if it is still connected (in the\
\n    sense of <Ref Prop=\"IsConnectedDigraph\"/>) when any vertex is removed.\
 \n    If the digraph <A>digraph</A> is not biconnected but is connected, then\
 any\n    vertex <C>v</C> of <A>digraph</A> whose removal makes the resulting \
digraph\n    disconnected is called an <E>articulation point</E>.<P/>\n\n    <\
C>ArticulationPoints</C> returns a list of the articulation points of\n    <A>\
digraph</A>, if any, and, in particular, returns the empty list if\n    <A>dig\
raph</A> is not connected. <P/>\n\n    Multiple edges are ignored by this meth\
od. <P/>\n\n    The method used in this operation has complexity <M>O(m+n)</M>\
 where\n    <M>m</M> is the number of edges and <M>n</M> is the number of vert\
ices in\n    the digraph.<P/>\n      \n    If <A>D</A> has a bridge (see <Ref \
Attr=\"Bridges\"/>), then a node incident\n    to the bridge is an articulatio\
n point if and only if it has degree at\n    least <M>2</M>.  It follows that \
if <A>D</A> has a bridge and at least\n    <M>3</M> nodes, then at least one o\
f the nodes incident to the bridge is\n    an articulation point.  The convers\
e does not hold, there are digraphs\n    with articulation points, but no brid\
ges.\n    <P/>\n\n    See also <Ref Prop=\"IsBiconnectedDigraph\"/> and \n    \
<Ref Prop=\"IsBridgelessDigraph\"/>.\n<Example><![CDATA[\ngap> ArticulationPoi\
nts(CycleDigraph(5));\n[  ]\ngap> D := Digraph([[2, 7], [3, 5], [4], [2], [6],\
 [1], []]);;\ngap> ArticulationPoints(D);\n[ 2, 1 ]\ngap> ArticulationPoints(C\
hainDigraph(5));\n[ 4, 3, 2 ]\ngap> ArticulationPoints(NullDigraph(5));\n[  ]\
\ngap> D := ChainDigraph(IsMutableDigraph, 4);\n<mutable digraph with 4 vertic\
es, 3 edges>\ngap> ArticulationPoints(D);\n[ 3, 2 ]\n]]></Example>\n  </Descri\
ption>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"Bridges\" Arg=\"D\"/\
>\n  <Returns>A (possibly empty) list of edges.</Returns>\n  <Description>\n  \
  A connected digraph is <E>2-edge-connected</E> if it is still connected (in\
\n    the sense of <Ref Prop=\"IsConnectedDigraph\"/>) when any edge is\n    r\
emoved.  If the digraph <A>D</A> is not 2-edge-connected but is\n    connected\
, then any edge <C>[u, v]</C> of <A>D</A> whose removal\n    makes the resulti\
ng digraph disconnected is called a <E>bridge</E>.<P/>\n\n    <C>Bridges</C> r\
eturns a list of the bridges of <A>D</A>, if any, and, in\n    particular, ret\
urns the empty list if <A>D</A> is not connected. <P/>\n\n    Multiple edges a\
re ignored by this method. <P/>\n\n    The method used in this operation has c\
omplexity <M>O(m+n)</M> where\n    <M>m</M> is the number of edges and <M>n</M\
> is the number of vertices in\n    the digraph.\n    <P/>\n\n    If <A>D</A> \
has a bridge, then a node incident to the bridge is an\n    articulation point\
 (see <Ref Attr=\"ArticulationPoints\"/>) if and only if\n    it has degree at\
 least <M>2</M>.  It follows that if <A>D</A> has a\n    bridge and at least <\
M>3</M> nodes, then at least one of the nodes\n    incident to the bridge is a\
n articulation point. The converse does not\n    hold, there are digraphs with\
 articulation points, but no bridges.\n    <P/>\n\n    See also <Ref Prop=\"Is\
BiconnectedDigraph\"/> and \n    <Ref Prop=\"IsBridgelessDigraph\"/>.\n<Exampl\
e><![CDATA[\ngap> D := Digraph([[2, 5], [1, 3, 4, 5], [2, 4], [2, 3], [1, 2]])\
;\n<immutable digraph with 5 vertices, 12 edges>\ngap> Bridges(D);\n[  ]\ngap>\
 D := Digraph([[2], [3], [4], [2]]);\n<immutable digraph with 4 vertices, 4 ed\
ges>\ngap> Bridges(D);\n[ [ 1, 2 ] ]\ngap> Bridges(ChainDigraph(2));\n[ [ 1, 2\
 ] ]\ngap> ArticulationPoints(ChainDigraph(2));\n[  ]\n]]></Example>\n  </Desc\
ription>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"StrongOrientation\
\" Arg=\"D\"/>\n  <Attr Name=\"StrongOrientationAttr\" Arg=\"D\"/>\n  <Returns\
>A digraph or <K>fail</K>.</Returns>\n  <Description>\n    A <E>strong orienta\
tion</E> of a connected symmetric digraph <A>D</A> (if\n    it exists) is a st\
rongly connected subdigraph <C>C</C> of <A>D</A> such\n    that for every edge\
 <C>[u, v]</C> of <A>D</A> either <C>[u, v]</C> or\n    <C>[v, u]</C> is an ed\
ge of <C>C</C> but not both.  Robbin's Theorem states\n    that a digraph admi\
ts a strong orientation if and only if it is\n    bridgeless (see <Ref Prop=\"\
IsBridgelessDigraph\"/>). \n    <P/>\n\n    This operation returns a strong or\
ientation of the digraph <A>D</A> if \n    <A>D</A> is symmetric and <A>D</A> \
admits a strong orientation. If <A>D</A>\n    is symmetric but does not admit \
a strong orientation, then <K>fail</K> is\n    returned. If <A>D</A> is not sy\
mmetric, then an error is given. \n    <P/>\n\n    If <A>D</A> is immutable, <\
C>StrongOrientation(<A>D</A>)</C> returns an\n    immutable digraph, and if <A\
>D</A> is mutable, then\n    <C>StrongOrientation(<A>D</A>)</C> returns a muta\
ble digraph. <P/>\n\n    The method used in this operation has complexity <M>O\
(m+n)</M> where\n    <M>m</M> is the number of edges and <M>n</M> is the numbe\
r of vertices in\n    the digraph.\n<Example><![CDATA[\ngap> StrongOrientation\
(DigraphSymmetricClosure(CycleDigraph(5))) \n> = CycleDigraph(5);\ntrue\ngap> \
D := DigraphSymmetricClosure(Digraph(\n> [[2, 7], [3, 5], [4], [2], [6], [1], \
[]]));;\ngap> IsBridgelessDigraph(D);\nfalse\ngap> StrongOrientation(D);\nfail\
\ngap> StrongOrientation(NullDigraph(0));\n<immutable empty digraph with 0 ver\
tices>\ngap> StrongOrientation(DigraphDisjointUnion(CompleteDigraph(3), \n>   \
                                        CompleteDigraph(3)));\nfail\n]]></Exam\
ple>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"Digr\
aphPeriod\" Arg=\"digraph\"/>\n  <Returns>An integer.</Returns>\n  <Descriptio\
n>\n    This function returns the period of the digraph <A>digraph</A>.<P/>\n\
\n    If a digraph <A>digraph</A> has at least one directed cycle, then the pe\
riod\n    is the greatest positive integer which divides the lengths of all di\
rected\n    cycles of <A>digraph</A>.  If <A>digraph</A> has no directed cycle\
s, then\n    this function returns <M>0</M>.  See Section <Ref Subsect=\"Defin\
itions\"\n      Style=\"Number\" /> for the definition of a directed cycle. <P\
/>\n\n    A digraph with a period of <M>1</M> is said to be <E>aperiodic</E>. \
 See\n    <Ref Prop=\"IsAperiodicDigraph\"/>. <P/>\n    <Example><![CDATA[\nga\
p> D := Digraph([[6], [1], [2], [3], [4, 4], [5]]);\n<immutable multidigraph w\
ith 6 vertices, 7 edges>\ngap> DigraphPeriod(D);\n6\ngap> D := Digraph([[2], [\
3, 5], [4], [5], [1, 2]]);\n<immutable digraph with 5 vertices, 7 edges>\ngap>\
 DigraphPeriod(D);\n1\ngap> D := ChainDigraph(2);\n<immutable chain digraph wi\
th 2 vertices>\ngap> DigraphPeriod(D);\n0\ngap> IsAcyclicDigraph(D);\ntrue\nga\
p> D := GeneralisedPetersenGraph(IsMutableDigraph, 5, 2);\n<mutable digraph wi\
th 10 vertices, 30 edges>\ngap> DigraphPeriod(D);\n1\n]]></Example>\n  </Descr\
iption>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphFloydWarshal\
l\" Arg=\"digraph, func, nopath, edge\"/>\n  <Returns>A matrix.</Returns>\n  <\
Description>\n    If <A>digraph</A> is a digraph with <M>n</M> vertices, then\
\n    this operation returns an <M>n \\times n</M> matrix <C>mat</C> containin\
g\n    the output of a generalised version of the Floyd-Warshall algorithm,\n \
   applied to <A>digraph</A>. <P/>\n\n    The operation <C>DigraphFloydWarshal\
l</C> is customised by the arguments\n    <A>func</A>, <A>nopath</A>, and <A>e\
dge</A>.\n    The arguments <A>nopath</A> and <A>edge</A> can be arbitrary &GA\
P; objects.\n    The argument <A>func</A> must be a function which accepts 4 a\
rguments:\n    the matrix <C>mat</C>, followed by 3 postive integers. The func\
tion\n    <A>func</A> is where the work to calculate the desired outcome must \
be\n    performed. <P/>\n\n    This method initialises the matrix <C>mat</C> b\
y setting entry\n    <C>mat[i][j]</C> to equal <A>edge</A> if there is an edge\
 with source\n    <C>i</C> and range <C>j</C>, and by setting entry <C>mat[i][\
j]</C> to equal\n    <A>nopath</A> otherwise.\n    The final part of <C>Digrap\
hFloydWarshall</C> then calls the function\n    <A>func</A> inside three neste\
d for loops, over the vertices of\n    <A>digraph</A>: <P/>\n\n<Listing><![CDA\
TA[\nfor i in DigraphsVertices(digraph) do\n  for j in DigraphsVertices(digrap\
h) do\n    for k in DigraphsVertices(digraph) do\n      func(mat, i, j, k);\n \
   od;\n  od;\nod;\n]]></Listing>\n\n    The matrix <C>mat</C> is then returne\
d as the result. An example of using\n    <C>DigraphFloydWarshall</C> to calcu\
late the shortest (non-zero) distances\n    between the vertices of a digraph \
is shown below: <P/>\n\n    <Example><![CDATA[\ngap> D := DigraphFromDigraph6S\
tring(\"&EAHQeDB\");\n<immutable digraph with 6 vertices, 12 edges>\ngap> func\
 := function(mat, i, j, k)\n>   if mat[i][k] <> -1 and mat[k][j] <> -1 then\n>\
     if (mat[i][j] = -1) or (mat[i][j] > mat[i][k] + mat[k][j]) then\n>       \
mat[i][j] := mat[i][k] + mat[k][j];\n>     fi;\n>   fi;\n> end;\nfunction( mat\
, i, j, k ) ... end\ngap> shortest_distances := DigraphFloydWarshall(D, func, \
-1, 1);;\ngap> Display(shortest_distances);\n[ [   3,  -1,  -1,   2,   1,   2 \
],\n  [   4,   2,   1,   3,   2,   1 ],\n  [   3,   1,   2,   2,   1,   2 ],\n\
  [   1,  -1,  -1,   1,   1,   2 ],\n  [   2,  -1,  -1,   1,   2,   1 ],\n  [ \
  3,  -1,  -1,   2,   1,   1 ] ]\n]]></Example>\n  </Description>\n</ManSectio\
n>\n\n    <ManSection>\n  <Oper Name=\"IsReachable\" Arg=\"digraph, u, v\"/>\n\
  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    This o\
peration returns <K>true</K> if there exists a non-trivial directed\n    walk \
from vertex <A>u</A> to vertex <A>v</A> in the digraph <A>digraph</A>,\n    an\
d <K>false</K> if there does not exist such a directed walk.  See Section\n   \
 <Ref Subsect=\"Definitions\" Style=\"Number\" /> for the definition of a\n   \
 non-trivial directed walk.\n    <P/>\n\n    The method for <C>IsReachable</C>\
 has worst case complexity of <M>O(m +\n      n)</M> where <M>m</M> is the num\
ber of edges and <M>n</M> the number of\n    vertices in <A>digraph</A>.\n\n<E\
xample><![CDATA[\ngap> D := Digraph([[2], [3], [2, 3]]);\n<immutable digraph w\
ith 3 vertices, 4 edges>\ngap> IsReachable(D, 1, 3);\ntrue\ngap> IsReachable(D\
, 2, 1);\nfalse\ngap> IsReachable(D, 3, 3);\ntrue\ngap> IsReachable(D, 1, 1);\
\nfalse\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n \
 <Oper Name=\"VerticesReachableFrom\" Arg=\"digraph, root\"/>\n  <Returns>A li\
st.</Returns>\n  <Description>\n    This operation returns a list of the verti\
ces  <A>v</A>, for which there exists\n    a non-trivial directed walk from ve\
rtex <A>root</A> to vertex <A>v</A> in the digraph\n    <A>digraph</A>. See Se\
ction <Ref Subsect=\"Definitions\" Style=\"Number\" />\n    for the definition\
 of a non-trivial directed walk.\n    <P/>\n\n    The method for <C>VerticesRe\
achableFrom</C> has worst case complexity of <M>O(m +\n      n)</M> where <M>m\
</M> is the number of edges and <M>n</M> the number of\n    vertices in <A>dig\
raph</A>.\n\n<Example><![CDATA[\ngap> D := CompleteDigraph(5);\n<immutable com\
plete digraph with 5 vertices>\ngap> VerticesReachableFrom(D, 1);\n[ 2, 1, 3, \
4, 5 ]\ngap> VerticesReachableFrom(D, 3);\n[ 1, 2, 3, 4, 5 ]\ngap> D := EmptyD\
igraph(5);\n<immutable empty digraph with 5 vertices>\ngap> VerticesReachableF\
rom(D, 1);\n[  ]\ngap> VerticesReachableFrom(D, 3);\n[  ]\ngap> D := CycleDigr\
aph(4);\n<immutable cycle digraph with 4 vertices>\ngap> VerticesReachableFrom\
(D, 1);\n[ 2, 3, 4, 1 ]\ngap> VerticesReachableFrom(D, 3);\n[ 4, 1, 2, 3 ]\nga\
p> D := ChainDigraph(5);\n<immutable chain digraph with 5 vertices>\ngap> Vert\
icesReachableFrom(D, 1);\n[ 2, 3, 4, 5 ]\ngap> VerticesReachableFrom(D, 3);\n[\
 4, 5 ]\ngap> VerticesReachableFrom(D, 5);\n[  ]\n]]></Example>\n  </Descripti\
on>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphPath\" Arg=\"dig\
raph, u, v\"/>\n  <Returns>A pair of lists, or <K>fail</K>.</Returns>\n  <Desc\
ription>\n    If there exists a non-trivial directed path (or a non-trivial cy\
cle, in the\n    case that <A>u</A> <C>=</C> <A>v</A>) from vertex <A>u</A> to\
 vertex\n    <A>v</A> in the digraph <A>digraph</A>, then this operation retur\
ns such a\n    directed path (or directed cycle). Otherwise, this operation re\
turns\n    <K>fail</K>.  See Section <Ref Subsect=\"Definitions\" Style=\"Text\
\"/> for the\n    definition of a directed path and a directed cycle.\n    <P/\
>\n\n    A directed path (or directed cycle) of non-zero length <C>n-1</C>,\n \
   <M>(v_1, e_1, v_2, e_2, ..., e_{n-1}, v_n)</M>,\n    is represented by a pa\
ir of lists <C>[v,a]</C> as follows:\n\n    <List>\n      <Item>\n        <C>v\
</C> is the list <M>[v_1, v_2, ..., v_n]</M>.\n      </Item>\n      <Item>\n  \
      <C>a</C> is the list of positive integers <M>[a_1, a_2, ..., a_{n-1}]</M\
>\n        where for each each <M>i &lt; n</M>, <M>a_i</M> is the position of\
\n        <M>v_{i+1}</M> in\n        <C>OutNeighboursOfVertex(</C><A>digraph</\
A><C>,</C><M>v_i</M><C>)</C>\n        corresponding to the edge <M>e_i</M>.  T\
his is can be useful if the\n        position of a vertex in a list of out-nei\
ghours is significant, for\n        example in orbit digraphs.\n      </Item>\
\n    </List>\n\n    The method for <C>DigraphPath</C> has worst case complexi\
ty of <M>O(m +\n      n)</M> where <M>m</M> is the number of edges and <M>n</M\
> the number of\n    vertices in <A>digraph</A>.\n\n<Example><![CDATA[\ngap> D\
 := Digraph([[2], [3], [2, 3]]);\n<immutable digraph with 3 vertices, 4 edges>\
\ngap> DigraphPath(D, 1, 3);\n[ [ 1, 2, 3 ], [ 1, 1 ] ]\ngap> DigraphPath(D, 2\
, 1);\nfail\ngap> DigraphPath(D, 3, 3);\n[ [ 3, 3 ], [ 2 ] ]\ngap> DigraphPath\
(D, 1, 1);\nfail\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSe\
ction>\n  <Oper Name=\"DigraphShortestPath\" Arg=\"digraph, u, v\"/>\n  <Retur\
ns>A pair of lists, or <K>fail</K>.</Returns>\n  <Description>\n    Returns th\
e shortest directed path in the digraph digraph from the vertex\n    <A>u</A> \
to the vertex <A>v</A>, if such a path exists. If <C><A>u</A> =\n    <A>v</A><\
/C>, then the shortest non-trivial cycle is returned, again, if it\n    exists\
. Otherwise, this operation returns <K>fail</K>.  See Section\n    <Ref Subsec\
t=\"Definitions\" Style=\"Text\"/> for the definition of a directed\n    path \
and a directed cycle.\n    <P/>\n\n    See <Ref Oper=\"DigraphPath\"/> for det\
ails on the output.\n\n    The method for <C>DigraphShortestPath</C> has worst\
 case complexity of\n    <M>O(m + n)</M> where <M>m</M> is the number of edges\
 and <M>n</M> the\n    number of vertices in <A>digraph</A>.\n\n<Example><![CD\
ATA[\ngap> D := Digraph([[1, 2], [3], [2, 4], [1], [2, 4]]);\n<immutable digra\
ph with 5 vertices, 8 edges>\ngap> DigraphShortestPath(D, 5, 1);\n[ [ 5, 4, 1 \
], [ 2, 1 ] ]\ngap> DigraphShortestPath(D, 3, 3);\n[ [ 3, 2, 3 ], [ 1, 1 ] ]\n\
gap> DigraphShortestPath(D, 5, 5);\nfail\ngap> DigraphShortestPath(D, 1, 1);\n\
[ [ 1, 1 ], [ 1 ] ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <Ma\
nSection>\n  <Oper Name=\"IteratorOfPaths\" Arg=\"digraph, u, v\"/>\n  <Return\
s>An iterator.</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph \
or a list of adjacencies which defines a\n    digraph - see <Ref Attr=\"OutNei\
ghbours\"/> - then this operation returns an\n    iterator of the non-trivial \
directed paths (or directed cycles, in the case\n    that <A>u</A> <C>=</C> <A\
>v</A>) in <A>digraph</A> from the vertex <A>u</A>\n    to the vertex <A>v</A>\
.\n    <P/>\n\n    See <Ref Oper=\"DigraphPath\"/> for more information about \
the repesentation\n    of a directed path or directed cycle which is used, and\
 see <Ref\n      Sect=\"Iterators\" BookName=\"ref\"/> for more information ab\
out iterators.\n    See Section <Ref Subsect=\"Definitions\" Style=\"Text\"/> \
for the definition of\n    a directed path and a directed cycle.\n    <P/>\n\n\
<Example><![CDATA[\ngap> D := Digraph([[1, 4, 4, 2], [3, 5], [2, 3], [1, 2], [\
4]]);\n<immutable multidigraph with 5 vertices, 11 edges>\ngap> iter := Iterat\
orOfPaths(D, 1, 4);\n<iterator>\ngap> NextIterator(iter);\n[ [ 1, 4 ], [ 2 ] ]\
\ngap> NextIterator(iter);\n[ [ 1, 4 ], [ 3 ] ]\ngap> NextIterator(iter);\n[ [\
 1, 2, 5, 4 ], [ 4, 2, 1 ] ]\ngap> IsDoneIterator(iter);\ntrue\ngap> iter := I\
teratorOfPaths(D, 4, 3);\n<iterator>\ngap> NextIterator(iter);\n[ [ 4, 1, 2, 3\
 ], [ 1, 4, 1 ] ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManS\
ection>\n  <Attr Name=\"DigraphAllSimpleCircuits\" Arg=\"digraph\"/>\n  <Retur\
ns>A list of lists of vertices.</Returns>\n  <Description>\n    If <A>digraph<\
/A> is a digraph, then <C>DigraphAllSimpleCircuits</C>\n    returns a list of \
the <E>simple circuits</E> in <A>digraph</A>. <P/>\n\n    See Section <Ref Sub\
sect=\"Definitions\" Style=\"Number\" /> for the definition\n    of a simple c\
ircuit, and related notions. Note that a loop is a simple\n    circuit. <P/>\n\
\n    For a digraph without multiple edges, a simple circuit is uniquely\n    \
determined by its subsequence of vertices. However this is not the case for\n \
   a multidigraph.  The attribute <C>DigraphAllSimpleCircuits</C> ignores\n   \
 multiple edges, and identifies a simple circuit using only its subsequence\n \
   of vertices. For example, although the simple circuits <M>(v, e, v)</M> and\
\n    <M>(v, e', v)</M> (for distinct edges <M>e</M> and <M>e'</M>) are\n    m\
athematically distinct, <C>DigraphAllSimpleCircuits</C> considers them to\n   \
 be the same. <P/>\n\n    With this approach, a directed circuit of length <C>\
n</C> can be determined\n    by a list of its first <C>n</C> vertices. Thus a \
simple circuit <M>(v_1,\n      e_1, v_2, e_2, ..., e_{n-1}, v_n, e_{n+1}, v_1)\
</M> can be represented as\n    the list <M>[v_1, \\ldots, v_n]</M>, or any cy\
clic permutation thereof.  For\n    each simple circuit of <A>digraph</A>,\n  \
  <C>DigraphAllSimpleCircuits(<A>digraph</A>)</C> includes precisely one such\
\n    list to represent the circuit.  <P/>\n\n    <Example><![CDATA[\ngap> D :\
= Digraph([[], [3], [2, 4], [5, 4], [4]]);\n<immutable digraph with 5 vertices\
, 6 edges>\ngap> DigraphAllSimpleCircuits(D);\n[ [ 4 ], [ 4, 5 ], [ 2, 3 ] ]\n\
gap> D := ChainDigraph(10);;\ngap> DigraphAllSimpleCircuits(D);\n[  ]\ngap> D \
:= Digraph([[3], [1], [1]]);\n<immutable digraph with 3 vertices, 3 edges>\nga\
p> DigraphAllSimpleCircuits(D);\n[ [ 1, 3 ] ]\ngap> D := Digraph([[1, 1]]);\n<\
immutable multidigraph with 1 vertex, 2 edges>\ngap> DigraphAllSimpleCircuits(\
D);\n[ [ 1 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 3);\n<mutable digraph\
 with 3 vertices, 3 edges>\ngap> DigraphAllSimpleCircuits(D);\n[ [ 1, 2, 3 ] ]\
\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr \
Name=\"DigraphLongestSimpleCircuit\" Arg=\"digraph\"/>\n  <Returns>A list of v\
ertices, or <K>fail</K>.</Returns>\n  <Description>\n    If <A>digraph</A> is \
a digraph, then <C>DigraphLongestSimpleCircuit</C>\n    returns the longest <E\
>simple circuit</E> in <A>digraph</A>. See Section\n    <Ref Subsect=\"Definit\
ions\" Style=\"Number\" /> for the definition of simple\n    circuit, and the \
definition of length for a simple circuit.<P/>\n\n    This attribute computes\
\n    <C>DigraphAllSimpleCircuits(</C><A>digraph</A><C>)</C> to find all the\n\
    simple circuits of <A>digraph</A>, and returns one of maximal length.  A\n\
    simple circuit is represented as a list of vertices, in the same way as\n \
   described in <Ref Attr=\"DigraphAllSimpleCircuits\"/>.<P/>\n\n    If <A>dig\
raph</A> has no simple circuits, then this attribute returns\n    <K>fail</K>.\
  If <A>digraph</A> has multiple simple circuits of maximal\n    length, then \
this attribute returns one of them.<P/>\n\n    <Example><![CDATA[\ngap> D := D\
igraph([[], [3], [2, 4], [5, 4], [4]]);;\ngap> DigraphLongestSimpleCircuit(D);\
\n[ 4, 5 ]\ngap> D := ChainDigraph(10);;\ngap> DigraphLongestSimpleCircuit(D);\
\nfail\ngap> D := Digraph([[3], [1], [1, 4], [1, 1]]);;\ngap> DigraphLongestSi\
mpleCircuit(D);\n[ 1, 3, 4 ]\ngap> D := GeneralisedPetersenGraph(IsMutableDigr\
aph, 4, 1);\n<mutable digraph with 8 vertices, 24 edges>\ngap> DigraphLongestS\
impleCircuit(D);\n[ 1, 2, 3, 4, 8, 7, 6, 5 ]\n]]></Example>\n  </Description>\
\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphLayers\" Arg=\"digr\
aph, vertex\"/>\n  <Returns>A list.</Returns>\n  <Description>\n    This opera\
tion returns a list <K>list</K> such that <K>list[i]</K> is the\n    list of v\
ertices whose minimum distance from the vertex <A>vertex</A> in\n    <A>digrap\
h</A> is <K>i - 1</K>. Vertex <A>vertex</A> is\n    assumed to be at distance \
<K>0</K> from itself.\n    <Example><![CDATA[\ngap> D := CompleteDigraph(4);;\
\ngap> DigraphLayers(D, 1);\n[ [ 1 ], [ 2, 3, 4 ] ]\n]]></Example>\n  </Descri\
ption>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphDegeneracy\" \
Arg=\"digraph\"/>\n  <Returns>A non-negative integer, or <K>fail</K>.</Returns\
>\n  <Description>\n    If <A>digraph</A> is a symmetric digraph without multi\
ple edges - see\n    <Ref Prop=\"IsSymmetricDigraph\"/> and <Ref Prop=\"IsMult\
iDigraph\"/> - then\n    this attribute returns the degeneracy of <A>digraph</\
A>. <P/>\n\n    The degeneracy of a digraph is the least integer <C>k</C> such\
\n    that every induced of <A>digraph</A> contains a vertex whose number of\n\
    neighbours (excluding itself) is at most <C>k</C>. Note that this means\n \
   that loops are ignored.<P/>\n\n    If <A>digraph</A> is not symmetric or ha\
s multiple edges then this\n    attribute returns <K>fail</K>.\n    <Example><\
![CDATA[\ngap> D := DigraphSymmetricClosure(ChainDigraph(5));;\ngap> DigraphDe\
generacy(D);\n1\ngap> D := CompleteDigraph(5);;\ngap> DigraphDegeneracy(D);\n4\
\ngap> D := Digraph([[1], [2, 4, 5], [3, 4], [2, 3, 4], [2], []]);\n<immutable\
 digraph with 6 vertices, 10 edges>\ngap> DigraphDegeneracy(D);\n1\ngap> D := \
GeneralisedPetersenGraph(IsMutableDigraph, 10, 3);\n<mutable digraph with 20 v\
ertices, 60 edges>\ngap> DigraphDegeneracy(D);\n3\n]]></Example>\n  </Descript\
ion>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphDegeneracyOrder\
ing\" Arg=\"digraph\"/>\n  <Returns>A list of integers, or <K>fail</K>.</Retur\
ns>\n  <Description>\n    If <A>digraph</A> is a digraph for which\n    <C>Dig\
raphDegeneracy(</C><A>digraph</A><C>)</C> is a non-negative integer\n    <C>k<\
/C> - see <Ref Attr=\"DigraphDegeneracy\"/> - then this attribute\n    returns\
 a degeneracy ordering of the vertices of the vertices of\n    <A>digraph</A>.\
<P/>\n\n    A degeneracy ordering of <A>digraph</A> is a list <C>ordering</C> \
of the\n    vertices of <A>digraph</A> ordered such that for any\n    position\
 <C>i</C> of the list, the vertex <C>ordering[i]</C> has at most\n    <C>k</C>\
 neighbours in later position of the list.<P/>\n\n    If <C>DigraphDegeneracy(\
</C><A>digraph</A><C>)</C> returns <K>fail</K>,\n    then this attribute retur\
ns <K>fail</K>.\n    <Example><![CDATA[\ngap> D := DigraphSymmetricClosure(Cha\
inDigraph(5));;\ngap> DigraphDegeneracyOrdering(D);\n[ 5, 4, 3, 2, 1 ]\ngap> D\
 := CompleteDigraph(5);;\ngap> DigraphDegeneracyOrdering(D);\n[ 5, 4, 3, 2, 1 \
]\ngap> D := Digraph([[1], [2, 4, 5], [3, 4], [2, 3, 4], [2], []]);\n<immutabl\
e digraph with 6 vertices, 10 edges>\ngap> DigraphDegeneracyOrdering(D);\n[ 1,\
 6, 5, 2, 4, 3 ]\ngap> D := GeneralisedPetersenGraph(IsMutableDigraph, 3, 1);\
\n<mutable digraph with 6 vertices, 18 edges>\ngap> DigraphDegeneracyOrdering(\
D);\n[ 6, 5, 4, 1, 3, 2 ]\n]]></Example>\n  </Description>\n</ManSection>\n\n \
   <ManSection>\n  <Attr Name=\"HamiltonianPath\" Arg=\"digraph\"/>\n  <Return\
s>A list or <K>fail</K>.</Returns>\n  <Description>\n    Returns a Hamiltonian\
 path if one exists, <K>fail</K> if not.<P/>\n\n    A <E>Hamiltonian path</E> \
of a digraph with <C>n</C> vertices is directed\n    cycle of length <C>n</C>.\
 If <A>digraph</A> is a digraph that contains a\n    Hamiltonian path, then th\
is function returns one, described in the form\n    used by <Ref Attr=\"Digrap\
hAllSimpleCircuits\"/>. Note if <A>digraph</A> has\n    0 or 1 vertices, then \
<C>HamiltonianPath</C> returns <C>[]</C> or\n    <C>[1]</C>, respectively.<P/>\
\n\n    The method used in this attribute has the same worst case complexity a\
s\n    <Ref Oper=\"DigraphMonomorphism\"/>.\n\n    <Example><![CDATA[\ngap> D \
:= Digraph([[]]);\n<immutable empty digraph with 1 vertex>\ngap> HamiltonianPa\
th(D);\n[ 1 ]\ngap> D := Digraph([[2], [1]]);\n<immutable digraph with 2 verti\
ces, 2 edges>\ngap> HamiltonianPath(D);\n[ 1, 2 ]\ngap> D := Digraph([[3], [],\
 [2]]);\n<immutable digraph with 3 vertices, 2 edges>\ngap> HamiltonianPath(D)\
;\nfail\ngap> D := Digraph([[2], [3], [1]]);\n<immutable digraph with 3 vertic\
es, 3 edges>\ngap> HamiltonianPath(D);\n[ 1, 2, 3 ]\ngap> D := GeneralisedPete\
rsenGraph(IsMutableDigraph, 5, 2);\n<mutable digraph with 10 vertices, 30 edge\
s>\ngap> HamiltonianPath(D);\nfail\n]]></Example>\n  </Description>\n</ManSect\
ion>\n\n    <ManSection>\n  <Attr Name=\"NrSpanningTrees\" Arg=\"digraph\"/>\n\
  <Returns>An integer.</Returns>\n  <Description>\n    Returns the number of s\
panning trees of the symmetric digraph\n    <A>digraph</A>.\n    <C>NrSpanning\
Trees</C> will return an error if <A>digraph</A> is not a\n    symmetric digra\
ph. <P/> \n\n    See <Ref Prop=\"IsSymmetricDigraph\"/> and\n    <Ref Oper=\"I\
sUndirectedSpanningTree\" /> for more information. \n\n    <Example><![CDATA[\
\ngap> D := CompleteDigraph(5);\n<immutable complete digraph with 5 vertices>\
\ngap> NrSpanningTrees(D);\n125\ngap> D := DigraphSymmetricClosure(CycleDigrap\
h(24));;\ngap> NrSpanningTrees(D);\n24\ngap> NrSpanningTrees(EmptyDigraph(0));\
\n0\ngap> D := GeneralisedPetersenGraph(IsMutableDigraph, 9, 2);\n<mutable dig\
raph with 18 vertices, 54 edges>\ngap> NrSpanningTrees(D);\n1134225\n]]></Exam\
ple>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"Digr\
aphDijkstra\" Arg=\"digraph, source, target\" Label=\"for a source and target\
\"/>\n  <Oper Name=\"DigraphDijkstra\" Arg=\"digraph, source\" Label=\"for a s\
ource\"/>\n  <Returns>Two lists.</Returns>\n  <Description>\n  If <A>digraph</\
A> is a digraph and <A>source</A> and <A>target</A>  are\n  vertices of <A>dig\
raph</A>, then <C>DigraphDijkstra</C> calculates the\n  length of the shortest\
 path from <A>source</A> to <A>target</A> and returns\n  two lists. Each eleme\
nt of the first list is the distance of the\n  corresponding element from <A>s\
ource</A>.  If a vertex was not visited in\n  the process of calculating the s\
hortest distance to <A>target</A> or if\n  there is no path connecting that ve\
rtex with <A>source</A>, then\n  the corresponding distance is <K>infinity</K>\
.  Each element of the\n  second list gives the previous vertex in the shortes\
t path\n  from <A>source</A> to the corresponding vertex.  For\n  <A>source</A\
> and for any vertices that remained unvisited this\n    will be <C>-1</C>.<P/\
>\n\n    If the optional second argument <A>target</A> is not present, then\n \
   <C>DigraphDijkstra</C> returns the shortest path from <A>source</A> to\n   \
 every vertex that is reachable from <A>source</A>.\n\n  <Example><![CDATA[\ng\
ap> mat := [[0, 1, 1], [0, 0, 1], [0, 0, 0]];\n[ [ 0, 1, 1 ], [ 0, 0, 1 ], [ 0\
, 0, 0 ] ]\ngap> D := DigraphByAdjacencyMatrix(mat);\n<immutable digraph with \
3 vertices, 3 edges>\ngap> DigraphDijkstra(D, 2, 3);\n[ [ infinity, 0, 1 ], [ \
-1, -1, 2 ] ]\ngap> DigraphDijkstra(D, 1, 3);\n[ [ 0, 1, 1 ], [ -1, 1, 1 ] ]\n\
gap> DigraphDijkstra(D, 1, 2);\n[ [ 0, 1, 1 ], [ -1, 1, 1 ] ]\n]]></Example>\n\
</Description>\n</ManSection>\n\n  </Section>\n\n  <Section><Heading>Cayley gr\
aphs of groups</Heading>\n    <ManSection>\n  <Attr Name=\"GroupOfCayleyDigrap\
h\" Arg=\"digraph\"/>\n  <Attr Name=\"SemigroupOfCayleyDigraph\" Arg=\"digraph\
\"/>\n  <Returns>A group or semigroup.</Returns>\n  <Description>\n    If <A>d\
igraph</A> is an immutable Cayley graph of a group <C>G</C> and\n    <A>digrap\
h</A> belongs to the category <Ref Filt=\"IsCayleyDigraph\"/>, then\n    <C>Gr\
oupOfCayleyDigraph</C> returns <C>G</C>.\n    <P/>\n\n    If <A>digraph</A> is\
 a Cayley graph of a semigroup <C>S</C> and\n    <A>digraph</A> belongs to the\
 category <Ref Filt=\"IsCayleyDigraph\"/>, then\n    <C>SemigroupOfCayleyDigra\
ph</C> returns <C>S</C>.\n    <P/>\n\n    See also <Ref Attr=\"GeneratorsOfCay\
leyDigraph\"/>.\n    <Example><![CDATA[\ngap> G := DihedralGroup(IsPermGroup, \
8);\nGroup([ (1,2,3,4), (2,4) ])\ngap> digraph := CayleyDigraph(G);\n<immutabl\
e digraph with 8 vertices, 16 edges>\ngap> GroupOfCayleyDigraph(digraph) = G;\
\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  \
<Attr Name=\"GeneratorsOfCayleyDigraph\" Arg=\"digraph\"/>\n  <Returns>A list \
of generators.</Returns>\n  <Description>\n    If <A>digraph</A> is an immutab\
le Cayley graph of a group or semigroup with\n    respect to a set of generato\
rs <C>gens</C> and <A>digraph</A> belongs to\n    the category <Ref Filt=\"IsC\
ayleyDigraph\"/>, then\n    <C>GeneratorsOfCayleyDigraph</C> return the list o\
f generators <C>gens</C>\n    over which <A>digraph</A> is defined.\n    <P/>\
\n\n    See also <Ref Attr=\"GroupOfCayleyDigraph\"/> \n    or <Ref Attr=\"Sem\
igroupOfCayleyDigraph\"/>.\n    <Example><![CDATA[\ngap> G := DihedralGroup(Is\
PermGroup, 8);\nGroup([ (1,2,3,4), (2,4) ])\ngap> digraph := CayleyDigraph(G);\
\n<immutable digraph with 8 vertices, 16 edges>\ngap> GeneratorsOfCayleyDigrap\
h(digraph) = GeneratorsOfGroup(G);\ntrue\ngap> digraph := CayleyDigraph(G, [()\
]);\n<immutable digraph with 8 vertices, 8 edges>\ngap> GeneratorsOfCayleyDigr\
aph(digraph) = [()];\ntrue]]></Example>\n  </Description>\n</ManSection>\n\n  \
</Section>\n\n  <Section><Heading>Associated semigroups</Heading>\n      <ManS\
ection>\n    <Oper Name=\"AsSemigroup\" Arg=\"filt, digraph\"\n      Label=\"f\
or a filter and a digraph\"/>\n    <Oper Name=\"AsMonoid\" Arg=\"filt, digraph\
\"/>\n    <Returns>A semilattice of partial perms.</Returns>\n    <Description\
>\n      The operation <C>AsSemigroup</C> requires that <A>filt</A> be equal t\
o\n      <Ref Filt=\"IsPartialPermSemigroup\" BookName=\"ref\"/>.\n      If <A\
>digraph</A> is a\n      <Ref Prop=\"IsJoinSemilatticeDigraph\"/> or <Ref Prop\
=\"IsLatticeDigraph\"/>\n      then <C>AsSemigroup</C> returns a semigroup of \
partial perms which is\n      isomorphic to the semigroup whose elements are t\
he vertices of\n      <A>digraph</A> with the binary operation\n      <Ref Ope\
r=\"PartialOrderDigraphJoinOfVertices\"/>.\n      If <A>digraph</A>\n      sat\
isfies  <Ref Prop=\"IsMeetSemilatticeDigraph\"/> but not\n      <Ref Prop=\"Is\
JoinSemilatticeDigraph\"/> then\n      <C>AsSemigroup</C> returns a semigroup \
of partial perms which is\n      isomorphic to the semigroup whose elements ar\
e the vertices of\n      <A>digraph</A> with the binary operation\n      <Ref \
Oper=\"PartialOrderDigraphMeetOfVertices\"/>.\n      <P/>\n\n      The operati\
on <C>AsMonoid</C> behaves similarly to <C>AsSemigroup</C>\n      except that \
<A>filt</A> may also be equal to\n      <Ref Filt=\"IsPartialPermMonoid\" Book\
Name=\"ref\"/>,\n      <A>digraph</A> must satisfy <Ref Prop=\"IsLatticeDigrap\
h\"/>, and the\n      output satisfies <Ref Filt=\"IsMonoid\" BookName=\"ref\"\
/>. <P/>\n\n      The output of both of these operations is guaranteed to be o\
f minimal\n      degree (see <Ref Attr=\"DegreeOfPartialPermSemigroup\" BookNa\
me=\"ref\"/>).\n      Furthermore the <Ref Attr=\"GeneratorsOfSemigroup\" Book\
Name=\"ref\"/> of\n      the output is guaranteed to be the unique generating \
set of minimal size.\n      <Example><![CDATA[\ngap> di := Digraph([[1], [1, 2\
], [1, 3], [1, 4], [1, 2, 3, 5]]);\n<immutable digraph with 5 vertices, 11 edg\
es>\ngap> S := AsSemigroup(IsPartialPermSemigroup, di);\n<partial perm semigro\
up of rank 3 with 4 generators>\ngap> ForAll(Elements(S), IsIdempotent);\ntrue\
\ngap> IsInverseSemigroup(S);\ntrue\ngap> Size(S);\n5\ngap> di := Digraph([[1]\
, [1, 2], [1, 2, 3]]);\n<immutable digraph with 3 vertices, 6 edges>\ngap> M :\
= AsMonoid(IsPartialPermMonoid, di);\n<partial perm monoid of rank 2 with 3 ge\
nerators>\ngap> Size(M);\n3]]></Example>\n    </Description>\n  </ManSection>\
\n\n      <ManSection>\n    <Oper Name=\"AsSemigroup\" Arg=\"filt, Y, gps, hom\
s\"\n      Label=\"for a filter, semilattice digraph, and two lists\"/>\n    <\
Returns> A Clifford semigroup of partial perms. </Returns>\n    <Description>\
\n      The operation <C>AsSemigroup</C> requires that <A>filt</A> be equal to\
\n      <Ref Filt=\"IsPartialPermSemigroup\" BookName=\"ref\"/>.\n      If <A>\
Y</A> is a <Ref Prop=\"IsJoinSemilatticeDigraph\"/> or\n      <Ref Prop=\"IsMe\
etSemilatticeDigraph\"/>,\n      <A>gps</A> is a list of groups corresponding \
to each vertex, and\n      <A>homs</A> is a list containing for each edge <C>(\
i, j)</C> in\n      the transitive reduction of <A>digraph</A> a triple <C>[i,\
 j, hom]</C>\n      where <C>hom</C> is a group homomorphism from <C>gps[i]</C\
> to\n      <C>gps[j]</C>, and the diagram of homomorphisms commutes, then\n  \
    <C>AsSemigroup</C> returns a semigroup of partial perms which is\n      is\
omorphic to the strong semilattice of groups <M>S[Y; gps; homs]</M>.\n      <E\
xample><![CDATA[\ngap> G1 := AlternatingGroup(4);;\ngap> G2 := SymmetricGroup(\
2);;\ngap> G3 := SymmetricGroup(3);;\ngap> gr := Digraph([[1, 3], [2, 3], [3]]\
);;\ngap> sgn := function(x)\n> if SignPerm(x) = 1 then\n> return ();\n> fi;\n\
> return (1, 2);\n> end;;\ngap> hom13 := GroupHomomorphismByFunction(G1, G3, s\
gn);;\ngap> hom23 := GroupHomomorphismByFunction(G2, G3, sgn);;\ngap> T := AsS\
emigroup(IsPartialPermSemigroup,\n> gr,\n> [G1, G2, G3], [[1, 3, hom13], [2, 3\
, hom23]]);;\ngap> Size(T);\n20\ngap> D := GreensDClasses(T);;\ngap> List(D, x\
 -> Size(x));\n[ 6, 12, 2 ]\n]]></Example>\n    </Description>\n  </ManSection\
>\n\n  </Section>\n\n  <Section><Heading>Planarity</Heading>\n    <ManSection>\
\n  <Attr Name=\"KuratowskiPlanarSubdigraph\" Arg=\"digraph\"/>\n  <Returns>A \
list or <K>fail</K>.</Returns>\n  <Description>\n    <C>KuratowskiPlanarSubdig\
raph</C> returns the immutable list of\n    lists of out-neighbours of a (not \
necessarily induced) subdigraph of the\n    digraph <A>digraph</A> that witnes\
ses the fact that <A>digraph</A> is not\n    planar, or <K>fail</K> if <A>digr\
aph</A> is planar.  In other words,\n    <C>KuratowskiPlanarSubdigraph</C> ret\
urns the out-neighbours of a\n    subdigraph of <A>digraph</A> that is homeomo\
rphic to the complete graph\n    with <C>5</C> vertices, or to the complete bi\
partite graph with vertex sets\n    of sizes <C>3</C> and <C>3</C>. <P/>\n    \
\n    The directions and multiplicities of any edges in <A>digraph</A> are\n  \
  ignored when considering whether or not <A>digraph</A> is planar. <P/>\n\n  \
  See also <Ref Prop=\"IsPlanarDigraph\"/>\n    and <Ref Attr=\"SubdigraphHome\
omorphicToK33\"/>.\n    <P/>\n    \n    This method uses the reference impleme\
ntation in\n    &edge-addition-planarity-suite; by John Boyer of the algorithm\
s described\n    in <Cite Key=\"BM06\"/>.\n\n<Example><![CDATA[\ngap> D := Dig\
raph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4, 7], [6, 8], \
[2, 7], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 vertices, 25 ed\
ges>\ngap> KuratowskiPlanarSubdigraph(D);\nfail\ngap> D := Digraph([[2, 4, 7, \
9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, \
10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, \
6, 7, 8], [3, 5]]);\n<immutable digraph with 10 vertices, 50 edges>\ngap> IsPl\
anarDigraph(D);\nfalse\ngap> KuratowskiPlanarSubdigraph(D);\n[ [ 2, 9, 7 ], [ \
3 ], [ 6 ], [ 5, 9 ], [ 6 ], [  ], [ 4 ], \n  [ 7, 9, 3 ], [  ], [  ] ]\ngap> \
D := Digraph(IsMutableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1,\
 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<mutable digraph \
with 11 vertices, 25 edges>\ngap> KuratowskiPlanarSubdigraph(D);\nfail\ngap> D\
 := Digraph(IsMutableDigraph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6, 9, 10], [6, 1\
0], [2, 5, 8, 9],\n> [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10],\n> [3, 4,\
 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n<mutable digrap\
h with 10 vertices, 50 edges>\ngap> IsPlanarDigraph(D);\nfalse\ngap> Kuratowsk\
iPlanarSubdigraph(D);\n[ [ 2, 9, 7 ], [ 3 ], [ 6 ], [ 5, 9 ], [ 6 ], [  ], [ 4\
 ], \n  [ 7, 9, 3 ], [  ], [  ] ]\n]]></Example>\n  </Description>\n</ManSecti\
on>\n\n    <ManSection>\n  <Attr Name=\"KuratowskiOuterPlanarSubdigraph\" Arg=\
\"digraph\"/>\n  <Returns>A list or <K>fail</K>.</Returns>\n  <Description>\n \
   <C>KuratowskiOuterPlanarSubdigraph</C> returns the immutable list of\n    i\
mmutable lists of out-neighbours of a (not necessarily induced)\n    subdigrap\
h of the digraph <A>digraph</A> that witnesses the fact\n    that <A>digraph</\
A> is not outer planar, or <K>fail</K> if\n    <A>digraph</A> is outer planar.\
  In other words,\n    <C>KuratowskiOuterPlanarSubdigraph</C> returns the out-\
neighbours of a\n    subdigraph of <A>digraph</A> that is homeomorphic to the \
complete graph\n    with <C>4</C> vertices, or to the complete bipartite graph\
 with vertex sets\n    of sizes <C>2</C> and <C>3</C>. <P/>\n    \n    The dir\
ections and multiplicities of any edges in <A>digraph</A> are\n    ignored whe\
n considering whether or not <A>digraph</A> is outer planar. \n    <P/>\n\n   \
 See also \n    <Ref Prop=\"IsOuterPlanarDigraph\"/>,\n    <Ref Attr=\"Subdigr\
aphHomeomorphicToK4\"/>, and \n    <Ref Attr=\"SubdigraphHomeomorphicToK23\"/>\
.\n    <P/>\n\n    This method uses the reference implementation in\n    &edge\
-addition-planarity-suite; by John Boyer of the algorithms described\n    in <\
Cite Key=\"BM06\"/>.\n\n<Example><![CDATA[\ngap> D := Digraph([[3, 5, 10], [8,\
 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, \
2], [5, 9]]);\n<immutable digraph with 11 vertices, 25 edges>\ngap> Kuratowski\
OuterPlanarSubdigraph(D);\n[ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [ 6 ], [ 11 ],\
 [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D := Digraph([[2, 4, 7, 9,\
 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1, 2, 3, 4, 6, 7, 9, 10\
], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6,\
 7, 8], [3, 5]]);\n<immutable digraph with 10 vertices, 50 edges>\ngap> IsOute\
rPlanarDigraph(D);\nfalse\ngap> KuratowskiOuterPlanarSubdigraph(D);\n[ [  ], [\
  ], [  ], [ 8, 9 ], [  ], [  ], [ 9, 4 ], [ 7, 9 ], [  ], \n  [  ] ]\ngap> D \
:= Digraph(IsMutableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7\
, 11], [4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<mutable digraph wi\
th 11 vertices, 25 edges>\ngap> KuratowskiOuterPlanarSubdigraph(D);\n[ [ 3, 5,\
 10 ], [ 9, 8, 10 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  \
], [  ] ]\ngap> D := Digraph(IsMutableDigraph, [[2, 4, 7, 9, 10],\n> [1, 3, 4,\
 6, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1, 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, \
9, 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\
\n<mutable digraph with 10 vertices, 50 edges>\ngap> IsOuterPlanarDigraph(D);\
\nfalse\ngap> KuratowskiOuterPlanarSubdigraph(D);\n[ [  ], [  ], [  ], [ 8, 9 \
], [  ], [  ], [ 9, 4 ], [ 7, 9 ], [  ], \n  [  ] ]]]></Example>\n  </Descript\
ion>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"PlanarEmbedding\" Arg=\
\"digraph\"/>\n  <Returns>A list or <K>fail</K>.</Returns>\n  <Description>\n \
   If <A>digraph</A> is a planar digraph, then \n    <C>PlanarEmbedding</C> re\
turns the immutable list of lists of\n    out-neighbours of a subdigraph of <A\
>digraph</A> such that each vertex's\n    neighbours are given in clockwise or\
der. If <A>digraph</A> is not planar,\n    then <K>fail</K> is returned. <P/>\
\n    \n    The directions and multiplicities of any edges in <A>digraph</A> a\
re\n    ignored by <C>PlanarEmbedding</C>.\n    <P/>\n\n    See also \n    <Re\
f Prop=\"IsPlanarDigraph\"/>.\n    <P/>\n\n    This method uses the reference \
implementation in\n    &edge-addition-planarity-suite; by John Boyer of the al\
gorithms described\n    in <Cite Key=\"BM06\"/>.\n\n<Example><![CDATA[\ngap> D\
 := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [4, 7], [\
6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 vertices\
, 25 edges>\ngap> PlanarEmbedding(D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ \
6 ], [ 11, 7 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D := Digrap\
h([[2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1, 2, 3,\
 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9\
], [2, 3, 5, 6, 7, 8], [3, 5]]);\n<immutable digraph with 10 vertices, 50 edge\
s>\ngap> PlanarEmbedding(D);\nfail\ngap> D := Digraph(IsMutableDigraph, [[3, 5\
, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, 7], [6, 8], [2, 7], [2, \
11], [1, 2], [5, 9]]);\n<mutable digraph with 11 vertices, 25 edges>\ngap> Pla\
narEmbedding(D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11, 7 ], [ 7 ]\
, [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D := Digraph(IsMutableDigraph, [\
[2, 4, 7, 9, 10],\n> [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1, 2, 3, \
4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9],\
 [2, 3, 5, 6, 7, 8], [3, 5]]);\n<mutable digraph with 10 vertices, 50 edges>\n\
gap> PlanarEmbedding(D);\nfail\n]]></Example>\n  </Description>\n</ManSection>\
\n\n    <ManSection>\n  <Attr Name=\"OuterPlanarEmbedding\" Arg=\"digraph\"/>\
\n  <Returns>A list or <K>fail</K>.</Returns>\n  <Description>\n    If <A>digr\
aph</A> is an outer planar digraph, then\n    <C>OuterPlanarEmbedding</C> retu\
rns the immutable list of lists\n    of out-neighbours of a subdigraph of <A>d\
igraph</A> such that each\n    vertex's neighbours are given in clockwise orde\
r. If <A>digraph</A> is not\n    outer planar, then <K>fail</K> is returned. <\
P/>\n    \n    The directions and multiplicities of any edges in <A>digraph</A\
> are\n    ignored by <C>OuterPlanarEmbedding</C>.\n    <P/>\n\n    See also <\
Ref Prop=\"IsOuterPlanarDigraph\"/>.\n    <P/>\n\n    This method uses the ref\
erence implementation in\n    &edge-addition-planarity-suite; by John Boyer of\
 the algorithms described\n    in <Cite Key=\"BM06\"/>.\n\n<Example><![CDATA[\
\ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], \n> [1, 7, 11], [\
4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 \
vertices, 25 edges>\ngap> OuterPlanarEmbedding(D);\nfail\ngap> D := Digraph([[\
2, 4, 7, 9, 10], [1, 3, 4, 6, 9, 10], [6, 10], \n> [2, 5, 8, 9], [1, 2, 3, 4, \
6, 7, 9, 10], [3, 4, 5, 7, 9, 10], \n> [3, 4, 5, 6, 9, 10], [3, 4, 5, 7, 9], [\
2, 3, 5, 6, 7, 8], [3, 5]]);\n<immutable digraph with 10 vertices, 50 edges>\n\
gap> OuterPlanarEmbedding(D);\nfail\ngap> OuterPlanarEmbedding(CompleteBiparti\
teDigraph(2, 2));\n[ [ 3, 4 ], [ 4, 3 ], [  ], [  ] ]\ngap> D := Digraph(IsMut\
ableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [4, 7], [\
6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<mutable digraph with 11 vertices, \
25 edges>\ngap> OuterPlanarEmbedding(D);\nfail\ngap> D := Digraph(IsMutableDig\
raph, [[2, 4, 7, 9, 10],\n> [1, 3, 4, 6, 9, 10], [6, 10], [2, 5, 8, 9],\n> [1,\
 2, 3, 4, 6, 7, 9, 10], [3, 4, 5, 7, 9, 10],\n> [3, 4, 5, 6, 9, 10], [3, 4, 5,\
 7, 9], [2, 3, 5, 6, 7, 8], [3, 5]]);\n<mutable digraph with 10 vertices, 50 e\
dges>\ngap> OuterPlanarEmbedding(D);\nfail\ngap> OuterPlanarEmbedding(Complete\
BipartiteDigraph(2, 2));\n[ [ 3, 4 ], [ 4, 3 ], [  ], [  ] ]\n]]></Example>\n \
 </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"SubdigraphH\
omeomorphicToK23\" Arg=\"digraph\"/>\n  <Attr Name=\"SubdigraphHomeomorphicToK\
33\" Arg=\"digraph\"/>\n  <Attr Name=\"SubdigraphHomeomorphicToK4\" Arg=\"digr\
aph\"/>\n  <Returns>A list or <K>fail</K>.</Returns>\n  <Description>\n    The\
se attributes return the immutable list of lists of\n    out-neighbours of a s\
ubdigraph of the digraph <A>digraph</A> which is\n    homeomorphic to one of t\
he following:\n    the complete bipartite graph with vertex sets of sizes <C>2\
</C> and\n    <C>3</C>; the complete bipartite graph with vertex sets of sizes\
 <C>3</C>\n    and <C>3</C>; or the complete graph with <C>4</C> vertices. If\
\n    <A>digraph</A> has no such subdigraphs, then <K>fail</K> is returned. \n\
    <P/>\n\n    See also <Ref Prop=\"IsPlanarDigraph\"/> and <Ref\n      Prop=\
\"IsOuterPlanarDigraph\"/> for more details.<P/>\n\n    This method uses the r\
eference implementation in\n    &edge-addition-planarity-suite; by John Boyer \
of the algorithms described\n    in <Cite Key=\"BM06\"/>.\n\n<Example><![CDATA\
[\ngap> D := Digraph([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 7, 11], \n> \
[4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11\
 vertices, 25 edges>\ngap> SubdigraphHomeomorphicToK4(D);\n[ [ 3, 5, 10 ], [ 9\
, 8, 10 ], [ 4 ], [ 6 ], [ 7, 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ]\
 ]\ngap> SubdigraphHomeomorphicToK23(D);\n[ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ],\
 [ 6 ], [ 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D := Digrap\
h([[3, 5, 10], [8, 9, 10], [1, 4], [3, 6], [1, 11], \n>  [4, 7], [6, 8], [2, 7\
], [2, 11], [1, 2], [5, 9]]);\n<immutable digraph with 11 vertices, 24 edges>\
\ngap> SubdigraphHomeomorphicToK4(D);\nfail\ngap> SubdigraphHomeomorphicToK23(\
D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8 ], \n  [  \
], [ 11 ], [  ], [  ] ]\ngap> SubdigraphHomeomorphicToK33(D);\nfail\ngap> Subd\
igraphHomeomorphicToK23(NullDigraph(0));\nfail\ngap> SubdigraphHomeomorphicToK\
33(CompleteDigraph(5));\nfail\ngap> SubdigraphHomeomorphicToK33(CompleteBipart\
iteDigraph(3, 3));\n[ [ 4, 6, 5 ], [ 4, 5, 6 ], [ 6, 5, 4 ], [  ], [  ], [  ] \
]\ngap> SubdigraphHomeomorphicToK4(CompleteDigraph(3));\nfail\ngap> D := Digra\
ph(IsMutableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 7, 11], [\
4, 7], [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<mutable digraph with 11 ve\
rtices, 25 edges>\ngap> SubdigraphHomeomorphicToK4(D);\n[ [ 3, 5, 10 ], [ 9, 8\
, 10 ], [ 4 ], [ 6 ], [ 7, 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\
\ngap> SubdigraphHomeomorphicToK23(D);\n[ [ 3, 5, 10 ], [ 9, 8, 10 ], [ 4 ], [\
 6 ], [ 11 ], [ 7 ], [ 8 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> D := Digraph(\
IsMutableDigraph, [[3, 5, 10], [8, 9, 10], [1, 4],\n> [3, 6], [1, 11], [4, 7],\
 [6, 8], [2, 7], [2, 11], [1, 2], [5, 9]]);\n<mutable digraph with 11 vertices\
, 24 edges>\ngap> SubdigraphHomeomorphicToK4(D);\nfail\ngap> SubdigraphHomeomo\
rphicToK23(D);\n[ [ 3, 10, 5 ], [ 10, 8, 9 ], [ 4 ], [ 6 ], [ 11 ], [ 7 ], [ 8\
 ], \n  [  ], [ 11 ], [  ], [  ] ]\ngap> SubdigraphHomeomorphicToK33(D);\nfail\
\ngap> SubdigraphHomeomorphicToK23(NullDigraph(0));\nfail\ngap> SubdigraphHome\
omorphicToK33(CompleteDigraph(5));\nfail\ngap> SubdigraphHomeomorphicToK33(Com\
pleteBipartiteDigraph(3, 3));\n[ [ 4, 6, 5 ], [ 4, 5, 6 ], [ 6, 5, 4 ], [  ], \
[  ], [  ] ]\ngap> SubdigraphHomeomorphicToK4(CompleteDigraph(3));\nfail\n]]><\
/Example>\n  </Description>\n</ManSection>\n\n  </Section>\n\n</Chapter>\n <!-\
- attributes, operations -->\n  <Chapter Label=\"Properties of digraphs\"><Hea\
ding>Properties of digraphs</Heading>\n\n  <Section><Heading>Edge properties</\
Heading>\n    <ManSection>\n  <Prop Name=\"DigraphHasLoops\" Arg=\"digraph\"/>\
\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    Retu\
rns <K>true</K> if the digraph <A>digraph</A> has loops, and\n    <K>false</K>\
 if it does not. A loop is an edge with equal source and range.\n    <P/>\n   \
   \n    If the argument <A>digraph</A> is mutable, then the return value of\n\
    this property is recomputed every time it is called. \n\n<Example><![CDATA\
[\ngap> D := Digraph([[1, 2], [2]]);\n<immutable digraph with 2 vertices, 3 ed\
ges>\ngap> DigraphEdges(D);\n[ [ 1, 1 ], [ 1, 2 ], [ 2, 2 ] ]\ngap> DigraphHas\
Loops(D);\ntrue\ngap> D := Digraph([[2, 3], [1], [2]]);\n<immutable digraph wi\
th 3 vertices, 4 edges>\ngap> DigraphEdges(D);\n[ [ 1, 2 ], [ 1, 3 ], [ 2, 1 ]\
, [ 3, 2 ] ]\ngap> DigraphHasLoops(D);\nfalse\ngap> D := CompleteDigraph(IsMut\
ableDigraph, 4);\n<mutable digraph with 4 vertices, 12 edges>\ngap> DigraphHas\
Loops(D);\nfalse]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSect\
ion>\n  <Prop Name=\"IsAntiSymmetricDigraph\" Arg=\"digraph\"/>\n  <Prop Name=\
\"IsAntisymmetricDigraph\" Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>fal\
se</K>.</Returns>\n  <Description>\n    This property is <K>true</K> if the di\
graph <A>digraph</A>\n    is antisymmetric, and <K>false</K> if it is not.\n  \
  <P/>\n\n    A digraph is <E>antisymmetric</E> if whenever there is an edge w\
ith source\n    <C>u</C> and range <C>v</C>, and an edge with source <C>v</C> \
and range\n    <C>u</C>, then the vertices <C>u</C> and <C>v</C> are equal.\n \
   <P/>\n      \n    If the argument <A>digraph</A> is mutable, then the retur\
n value of\n    this property is recomputed every time it is called. \n\n    <\
Example><![CDATA[\ngap> gr1 := Digraph([[2], [1, 3], [2, 3]]);\n<immutable dig\
raph with 3 vertices, 5 edges>\ngap> IsAntisymmetricDigraph(gr1);\nfalse\ngap>\
 DigraphEdges(gr1){[1, 2]};\n[ [ 1, 2 ], [ 2, 1 ] ]\ngap> gr2 := Digraph([[1, \
2], [3, 3], [1]]);\n<immutable multidigraph with 3 vertices, 5 edges>\ngap> Is\
AntisymmetricDigraph(gr2);\ntrue\ngap> DigraphEdges(gr2);\n[ [ 1, 1 ], [ 1, 2 \
], [ 2, 3 ], [ 2, 3 ], [ 3, 1 ] ]\n]]></Example>\n  </Description>\n</ManSecti\
on>\n\n    <ManSection>\n  <Prop Name=\"IsBipartiteDigraph\" Arg=\"digraph\"/>\
\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n  This p\
roperty is <K>true</K> if the digraph <A>digraph</A> is bipartite, and\n  <K>f\
alse</K> if it is not.  A digraph is bipartite if and only if the\n  vertices \
of <A>digraph</A> can be partitioned into two non-empty sets such\n  that the \
source and range of any edge of <A>digraph</A> lie in distinct sets.\n  Equiva\
lently, a digraph is bipartite if and only if it is 2-colorable; see\n  <Ref A\
ttr=\"DigraphGreedyColouring\" Label=\"for a digraph\"/>. <P/>\n\n  See also <\
Ref Attr=\"DigraphBicomponents\"/>.\n    <P/>\n      \n    If the argument <A>\
digraph</A> is mutable, then the return value of\n    this property is recompu\
ted every time it is called. \n    <Example><![CDATA[\ngap> D := ChainDigraph(\
4);\n<immutable chain digraph with 4 vertices>\ngap> IsBipartiteDigraph(D);\nt\
rue\ngap> D := CycleDigraph(3);\n<immutable cycle digraph with 3 vertices>\nga\
p> IsBipartiteDigraph(D);\nfalse\ngap> D := CompleteBipartiteDigraph(IsMutable\
Digraph, 5, 4);\n<mutable digraph with 9 vertices, 40 edges>\ngap> IsBipartite\
Digraph(D);\ntrue]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSec\
tion>\n  <Prop Name=\"IsCompleteBipartiteDigraph\" Arg=\"digraph\"/>\n  <Retur\
ns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    Returns <K>tru\
e</K> if the digraph <A>digraph</A> is a complete bipartite\n    digraph, and \
<K>false</K> if it is not. <P/>\n\n    A digraph is a <E>complete bipartite di\
graph</E> if it is bipartite, see\n    <Ref Prop=\"IsBipartiteDigraph\"/>, and\
 there exists a unique edge with\n    source <C>i</C> and range <C>j</C> if an\
d only if <C>i</C> and <C>j</C> lie\n    in different bicomponents of <A>digra\
ph</A>, see <Ref\n      Attr=\"DigraphBicomponents\"/>. <P/>\n\n    Equivalent\
ly, a bipartite digraph with bicomponents of size <M>m</M> and\n    <M>n</M> i\
s complete precisely when it has <M>2mn</M> edges, none of which\n    are mult\
iple edges. <P/>\n\n    See also <Ref Oper=\"CompleteBipartiteDigraph\"/>.\n  \
  <P/>\n      \n    If the argument <A>digraph</A> is mutable, then the return\
 value of\n    this property is recomputed every time it is called. \n\n    <E\
xample><![CDATA[\ngap> D := CycleDigraph(2);\n<immutable cycle digraph with 2 \
vertices>\ngap> IsCompleteBipartiteDigraph(D);\ntrue\ngap> D := CycleDigraph(4\
);\n<immutable cycle digraph with 4 vertices>\ngap> IsBipartiteDigraph(D);\ntr\
ue\ngap> IsCompleteBipartiteDigraph(D);\nfalse\ngap> D := CompleteBipartiteDig\
raph(IsMutableDigraph, 5, 4);\n<mutable digraph with 9 vertices, 40 edges>\nga\
p> IsCompleteBipartiteDigraph(D);\ntrue]]></Example>\n  </Description>\n</ManS\
ection>\n\n    <ManSection>\n  <Prop Name=\"IsCompleteDigraph\" Arg=\"digraph\
\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    \
Returns <K>true</K> if the digraph <A>digraph</A> is complete, and\n    <K>fal\
se</K> if it is not. <P/>\n\n    A digraph is <E>complete</E> if it has no loo\
ps, and for all\n    <E>distinct</E> vertices <C>i</C> and <C>j</C>,\n    ther\
e is exactly one edge with source <C>i</C> and range <C>j</C>.\n\n    Equivale\
ntly, a digraph with <M>n</M> vertices is complete precisely when\n    it has \
<M>n(n - 1)</M> edges, no loops, and no multiple edges.\n    <P/>\n      \n   \
 If the argument <A>digraph</A> is mutable, then the return value of\n    this\
 property is recomputed every time it is called. \n\n    <Example><![CDATA[\ng\
ap> D := Digraph([[2, 3], [1, 3], [1, 2]]);\n<immutable digraph with 3 vertice\
s, 6 edges>\ngap> IsCompleteDigraph(D);\ntrue\ngap> D := Digraph([[2, 2], [1]]\
);\n<immutable multidigraph with 2 vertices, 3 edges>\ngap> IsCompleteDigraph(\
D);\nfalse\ngap> D := CompleteBipartiteDigraph(IsMutableDigraph, 5, 4);\n<muta\
ble digraph with 9 vertices, 40 edges>\ngap> IsCompleteDigraph(D);\nfalse]]></\
Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"\
IsCompleteMultipartiteDigraph\" Arg=\"digraph\"/>\n  <Returns><K>true</K> or <\
K>false</K>.</Returns>\n  <Description>\n    This property returns <K>true</K>\
 if <A>digraph</A> is a complete\n    multipartite digraph, and <K>false</K> i\
f not. <P/>\n\n    A digraph is a <E>complete multipartite digraph</E> if and \
only if\n    its vertices can be partitioned into at least two maximal indepen\
dent sets,\n    where every possible edge between these independent sets occur\
s in the\n    digraph exactly once.\n    <P/>\n      \n    If the argument <A>\
digraph</A> is mutable, then the return value of\n    this property is recompu\
ted every time it is called. \n\n    <Example><![CDATA[\ngap> D := CompleteMul\
tipartiteDigraph([2, 4, 6]);\n<immutable complete multipartite digraph with 12\
 vertices, 88 edges>\ngap> IsCompleteMultipartiteDigraph(D);\ntrue\ngap> D := \
CompleteBipartiteDigraph(IsMutableDigraph, 5, 4);\n<mutable digraph with 9 ver\
tices, 40 edges>\ngap> IsCompleteMultipartiteDigraph(D);\ntrue]]></Example>\n \
 </Description>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsEmptyDigr\
aph\" Arg=\"digraph\"/>\n  <Prop Name=\"IsNullDigraph\" Arg=\"digraph\"/>\n  <\
Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    Returns <\
K>true</K> if the digraph <A>digraph</A> is empty, and\n    <K>false</K> if it\
 is not. A digraph is <E>empty</E> if it has no\n    edges.<P/>\n\n    <C>IsNu\
llDigraph</C> is a synonym for <C>IsEmptyDigraph</C>.\n    <P/>\n      \n    I\
f the argument <A>digraph</A> is mutable, then the return value of\n    this p\
roperty is recomputed every time it is called. \n\n    <Example><![CDATA[\ngap\
> D := Digraph([[], []]);\n<immutable empty digraph with 2 vertices>\ngap> IsE\
mptyDigraph(D);\ntrue\ngap> IsNullDigraph(D);\ntrue\ngap> D := Digraph([[], [1\
]]);\n<immutable digraph with 2 vertices, 1 edge>\ngap> IsEmptyDigraph(D);\nfa\
lse\ngap> IsNullDigraph(D);\nfalse]]></Example>\n  </Description>\n</ManSectio\
n>\n\n    <ManSection>\n  <Prop Name=\"IsEquivalenceDigraph\" Arg=\"digraph\"/\
>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    A d\
igraph is an equivalence digraph if and only if the digraph satisifies\n    al\
l of <Ref Prop=\"IsReflexiveDigraph\"/>,\n    <Ref Prop=\"IsSymmetricDigraph\"\
/> and <Ref Prop=\"IsTransitiveDigraph\"/>.\n    A partial order <A>digraph</A\
> corresponds to an equivalence relation.\n    <P/>\n      \n    If the argume\
nt <A>digraph</A> is mutable, then the return value of\n    this property is r\
ecomputed every time it is called. \n\n<Example><![CDATA[\ngap> D := Digraph([\
[1, 3], [2], [1, 3]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> IsE\
quivalenceDigraph(D);\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\
\n    <ManSection>\n  <Prop Name=\"IsFunctionalDigraph\" Arg=\"digraph\"/>\n  \
<Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    This pro\
perty is <K>true</K> if the digraph <A>digraph</A> is\n    functional. <P/>\n\
\n    A digraph is <E>functional</E> if every vertex is the source of a\n    u\
nique edge.\n    <P/>\n      \n    If the argument <A>digraph</A> is mutable, \
then the return value of\n    this property is recomputed every time it is cal\
led. \n    <Example><![CDATA[\ngap> gr1 := Digraph([[3], [2], [2], [1], [6], [\
5]]);\n<immutable digraph with 6 vertices, 6 edges>\ngap> IsFunctionalDigraph(\
gr1);\ntrue\ngap> gr2 := Digraph([[1, 2], [1]]);\n<immutable digraph with 2 ve\
rtices, 3 edges>\ngap> IsFunctionalDigraph(gr2);\nfalse\ngap> gr3 := Digraph(3\
, [1, 2, 3], [2, 3, 1]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> I\
sFunctionalDigraph(gr3);\ntrue\n]]></Example>\n  </Description>\n</ManSection>\
\n\n    <ManSection>\n  <Prop Name=\"IsMultiDigraph\" Arg=\"digraph\"/>\n  <Re\
turns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    A <E>multid\
igraph</E> is one that has at least two\n    edges with equal source and range\
.<P/>\n\n    If the argument <A>digraph</A> is mutable, then the return value \
of\n    this property is recomputed every time it is called. \n\n    <Example>\
<![CDATA[\ngap> D := Digraph([\"a\", \"b\", \"c\"], [\"a\", \"b\", \"b\"], [\"\
b\", \"c\", \"a\"]);\n<immutable digraph with 3 vertices, 3 edges>\ngap> IsMul\
tiDigraph(D);\nfalse\ngap> D := DigraphFromDigraph6String(\"&Bug\");\n<immutab\
le digraph with 3 vertices, 6 edges>\ngap> IsDuplicateFree(DigraphEdges(D));\n\
true\ngap> IsMultiDigraph(D);\nfalse\ngap> D := Digraph([[1, 2, 3, 2], [2, 1],\
 [3]]);\n<immutable multidigraph with 3 vertices, 7 edges>\ngap> IsDuplicateFr\
ee(DigraphEdges(D));\nfalse\ngap> IsMultiDigraph(D);\ntrue\ngap> D := DigraphM\
utableCopy(D); \n<mutable multidigraph with 3 vertices, 7 edges>\ngap> IsMulti\
Digraph(D);\ntrue]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSec\
tion>\n  <Prop Name=\"IsReflexiveDigraph\" Arg=\"digraph\"/>\n  <Returns><K>tr\
ue</K> or <K>false</K>.</Returns>\n  <Description>\n    This property is <K>tr\
ue</K> if the digraph <A>digraph</A> is\n    reflexive, and <K>false</K> if it\
 is not.\n    A digraph is <E>reflexive</E> if it has a loop at every vertex. \
<P/>\n    <P/>\n      \n    If the argument <A>digraph</A> is mutable, then th\
e return value of\n    this property is recomputed every time it is called. \n\
    <Example><![CDATA[\ngap> D := Digraph([[1, 2], [2]]);\n<immutable digraph \
with 2 vertices, 3 edges>\ngap> IsReflexiveDigraph(D);\ntrue\ngap> D := Digrap\
h([[3, 1], [4, 2], [3], [2, 1]]);\n<immutable digraph with 4 vertices, 7 edges\
>\ngap> IsReflexiveDigraph(D);\nfalse\n]]></Example>\n  </Description>\n</ManS\
ection>\n\n    <ManSection>\n  <Prop Name=\"IsSymmetricDigraph\" Arg=\"digraph\
\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    \
This property is <K>true</K> if the digraph <A>digraph</A>\n    is symmetric, \
and <K>false</K> if it is not.<P/>\n\n    A <E>symmetric digraph</E> is one wh\
ere for each non-loop edge, having\n    source <C>u</C> and range <C>v</C>, th\
ere is a corresponding edge with\n    source <C>v</C> and range <C>u</C>.  If \
there are <C>n</C> edges with\n    source <C>u</C> and range <C>v</C>, then th\
ere must be precisely <C>n</C>\n    edges with source <C>v</C> and range <C>u<\
/C>.  In other words, a symmetric\n    digraph has a symmetric adjacency matri\
x <Ref Attr=\"AdjacencyMatrix\"/>.\n    <P/>\n      \n    If the argument <A>d\
igraph</A> is mutable, then the return value of\n    this property is recomput\
ed every time it is called. \n    <Example><![CDATA[\ngap> gr1 := Digraph([[2]\
, [1, 3], [2, 3]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> IsSymm\
etricDigraph(gr1);\ntrue\ngap> adj1 := AdjacencyMatrix(gr1);;\ngap> Display(ad\
j1);\n[ [  0,  1,  0 ],\n  [  1,  0,  1 ],\n  [  0,  1,  1 ] ]\ngap> adj1 = Tr\
ansposedMat(adj1);\ntrue\ngap> gr1 = DigraphReverse(gr1);\ntrue\ngap> gr2 := D\
igraph([[2, 3], [1, 3], [2, 3]]);\n<immutable digraph with 3 vertices, 6 edges\
>\ngap> IsSymmetricDigraph(gr2);\nfalse\ngap> adj2 := AdjacencyMatrix(gr2);;\n\
gap> Display(adj2);\n[ [  0,  1,  1 ],\n  [  1,  0,  1 ],\n  [  0,  1,  1 ] ]\
\ngap> adj2 = TransposedMat(adj2);\nfalse\n]]></Example>\n  </Description>\n</\
ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsTournament\" Arg=\"digraph\"\
/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    Th\
is property is <K>true</K> if the digraph <A>digraph</A> is a tournament,\n   \
 and <K>false</K> if it is not. <P/>\n\n    A tournament is an orientation of \
a complete (undirected) graph.\n    Specifically, a tournament is a digraph wh\
ich has a unique directed edge\n    (of some orientation) between any pair of \
distinct vertices, and no loops.\n    <P/>\n      \n    If the argument <A>dig\
raph</A> is mutable, then the return value of\n    this property is recomputed\
 every time it is called. \n    <Example><![CDATA[\ngap> D := Digraph([[2, 3, \
4], [3, 4], [4], []]);\n<immutable digraph with 4 vertices, 6 edges>\ngap> IsT\
ournament(D);\ntrue\ngap> D := Digraph([[2], [1], [3]]);\n<immutable digraph w\
ith 3 vertices, 3 edges>\ngap> IsTournament(D);\nfalse\ngap> D := CycleDigraph\
(IsMutableDigraph, 3);\n<mutable digraph with 3 vertices, 3 edges>\ngap> IsTou\
rnament(D);\ntrue\ngap> DigraphRemoveEdge(D, 1, 2);\n<mutable digraph with 3 v\
ertices, 2 edges>\ngap> IsTournament(D);\nfalse\n]]></Example>\n  </Descriptio\
n>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsTransitiveDigraph\" Ar\
g=\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Descrip\
tion>\n    This property is <K>true</K> if the digraph <A>digraph</A>\n    is \
transitive, and <K>false</K> if it is not.\n\n    A digraph is <E>transitive</\
E> if whenever <C>[ i, j ]</C> and\n    <C>[ j, k ]</C> are edges of the digra\
ph, then <C>[ i, k ]</C> is also an\n    edge of the digraph. <P/>\n\n    Let \
<M>n</M> be the number of vertices of an arbitrary digraph, and let\n        <\
M>m</M> be the number of edges.\n    For general digraphs, the methods used fo\
r this property use a version\n    of the Floyd-Warshall algorithm, and have c\
omplexity <M>O(n^3)</M>.\n\n    However for digraphs which are topologically s\
ortable\n    [<Ref Attr=\"DigraphTopologicalSort\"/>], then methods with\n    \
complexity <M>O(m + n + m \\cdot n)</M> will be used when appropriate.\n    <P\
/>\n      \n    If the argument <A>digraph</A> is mutable, then the return val\
ue of\n    this property is recomputed every time it is called. \n    <P/>\n  \
  <Example><![CDATA[\ngap> D := Digraph([[1, 2], [3], [3]]);\n<immutable digra\
ph with 3 vertices, 4 edges>\ngap> IsTransitiveDigraph(D);\nfalse\ngap> gr2 :=\
 Digraph([[1, 2, 3], [3], [3]]);\n<immutable digraph with 3 vertices, 5 edges>\
\ngap> IsTransitiveDigraph(gr2);\ntrue\ngap> gr2 = DigraphTransitiveClosure(D)\
;\ntrue\ngap> gr3 := Digraph([[1, 2, 2, 3], [3, 3], [3]]);\n<immutable multidi\
graph with 3 vertices, 7 edges>\ngap> IsTransitiveDigraph(gr3);\ntrue\n]]></Ex\
ample>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"Is\
PreorderDigraph\" Arg=\"digraph\"/>\n  <Prop Name=\"IsQuasiorderDigraph\" Arg=\
\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Descripti\
on>\n    A digraph is a preorder digraph if and only if the digraph satisifies\
 both\n    <Ref Prop=\"IsReflexiveDigraph\"/> and <Ref Prop=\"IsTransitiveDigr\
aph\"/>.\n    A preorder digraph (or quasiorder digraph) <A>digraph</A> corres\
ponds to\n    the preorder relation <M>\\leq</M> defined by <M>x \\leq y</M> i\
f and only\n    if <C>[x, y]</C> is an edge of <A>digraph</A>.\n    <P/>\n    \
  \n    If the argument <A>digraph</A> is mutable, then the return value of\n \
   this property is recomputed every time it is called. \n\n<Example><![CDATA[\
\ngap> D := Digraph([[1], [2, 3], [2, 3]]);\n<immutable digraph with 3 vertice\
s, 5 edges>\ngap> IsPreorderDigraph(D);\ntrue\ngap> D := Digraph([[1 .. 4], [1\
 .. 4], [1 .. 4], [1 .. 4]]);\n<immutable digraph with 4 vertices, 16 edges>\n\
gap> IsPreorderDigraph(D);\ntrue\ngap> D := Digraph([[2], [3], [4], [5], [1]])\
;\n<immutable digraph with 5 vertices, 5 edges>\ngap> IsPreorderDigraph(D);\nf\
alse\ngap> D := Digraph([[1], [1, 2], [2, 3]]);\n<immutable digraph with 3 ver\
tices, 5 edges>\ngap> IsQuasiorderDigraph(D);\nfalse\n]]></Example>\n  </Descr\
iption>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsPartialOrderDigra\
ph\" Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <\
Description>\n    A digraph is a partial order digraph if and only if the digr\
aph satisifies\n    all of <Ref Prop=\"IsReflexiveDigraph\"/>,\n    <Ref Prop=\
\"IsAntisymmetricDigraph\"/> and <Ref Prop=\"IsTransitiveDigraph\"/>.\n    A p\
artial order <A>digraph</A> corresponds\n    to the partial order relation <M>\
\\leq</M> defined by <M>x \\leq y</M> if and\n    only if <C>[x, y]</C> is an \
edge of <A>digraph</A>.\n    <P/>\n      \n    If the argument <A>digraph</A> \
is mutable, then the return value of\n    this property is recomputed every ti\
me it is called. \n\n<Example><![CDATA[\ngap> D := Digraph([[1, 3], [2, 3], [3\
]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> IsPartialOrderDigraph\
(D);\ntrue\ngap> D := CycleDigraph(5);\n<immutable cycle digraph with 5 vertic\
es>\ngap> IsPartialOrderDigraph(D);\nfalse\ngap> D := Digraph([[1, 1], [1, 1, \
2], [3], [3, 3, 4, 4]]);\n<immutable multidigraph with 4 vertices, 10 edges>\n\
gap> IsPartialOrderDigraph(D);\ntrue\n]]></Example>\n  </Description>\n</ManSe\
ction>\n\n    <ManSection>\n  <Prop Name=\"IsMeetSemilatticeDigraph\" Arg=\"di\
graph\"/>\n  <Prop Name=\"IsJoinSemilatticeDigraph\" Arg=\"digraph\"/>\n  <Pro\
p Name=\"IsLatticeDigraph\" Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>fa\
lse</K>.</Returns>\n  <Description>\n    <C>IsMeetSemilatticeDigraph</C> retur\
ns <K>true</K> if the digraph\n    <A>digraph</A> is a meet semilattice; <C>Is\
JoinSemilatticeDigraph</C>\n    returns <K>true</K> if the digraph <A>digraph<\
/A> is a join semilattice;\n    and  <C>IsLatticeDigraph</C> returns <K>true</\
K> if the digraph\n    <A>digraph</A> is both a meet and a join semilattice.\n\
    <P/>\n\n    For a partial order digraph <Ref Prop=\"IsPartialOrderDigraph\
\"/> the\n    corresponding partial order is the relation <M>\\leq</M>, define\
d by\n    <M>x \\leq y</M> if and only if <C>[x, y]</C> is an edge.\n    A dig\
raph is a <E>meet semilattice</E> if it is a partial order and every\n    pair\
 of vertices has a greatest lower bound (meet) with respect to the\n    aforem\
entioned relation. A <E>join semilattice</E> is a partial order where\n    eve\
ry pair of vertices has a least upper bound (join) with respect to\n    the re\
lation.\n    <P/>\n      \n    If the argument <A>digraph</A> is mutable, then\
 the return value of\n    this property is recomputed every time it is called.\
 \n\n    <Example><![CDATA[\ngap> D := Digraph([[1, 3], [2, 3], [3]]);\n<immut\
able digraph with 3 vertices, 5 edges>\ngap> IsMeetSemilatticeDigraph(D);\nfal\
se\ngap> IsJoinSemilatticeDigraph(D);\ntrue\ngap> IsLatticeDigraph(D);\nfalse\
\ngap> D := Digraph([[1], [2], [1 .. 3]]);\n<immutable digraph with 3 vertices\
, 5 edges>\ngap> IsJoinSemilatticeDigraph(D);\nfalse\ngap> IsMeetSemilatticeDi\
graph(D);\ntrue\ngap> IsLatticeDigraph(D);\nfalse\ngap> D := Digraph([[1 .. 4]\
, [2, 4], [3, 4], [4]]);\n<immutable digraph with 4 vertices, 9 edges>\ngap> I\
sMeetSemilatticeDigraph(D);\ntrue\ngap> IsJoinSemilatticeDigraph(D);\ntrue\nga\
p> IsLatticeDigraph(D);\ntrue\ngap> D := Digraph([[1, 1, 1], [1, 1, 2, 2],\n> \
                  [1, 3, 3], [1, 2, 3, 3, 4]]);\n<immutable multidigraph with \
4 vertices, 15 edges>\ngap> IsMeetSemilatticeDigraph(D);\ntrue\ngap> IsJoinSem\
ilatticeDigraph(D);\ntrue\ngap> IsLatticeDigraph(D);\ntrue\n]]></Example>\n  <\
/Description>\n</ManSection>\n\n  </Section>\n\n  <Section><Heading>Regularity\
</Heading>\n    <ManSection>\n  <Prop Name=\"IsInRegularDigraph\" Arg=\"digrap\
h\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n   \
 This property is <K>true</K> if there is an integer <C>n</C> such that\n    f\
or every vertex <C>v</C> of digraph <A>digraph</A> there are exactly\n    <C>n\
</C> edges terminating in <C>v</C>.\n\n    See also <Ref Prop=\"IsOutRegularDi\
graph\"/> and\n    <Ref Prop=\"IsRegularDigraph\"/>.\n    <P/>\n      \n    If\
 the argument <A>digraph</A> is mutable, then the return value of\n    this pr\
operty is recomputed every time it is called. \n    <Example><![CDATA[\ngap> I\
sInRegularDigraph(CompleteDigraph(4));\ntrue\ngap> IsInRegularDigraph(ChainDig\
raph(4));\nfalse\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSe\
ction>\n  <Prop Name=\"IsOutRegularDigraph\" Arg=\"digraph\"/>\n  <Returns><K>\
true</K> or <K>false</K>.</Returns>\n  <Description>\n    This property is <K>\
true</K> if there is an integer <C>n</C> such that\n    for every vertex <C>v<\
/C> of digraph <A>digraph</A> there are exactly\n    <C>n</C> edges starting a\
t <C>v</C>.\n    <P/>\n\n    See also <Ref Prop=\"IsInRegularDigraph\"/> and\n\
    <Ref Prop=\"IsRegularDigraph\"/>.\n    <P/>\n      \n    If the argument <\
A>digraph</A> is mutable, then the return value of\n    this property is recom\
puted every time it is called. \n    <Example><![CDATA[\ngap> IsOutRegularDigr\
aph(CompleteDigraph(4));\ntrue\ngap> IsOutRegularDigraph(ChainDigraph(4));\nfa\
lse\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Pr\
op Name=\"IsRegularDigraph\" Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>f\
alse</K>.</Returns>\n  <Description>\n    This property is <K>true</K> if ther\
e is an integer <C>n</C> such that\n    for every vertex <C>v</C> of digraph <\
A>digraph</A> there are exactly\n    <C>n</C> edges starting and terminating a\
t <C>v</C>. In other words,\n    the property is <K>true</K> if <A>digraph</A>\
 is both in-regular and\n    and out-regular.\n\n    See also <Ref Prop=\"IsIn\
RegularDigraph\"/> and\n    <Ref Prop=\"IsOutRegularDigraph\"/>.\n    <P/>\n  \
    \n    If the argument <A>digraph</A> is mutable, then the return value of\
\n    this property is recomputed every time it is called. \n    <Example><![C\
DATA[\ngap> IsRegularDigraph(CompleteDigraph(4));\ntrue\ngap> IsRegularDigraph\
(ChainDigraph(4));\nfalse\n]]></Example>\n  </Description>\n</ManSection>\n\n \
   <ManSection>\n  <Prop Name=\"IsDistanceRegularDigraph\" Arg=\"digraph\"/>\n\
  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    If <A>\
digraph</A> is a connected symmetric graph, this property returns\n    <K>true\
</K> if for any two vertices <C>u</C> and <C>v</C> of <A>digraph</A>\n    and \
any two integers <C>i</C> and <C>j</C> between <C>0</C> and the\n    diameter \
of <A>digraph</A>, the number of vertices at distance <C>i</C>\n    from <C>u<\
/C> and distance <C>j</C> from <C>v</C> depends only on\n    <C>i</C>, <C>j</C\
>, and the distance between vertices <C>u</C> and\n    <C>v</C>.<P/>\n\n    Al\
ternatively, a distance regular graph is a graph for which there exist\n    in\
tegers <C>b_i</C>, <C>c_i</C>, and <C>i</C> such that for any two\n    vertice\
s <C>u</C>, <C>v</C> in <A>digraph</A> which are distance <C>i</C>\n    apart,\
 there are exactly <C>b_i</C> neighbors of <C>v</C> which are at\n    distance\
 <C>i - 1</C> away from <C>u</C>, and <C>c_i</C> neighbors of\n    <C>v</C> wh\
ich are at distance <C>i + 1</C> away from <C>u</C>. This\n    definition is u\
sed to check whether <A>digraph</A> is distance regular.<P/>\n\n    In the cas\
e where <A>digraph</A> is not symmetric or not connected, the\n    property is\
 <K>false</K>.\n    <P/>\n      \n    If the argument <A>digraph</A> is mutabl\
e, then the return value of\n    this property is recomputed every time it is \
called. \n\n    <Example><![CDATA[\ngap> D := DigraphSymmetricClosure(ChainDig\
raph(5));;\ngap> IsDistanceRegularDigraph(D);\nfalse\ngap> D := Digraph([[2, 3\
, 4], [1, 3, 4], [1, 2, 4], [1, 2, 3]]);\n<immutable digraph with 4 vertices, \
12 edges>\ngap> IsDistanceRegularDigraph(D);\ntrue\n]]></Example>\n  </Descrip\
tion>\n</ManSection>\n\n  </Section>\n\n  <Section><Heading>Connectivity and c\
ycles</Heading>\n    <ManSection>\n  <Prop Name=\"IsAcyclicDigraph\" Arg=\"dig\
raph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n\
    This property is <K>true</K> if the digraph <A>digraph</A> is acyclic, and\
\n    <K>false</K> if it is not. A digraph is <E>acyclic</E> if every directed\
\n    cycle on the digraph is trivial. See Section <Ref Subsect=\"Definitions\
\"\n      Style=\"Number\" /> for the definition of a directed cycle, and of a\
 trivial\n    directed cycle.<P/>\n\n    The method used in this operation has\
 complexity <M>O(m+n)</M> where\n    <M>m</M> is the number of edges (counting\
 multiple edges as one) and\n    <M>n</M> is the number of vertices in the dig\
raph. <P/>\n\n    If the argument <A>digraph</A> is mutable, then the return v\
alue of\n    this property is recomputed every time it is called. \n\n    <Exa\
mple><![CDATA[\ngap> Petersen := Graph(SymmetricGroup(5), [[1, 2]], OnSets,\n>\
 function(x, y)\n>   return IsEmpty(Intersection(x, y));\n> end);;\ngap> D := \
Digraph(Petersen);\n<immutable digraph with 10 vertices, 30 edges>\ngap> IsAcy\
clicDigraph(D);\nfalse\ngap> D := DigraphFromDiSparse6String(\n> \".b_OGCIDBaP\
GkULEbQHCeRIdrHcuZMfRyDAbPhTi|zF\");\n<immutable digraph with 35 vertices, 34 \
edges>\ngap> IsAcyclicDigraph(D);\ntrue\ngap> IsAcyclicDigraph(ChainDigraph(10\
));\ntrue\ngap> D := CompleteDigraph(IsMutableDigraph, 4);\n<mutable digraph w\
ith 4 vertices, 12 edges>\ngap> IsAcyclicDigraph(D);\nfalse\ngap> IsAcyclicDig\
raph(CycleDigraph(10));\nfalse]]></Example>\n  </Description>\n</ManSection>\n\
\n    <ManSection>\n  <Prop Name=\"IsChainDigraph\" Arg=\"digraph\"/>\n  <Retu\
rns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    <C>IsChainDig\
raph</C> returns <K>true</K> if the digraph <A>digraph</A> is\n    isomorphic \
to the chain digraph with the same number of vertices as\n    <A>digraph</A>, \
and <K>false</K> if it is not; see <Ref\n      Oper=\"ChainDigraph\"/>.<P/>\n\
\n    A digraph is a <E>chain</E> if and only if it is a directed tree, in whi\
ch\n    every vertex has out degree at most one; see <Ref Prop=\"IsDirectedTre\
e\"/>\n    and <Ref Attr=\"OutDegrees\"/>.\n    <P/>\n      \n    If the argum\
ent <A>digraph</A> is mutable, then the return value of\n    this property is \
recomputed every time it is called. \n\n<Example><![CDATA[\ngap> D := Digraph(\
[[1, 3], [2, 3], [3]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> Is\
ChainDigraph(D);\nfalse\ngap> D := ChainDigraph(5);\n<immutable chain digraph \
with 5 vertices>\ngap> IsChainDigraph(D);\ntrue\ngap> D := DigraphReverse(D);\
\n<immutable digraph with 5 vertices, 4 edges>\ngap> IsChainDigraph(D);\ntrue\
\ngap> D := ChainDigraph(IsMutableDigraph, 5);\n<mutable digraph with 5 vertic\
es, 4 edges>\ngap> IsChainDigraph(D);\ntrue\ngap> DigraphReverse(D);\n<mutable\
 digraph with 5 vertices, 4 edges>\ngap> IsChainDigraph(D);\ntrue]]></Example>\
\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsConnec\
tedDigraph\" Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Retur\
ns>\n  <Description>\n    This property is <K>true</K> if the digraph <A>digra\
ph</A>\n    is weakly connected and <K>false</K> if it is not.  A digraph\n   \
 <A>digraph</A> is <E>weakly connected</E> if it is possible to travel\n    fr\
om any vertex to any other vertex by traversing edges in either\n    direction\
 (possibly against the orientation of some of them). <P/>\n\n    The method us\
ed in this function has complexity <M>O(m)</M> if the\n    digraph's <Ref Attr\
=\"DigraphSource\"/> attribute is set, otherwise it has\n    complexity <M>O(m\
+n)</M> (where\n    <M>m</M> is the number of edges and\n    <M>n</M> is the n\
umber of vertices of the digraph).\n    <P/>\n      \n    If the argument <A>d\
igraph</A> is mutable, then the return value of\n    this property is recomput\
ed every time it is called. \n\n    <Example><![CDATA[\ngap> D := Digraph([[2]\
, [3], []]);;\ngap> IsConnectedDigraph(D);\ntrue\ngap> D := Digraph([[1, 3], [\
4], [3], []]);;\ngap> IsConnectedDigraph(D);\nfalse\ngap> D := Digraph(IsMutab\
leDigraph, [[2], [3], []]);;\ngap> IsConnectedDigraph(D);\ntrue\ngap> D := Dig\
raph(IsMutableDigraph, [[1, 3], [4], [3], []]);;\ngap> IsConnectedDigraph(D);\
\nfalse]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <\
Prop Name=\"IsBiconnectedDigraph\" Arg=\"digraph\"/>\n  <Returns><K>true</K> o\
r <K>false</K>.</Returns>\n  <Description>\n    A connected digraph is <E>bico\
nnected</E> if it is still connected (in the\n    sense of <Ref Prop=\"IsConne\
ctedDigraph\"/>) when any vertex is removed. \n      If <A>D</A> has at least \
3 vertices, then <C>IsBiconnectedDigraph</C>\n      implies <Ref Prop=\"IsBrid\
gelessDigraph\"/>;\n    see <Ref Attr=\"ArticulationPoints\"/> or <Ref Attr=\"\
Bridges\"/> for a more\n    detailed explanation.\n    <P/>\n\n    <C>IsBiconn\
ectedDigraph</C> returns <K>true</K> if the digraph\n    <A>digraph</A> is bic\
onnected, and <K>false</K> if it is not. In\n    particular, <C>IsBiconnectedD\
igraph</C> returns <K>false</K> if\n    <A>digraph</A> is not connected. <P/>\
\n      \n    If the argument <A>digraph</A> is mutable, then the return value\
 of\n    this property is recomputed every time it is called. <P/>\n\n    Mult\
iple edges are ignored by this method. <P/>\n\n    The method used in this ope\
ration has complexity <M>O(m+n)</M> where\n    <M>m</M> is the number of edges\
 and <M>n</M> is the number of vertices in\n    the digraph.\n    <P/>\n\n    \
See also <Ref Attr=\"Bridges\"/>, <Ref Attr=\"ArticulationPoints\"/>, and \n  \
  <Ref Prop=\"IsBridgelessDigraph\"/>.\n    <P/>\n      \n<Example><![CDATA[\n\
gap> IsBiconnectedDigraph(Digraph([[1, 3], [2, 3], [3]]));\nfalse\ngap> IsBico\
nnectedDigraph(CycleDigraph(5));\ntrue\ngap> D := Digraph([[1, 1], [1, 1, 2], \
[3], [3, 3, 4, 4]]);;\ngap> IsBiconnectedDigraph(D);\nfalse\ngap> D := Complet\
eBipartiteDigraph(IsMutableDigraph, 5, 4);\n<mutable digraph with 9 vertices, \
40 edges>\ngap> IsBiconnectedDigraph(D);\ntrue]]></Example>\n  </Description>\
\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsBridgelessDigraph\" Arg=\
\"D\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n \
   A connected digraph is <E>bridgeless</E> if it is still connected (in the\n\
    sense of <Ref Prop=\"IsConnectedDigraph\"/>) when any edge is removed. \n \
   If <A>D</A> has at least 3 vertices, then <Ref\n    Prop=\"IsBiconnectedDig\
raph\"/> implies <C>IsBridgelessDigraph</C>;\n    see <Ref Attr=\"Articulation\
Points\"/> or <Ref Attr=\"Bridges\"/> for a more\n    detailed explanation.\n \
   <P/>\n\n    <C>IsBridgelessDigraph</C> returns <K>true</K> if the digraph\n\
    <A>D</A> is bridgeless, and <K>false</K> if it is not. In\n    particular,\
 <C>IsBridgelessDigraph</C> returns <K>false</K> if\n    <A>D</A> is not conne\
cted. <P/>\n      \n    If the argument <A>D</A> is mutable, then the return v\
alue of\n    this property is recomputed every time it is called. <P/>\n\n    \
Multiple edges are ignored by this method. <P/>\n\n    The method used in this\
 operation has complexity <M>O(m+n)</M> where\n    <M>m</M> is the number of e\
dges and <M>n</M> is the number of vertices in\n    the digraph.\n    <P/>\n\n\
    See also <Ref Attr=\"Bridges\"/>, <Ref Attr=\"ArticulationPoints\"/>, and \
\n    <Ref Prop=\"IsBiconnectedDigraph\"/>.\n      \n<Example><![CDATA[\ngap> \
IsBridgelessDigraph(Digraph([[1, 3], [2, 3], [3]]));\nfalse\ngap> IsBridgeless\
Digraph(CycleDigraph(5));\ntrue\ngap> D := Digraph([[1, 1], [1, 1, 2], [3], [3\
, 3, 4, 4]]);;\ngap> IsBridgelessDigraph(D);\nfalse\ngap> D := CompleteBiparti\
teDigraph(IsMutableDigraph, 5, 4);\n<mutable digraph with 9 vertices, 40 edges\
>\ngap> IsBridgelessDigraph(D);\ntrue\ngap> D := Digraph([[2, 5], [1, 3, 4, 5]\
, [2, 4], [2, 3], [1, 2]]);\n<immutable digraph with 5 vertices, 12 edges>\nga\
p> IsBridgelessDigraph(D);\ntrue\ngap> IsBiconnectedDigraph(D);\nfalse\ngap> D\
 := Digraph([[2], [3], [4], [2]]);\n<immutable digraph with 4 vertices, 4 edge\
s>\ngap> IsBridgelessDigraph(D);\nfalse\ngap> IsBiconnectedDigraph(D);\nfalse\
\ngap> IsBridgelessDigraph(ChainDigraph(2));\nfalse\ngap> IsBiconnectedDigraph\
(ChainDigraph(2));\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\n  \
  <ManSection>\n  <Prop Name=\"IsStronglyConnectedDigraph\" Arg=\"digraph\"/>\
\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    This\
 property is <K>true</K> if the digraph <A>digraph</A> is strongly\n    connec\
ted and <K>false</K> if it is not. <P/>\n\n    A digraph <A>digraph</A> is <E>\
strongly connected</E> if there is a directed\n    path from every vertex to e\
very other vertex.  See Section <Ref\n      Subsect=\"Definitions\" Style=\"Nu\
mber\" /> for the definition of a directed\n    path.    <P/>\n\n    The metho\
d used in this operation is based on Gabow's Algorithm <Cite\n      Key=\"Gab0\
0\"/> and has complexity <M>O(m+n)</M>, where <M>m</M> is\n    the number of e\
dges (counting multiple edges as one) and <M>n</M> is the\n    number of verti\
ces in the digraph.\n    <P/>\n      \n    If the argument <A>digraph</A> is m\
utable, then the return value of\n    this property is recomputed every time i\
t is called. \n\n    <Example><![CDATA[\ngap> D := CycleDigraph(250000);\n<imm\
utable cycle digraph with 250000 vertices>\ngap> IsStronglyConnectedDigraph(D)\
;\ntrue\ngap> D := DigraphRemoveEdges(D, [[250000, 1]]);\n<immutable digraph w\
ith 250000 vertices, 249999 edges>\ngap> IsStronglyConnectedDigraph(D);\nfalse\
\ngap> D := CycleDigraph(IsMutableDigraph, 250000);\n<mutable digraph with 250\
000 vertices, 250000 edges>\ngap> IsStronglyConnectedDigraph(D);\ntrue\ngap> D\
igraphRemoveEdge(D, [250000, 1]);\n<mutable digraph with 250000 vertices, 2499\
99 edges>\ngap> IsStronglyConnectedDigraph(D);\nfalse\n]]></Example>\n  </Desc\
ription>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsAperiodicDigraph\
\" Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <De\
scription>\n    This property is <K>true</K> if the digraph <A>digraph</A>\n  \
  is aperiodic, i.e. if its <Ref Attr = \"DigraphPeriod\"/> is equal to 1.\n  \
  Otherwise, the property is <K>false</K>.\n    <P/>\n      \n    If the argum\
ent <A>digraph</A> is mutable, then the return value of\n    this property is \
recomputed every time it is called. \n    <Example><![CDATA[\ngap> D := Digrap\
h([[6], [1], [2], [3], [4, 4], [5]]);\n<immutable multidigraph with 6 vertices\
, 7 edges>\ngap> IsAperiodicDigraph(D);\nfalse\ngap> D := Digraph([[2], [3, 5]\
, [4], [5], [1, 2]]);\n<immutable digraph with 5 vertices, 7 edges>\ngap> IsAp\
eriodicDigraph(D);\ntrue\ngap> D := Digraph(IsMutableDigraph, [[2], [3, 5], [4\
], [5], [1, 2]]);\n<mutable digraph with 5 vertices, 7 edges>\ngap> IsAperiodi\
cDigraph(D);\ntrue]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSe\
ction>\n  <Prop Name=\"IsDirectedTree\" Arg=\"digraph\"/>\n  <Returns><K>true<\
/K> or <K>false</K>.</Returns>\n  <Description>\n    Returns <K>true</K> if th\
e digraph <A>digraph</A> is a directed tree, and\n    <K>false</K> if it is no\
t. <P/>\n\n    A <E>directed tree</E> is an acyclic digraph with precisely 1 s\
ource,\n    such that no two vertices share an out-neighbour.\n    Note the em\
pty digraph is not considered a directed\n    tree as it has no source. <P/>\n\
\n    See also <Ref Attr=\"DigraphSources\"/>.\n    <P/>\n      \n    If the a\
rgument <A>digraph</A> is mutable, then the return value of\n    this property\
 is recomputed every time it is called. \n\n    <Example><![CDATA[\ngap> D := \
Digraph([[], [2]]);\n<immutable digraph with 2 vertices, 1 edge>\ngap> IsDirec\
tedTree(D);\nfalse\ngap> D := Digraph([[3], [3], []]);\n<immutable digraph wit\
h 3 vertices, 2 edges>\ngap> IsDirectedTree(D);\nfalse\ngap> D := Digraph([[2]\
, [3], []]);\n<immutable digraph with 3 vertices, 2 edges>\ngap> IsDirectedTre\
e(D);\ntrue\ngap> D := Digraph([[2, 3], [6], [4, 5], [], [], []]);\n<immutable\
 digraph with 6 vertices, 5 edges>\ngap> IsDirectedTree(D);\ntrue\n]]></Exampl\
e>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsUndi\
rectedTree\" Arg=\"digraph\"/>\n  <Prop Name=\"IsUndirectedForest\" Arg=\"digr\
aph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n \
   The property <C>IsUndirectedTree</C> returns <K>true</K> if the digraph\n  \
  <A>digraph</A> is an undirected tree, and the property\n    <C>IsUndirectedF\
orest</C> returns <K>true</K> if <A>digraph</A> is an\n    undirected forest; \
otherwise, these properties return <K>false</K>. <P/>\n\n    An <E>undirected \
tree</E> is a symmetric digraph without loops, in which for\n    any pair of d\
istinct vertices <C>u</C> and <C>v</C>, there is exactly one\n    directed pat\
h from <C>u</C> to <C>v</C>. See <Ref\n      Prop=\"IsSymmetricDigraph\"/> and\
 <Ref Prop=\"DigraphHasLoops\"/>, and see\n    Section <Ref Subsect=\"Definiti\
ons\" Style=\"Number\" /> for the definition of\n    directed path. This defin\
ition implies that an undirected tree has\n    no multiple edges. <P/>\n\n    \
An <E>undirected forest</E> is a digraph, each of whose connected components\n\
    is an undirected tree. In other words, an undirected forest is isomorphic \
to\n    a disjoint union of undirected trees. See <Ref\n      Attr=\"DigraphCo\
nnectedComponents\" /> and <Ref Func=\"DigraphDisjointUnion\"\n      Label=\"f\
or a list of digraphs\" />. In particular, every\n    undirected tree is an un\
directed forest. <P/>\n\n    Please note that the digraph with zero vertices i\
s considered to be neither\n    an undirected tree nor an undirected forest.\n\
    <P/>\n      \n    If the argument <A>digraph</A> is mutable, then the retu\
rn value of\n    this property is recomputed every time it is called. \n\n    \
<Example><![CDATA[\ngap> D := Digraph([[3], [3], [1, 2]]);\n<immutable digraph\
 with 3 vertices, 4 edges>\ngap> IsUndirectedTree(D);\ntrue\ngap> IsSymmetricD\
igraph(D) and not DigraphHasLoops(D);\ntrue\ngap> D := Digraph([[3], [5], [1, \
4], [3], [2]]);\n<immutable digraph with 5 vertices, 6 edges>\ngap> IsConnecte\
dDigraph(D);\nfalse\ngap> IsUndirectedTree(D);\nfalse\ngap> IsUndirectedForest\
(D);\ntrue\ngap> D := Digraph([[1, 2], [1], [2]]);\n<immutable digraph with 3 \
vertices, 4 edges>\ngap> IsUndirectedTree(D) or IsUndirectedForest(D);\nfalse\
\ngap> IsSymmetricDigraph(D) or not DigraphHasLoops(D);\nfalse]]></Example>\n \
 </Description>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsEulerianD\
igraph\" Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\
\n  <Description>\n    This property returns true if the digraph <A>digraph</A\
> is Eulerian.\n    <P/>\n\n    A connected digraph is called <E>Eulerian</E> \
if there exists a directed\n    circuit on the digraph which includes every ed\
ge exactly once.  See\n    Section <Ref Subsect=\"Definitions\" Style=\"Number\
\" /> for the definition of\n    a directed circuit. Note that the empty digra\
ph with at most one vertex is\n    considered to be Eulerian.\n    <P/>\n     \
 \n    If the argument <A>digraph</A> is mutable, then the return value of\n  \
  this property is recomputed every time it is called. \n\n    <Example><![CDA\
TA[\ngap> D := Digraph([[]]);\n<immutable empty digraph with 1 vertex>\ngap> I\
sEulerianDigraph(D);\ntrue\ngap> D := Digraph([[2], []]);\n<immutable digraph \
with 2 vertices, 1 edge>\ngap> IsEulerianDigraph(D);\nfalse\ngap> D := Digraph\
([[3], [], [2]]);\n<immutable digraph with 3 vertices, 2 edges>\ngap> IsEuleri\
anDigraph(D);\nfalse\ngap> D := Digraph([[2], [3], [1]]);\n<immutable digraph \
with 3 vertices, 3 edges>\ngap> IsEulerianDigraph(D);\ntrue\n]]></Example>\n  \
</Description>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsHamiltonia\
nDigraph\" Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns\
>\n  <Description>\n    If <A>digraph</A> is Hamiltonian, then this property r\
eturns\n    <K>true</K>, and <K>false</K> if it is not. <P/>\n\n    A digraph \
with <C>n</C> vertices is <E>Hamiltonian</E> if it has a\n    directed cycle o\
f length <C>n</C>. See Section <Ref Subsect=\"Definitions\"\n     Style=\"Numb\
er\" /> for the definition of a directed cycle.\n    Note the empty digraphs o\
n 0 and 1 vertices are considered to be\n    Hamiltonian.<P/>\n\n    The metho\
d used in this operation has the worst case complexity as\n    <Ref Oper=\"Dig\
raphMonomorphism\"/>.\n    <P/>\n      \n    If the argument <A>digraph</A> is\
 mutable, then the return value of\n    this property is recomputed every time\
 it is called. \n\n    <Example><![CDATA[\ngap> g := Digraph([[]]);\n<immutabl\
e empty digraph with 1 vertex>\ngap> IsHamiltonianDigraph(g);\ntrue\ngap> g :=\
 Digraph([[2], [1]]);\n<immutable digraph with 2 vertices, 2 edges>\ngap> IsHa\
miltonianDigraph(g);\ntrue\ngap> g := Digraph([[3], [], [2]]);\n<immutable dig\
raph with 3 vertices, 2 edges>\ngap> IsHamiltonianDigraph(g);\nfalse\ngap> g :\
= Digraph([[2], [3], [1]]);\n<immutable digraph with 3 vertices, 3 edges>\ngap\
> IsHamiltonianDigraph(g);\ntrue\n]]></Example>\n  </Description>\n</ManSectio\
n>\n\n    <ManSection>\n  <Prop Name=\"IsCycleDigraph\" Arg=\"digraph\"/>\n  <\
Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    <C>IsCycl\
eDigraph</C> returns <K>true</K> if the digraph <A>digraph</A> is\n    isomorp\
hic to the cycle digraph with the same number of vertices as\n    <A>digraph</\
A>, and <K>false</K> if it is not; see <Ref\n      Oper=\"CycleDigraph\"/>.<P/\
>\n\n    A digraph is a <E>cycle</E> if and only if it is strongly connected a\
nd has\n    the same number of edges as vertices. \n    <P/>\n      \n    If t\
he argument <A>digraph</A> is mutable, then the return value of\n    this prop\
erty is recomputed every time it is called. \n\n<Example><![CDATA[\ngap> D := \
Digraph([[1, 3], [2, 3], [3]]);\n<immutable digraph with 3 vertices, 5 edges>\
\ngap> IsCycleDigraph(D);\nfalse\ngap> D := CycleDigraph(5);\n<immutable cycle\
 digraph with 5 vertices>\ngap> IsCycleDigraph(D);\ntrue\ngap> D := OnDigraphs\
(D, (1, 2, 3));\n<immutable digraph with 5 vertices, 5 edges>\ngap> D = CycleD\
igraph(5);\nfalse\ngap> IsCycleDigraph(D);\ntrue]]></Example>\n  </Description\
>\n</ManSection>\n\n  </Section>\n  \n  <Section><Heading>Planarity</Heading>\
\n    <ManSection>\n  <Prop Name=\"IsPlanarDigraph\" Arg=\"digraph\"/>\n  <Ret\
urns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    A <E>planar<\
/E> digraph is a digraph that can be embedded in the plane in\n    such a way \
that its edges do not intersect. A digraph is planar if and only\n    if it do\
es not have a subdigraph that is homeomorphic to either the\n    complete grap\
h on <C>5</C> vertices or the complete bipartite graph with\n    vertex sets o\
f sizes <C>3</C> and <C>3</C>.\n    <P/>\n    \n    <C>IsPlanarDigraph</C> ret\
urns <K>true</K> if the digraph <A>digraph</A> is\n    planar and <K>false</K>\
 if it is not. The directions and multiplicities of\n    any edges in <A>digra\
ph</A> are ignored by <C>IsPlanarDigraph</C>.\n    <P/> \n\n    See also <Ref \
Prop=\"IsOuterPlanarDigraph\"/>.\n    <P/>\n\n    This method uses the referen\
ce implementation in\n    &edge-addition-planarity-suite; by John Boyer of the\
 algorithms described\n    in <Cite Key=\"BM06\"/>.\n\n    <Example><![CDATA[\
\ngap> IsPlanarDigraph(CompleteDigraph(4));\ntrue\ngap> IsPlanarDigraph(Comple\
teDigraph(5));\nfalse\ngap> IsPlanarDigraph(CompleteBipartiteDigraph(2, 3));\n\
true\ngap> IsPlanarDigraph(CompleteBipartiteDigraph(3, 3));\nfalse\ngap> IsPla\
narDigraph(CompleteDigraph(IsMutableDigraph, 4));\ntrue\ngap> IsPlanarDigraph(\
CompleteDigraph(IsMutableDigraph, 5));\nfalse\ngap> IsPlanarDigraph(CompleteBi\
partiteDigraph(IsMutableDigraph, 2, 3));\ntrue\ngap> IsPlanarDigraph(CompleteB\
ipartiteDigraph(IsMutableDigraph, 3, 3));\nfalse\n]]></Example>\n  </Descripti\
on>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsOuterPlanarDigraph\" \
Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Descr\
iption>\n    An <E>outer planar</E> digraph is a digraph that can be embedded \
in the\n    plane in such a way that its edges do not intersect, and all verti\
ces\n    belong to the unbounded face of the embedding.  A digraph is outer pl\
anar\n    if and only if it does not have a subdigraph that is homeomorphic to\
 either\n    the complete graph on <C>4</C> vertices or the complete bipartite\
 graph\n    with vertex sets of sizes <C>2</C> and <C>3</C>.\n    <P/>\n    \n\
    <C>IsOuterPlanarDigraph</C> returns <K>true</K> if the digraph\n    <A>dig\
raph</A> is outer planar and <K>false</K> if it is not. The\n    directions an\
d multiplicities of any edges in <A>digraph</A> are ignored by\n    <C>IsPlana\
rDigraph</C>.  <P/>\n\n    See also <Ref Prop=\"IsPlanarDigraph\"/>.\n\n    Th\
is method uses the reference implementation in\n    &edge-addition-planarity-s\
uite; by John Boyer of the algorithms described\n    in <Cite Key=\"BM06\"/>.\
\n\n<Example><![CDATA[\ngap> IsOuterPlanarDigraph(CompleteDigraph(4));\nfalse\
\ngap> IsOuterPlanarDigraph(CompleteDigraph(5));\nfalse\ngap> IsOuterPlanarDig\
raph(CompleteBipartiteDigraph(2, 3));\nfalse\ngap> IsOuterPlanarDigraph(Comple\
teBipartiteDigraph(3, 3));\nfalse\ngap> IsOuterPlanarDigraph(CycleDigraph(10))\
;\ntrue\ngap> IsOuterPlanarDigraph(CompleteDigraph(IsMutableDigraph, 4));\nfal\
se\ngap> IsOuterPlanarDigraph(CompleteDigraph(IsMutableDigraph, 5));\nfalse\ng\
ap> IsOuterPlanarDigraph(CompleteBipartiteDigraph(IsMutableDigraph,\n>        \
                                          2, 3));\nfalse\ngap> IsOuterPlanarDi\
graph(CompleteBipartiteDigraph(IsMutableDigraph,\n>                           \
                       3, 3));\nfalse\ngap> IsOuterPlanarDigraph(CycleDigraph(\
IsMutableDigraph, 10));\ntrue\n\n]]></Example>\n  </Description>\n</ManSection\
>\n\n  </Section>\n\n  <Section><Heading>Homomorphisms and transformations</He\
ading>\n    <ManSection>\n  <Prop Name=\"IsDigraphCore\" Arg=\"digraph\"/>\n  \
<Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    This pro\
perty returns <K>true</K> if <A>digraph</A> is a core,\n    and <K>false</K> i\
f it is not.<P/>\n\n    A digraph <C>D</C> is a <E>core</E> if and only if it \
has no proper\n    subdigraphs <C>A</C> such that there exists a homomorphism \
from <C>D</C>\n    to <C>A</C>. In other words, a digraph <C>D</C> is a core i\
f and only if\n    every endomorphism on <C>D</C> is an automorphism on <C>D</\
C>.\n    <P/>\n      \n    If the argument <A>digraph</A> is mutable, then the\
 return value of\n    this property is recomputed every time it is called. \n\
\n    <Example><![CDATA[\ngap> D := CompleteDigraph(6);\n<immutable complete d\
igraph with 6 vertices>\ngap> IsDigraphCore(D);\ntrue\ngap> D := DigraphSymmet\
ricClosure(CycleDigraph(6));\n<immutable symmetric digraph with 6 vertices, 12\
 edges>\ngap> DigraphHomomorphism(D, CompleteDigraph(2));\nTransformation( [ 1\
, 2, 1, 2, 1, 2 ] )\ngap> IsDigraphCore(D);\nfalse\n]]></Example>\n  </Descrip\
tion>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsEdgeTransitive\" Ar\
g=\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Descrip\
tion>\n    If <A>digraph</A> is a digraph without multiple edges, then\n    <C\
>IsEdgeTransitive</C> returns <K>true</K> if <A>digraph</A>\n    is edge trans\
itive, and <K>false</K> otherwise. A digraph is\n    <E>edge transitive</E> if\
 its automorphism group acts\n    transitively on its edges (via the action\n \
   <Ref Func=\"OnPairs\" BookName=\"ref\"/>).\n    <P/>\n      \n    If the ar\
gument <A>digraph</A> is mutable, then the return value of\n    this property \
is recomputed every time it is called. \n\n    <Example><![CDATA[\ngap> IsEdge\
Transitive(CompleteDigraph(2));\ntrue\ngap> IsEdgeTransitive(ChainDigraph(3));\
\nfalse\ngap> IsEdgeTransitive(Digraph([[2], [3, 3, 3], []]));\nError, the arg\
ument <D> must be a digraph with no multiple edges,\n]]></Example>\n  </Descri\
ption>\n</ManSection>\n\n    <ManSection>\n  <Prop Name=\"IsVertexTransitive\"\
 Arg=\"digraph\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Desc\
ription>\n    If <A>digraph</A> is a digraph, then <C>IsVertexTransitive</C> r\
eturns\n    <K>true</K> if <A>digraph</A> is vertex transitive, and <K>false</\
K>\n    otherwise. A digraph is <E>vertex transitive</E> if its automorphism g\
roup\n    acts transitively on its vertices.\n    <P/>\n      \n    If the arg\
ument <A>digraph</A> is mutable, then the return value of\n    this property i\
s recomputed every time it is called. \n\n    <Example><![CDATA[\ngap> IsVerte\
xTransitive(CompleteDigraph(2));\ntrue\ngap> IsVertexTransitive(ChainDigraph(3\
));\nfalse\n]]></Example>\n  </Description>\n</ManSection>\n\n  </Section>\n\n\
  \n</Chapter>\n <!-- properties -->\n  <Chapter Label=\"Homomorphisms\"><Head\
ing>Homomorphisms</Heading>\n  <!--Let $E_a=(E_a^0,E_a^1,\\ra_a,\\so_a)$ and $\
E_b=(E_b^0,E_b^1,\\ra_b,\\so_b)$ be two\ngraphs, and let $\\phi_0 : E_a^0 \\to\
 E_b^0$ and $\\phi_1 : E_a^1 \\to E_b^1$ be\nfunctions. Then the pair $\\phi =\
 (\\phi_0, \\phi_1)$ is a \\emph{graph homomorphism\nfrom} $E_a$ \\emph{to} $E\
_b$ if $\\phi_0(\\so_a(e)) = \\so_b(\\phi_1(e))$ and\n$\\phi_0(\\ra_a(e)) = \\\
ra_b(\\phi_1(e))$ for every $e \\in E_a^1$. If $\\phi_0$ and\n$\\phi_1$ are in\
 addition bijective, then $\\phi$ is a \\emph{graph isomorphism\nfrom} $E_a$ \
\\emph{to} $E_b$. In this case we say that $E_a$ and $E_b$ are\n\\emph{isomorp\
hic} and write $E_a \\cong E_b$.-->\n\n  <Section><Heading>Acting on digraphs<\
/Heading>\n    <ManSection>\n  <Oper Name=\"OnDigraphs\" Arg=\"digraph, perm\"\
\n    Label=\"for a digraph and a perm\"/>\n  <Oper Name=\"OnDigraphs\" Arg=\"\
digraph, trans\"\n    Label=\"for a digraph and a transformation\"/>\n  <Retur\
ns>A digraph.</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph, \
and the second argument <A>perm</A> is a\n    <E>permutation</E> of the vertic\
es of <A>digraph</A>, then this operation\n    returns a digraph constructed b\
y relabelling the vertices of\n    <A>digraph</A> according to <A>perm</A>.  N\
ote that for an automorphism\n    <C>f</C> of a digraph, we have <C>OnDigraphs\
(<A>digraph</A>, f) =\n    </C><A>digraph</A>.\n    <P/>\n\n    If the second \
argument is a <E>transformation</E> <A>trans</A> of the\n    vertices of <A>di\
graph</A>, then this operation returns a digraph\n    constructed by transform\
ing the source and range of each edge according to\n    <A>trans</A>. Thus a v\
ertex which does not appear in the image of\n    <A>trans</A> will be isolated\
 in the returned digraph, and the returned\n    digraph may contain multiple e\
dges, even if <A>digraph</A> does not.\n    If <A>trans</A> is mathematically \
a permutation, then the result coincides\n    with <C>OnDigraphs(<A>digraph</A\
>, AsPermutation(<A>trans</A>))</C>.\n    <P/>\n\n    The <Ref Oper=\"DigraphV\
ertexLabels\"/> of <A>digraph</A> will not be retained\n    in the returned di\
graph. <P/>\n\n    If <A>digraph</A> belongs to <Ref Filt=\"IsMutableDigraph\"\
/>, then\n    relabelling of the vertices is performed directly on <A>digraph<\
/A>.\n    If <A>digraph</A> belongs to <Ref Filt=\"IsImmutableDigraph\"/>, an \
immutable\n    copy of <A>digraph</A> with the vertices relabelled is returned\
.<P/>\n\n    <Example><![CDATA[\ngap> D := Digraph([[3], [1, 3, 5], [1], [1, 2\
, 4], [2, 3, 5]]);\n<immutable digraph with 5 vertices, 11 edges>\ngap> new :=\
 OnDigraphs(D, (1, 2));\n<immutable digraph with 5 vertices, 11 edges>\ngap> O\
utNeighbours(new);\n[ [ 2, 3, 5 ], [ 3 ], [ 2 ], [ 2, 1, 4 ], [ 1, 3, 5 ] ]\ng\
ap> D := Digraph([[2], [], [2]]);\n<immutable digraph with 3 vertices, 2 edges\
>\ngap> t := Transformation([1, 2, 1]);;\ngap> new := OnDigraphs(D, t);\n<immu\
table multidigraph with 3 vertices, 2 edges>\ngap> OutNeighbours(new);\n[ [ 2,\
 2 ], [  ], [  ] ]\ngap> ForAll(DigraphEdges(D),\n>  e -> IsDigraphEdge(new, [\
e[1] ^ t, e[2] ^ t]));\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\
\n    <ManSection>\n  <Oper Name=\"OnMultiDigraphs\" Arg=\"digraph, pair\"/>\n\
  <Oper Name=\"OnMultiDigraphs\" Arg=\"digraph, perm1, perm2\"\n    Label=\"fo\
r a digraph, perm, and perm\"/>\n  <Returns>A digraph.</Returns>\n  <Descripti\
on>\n    If <A>digraph</A> is a digraph, and <A>pair</A> is a pair consisting \
of a\n    permutation of the vertices and a permutation of the edges of\n    <\
A>digraph</A>, then this operation returns a digraph\n    constructed by relab\
elling the vertices and edges of <A>digraph</A>\n    according to <A>perm[1]</\
A> and <A>perm[2]</A>, respectively. <P/>\n\n    In its second form, <C>OnMult\
iDigraphs</C> returns a digraph with vertices\n    and edges permuted by <A>pe\
rm1</A> and <A>perm2</A>, respectively. <P/>\n\n    Note that <C>OnDigraphs(<A\
>digraph</A>,\n      perm)=OnMultiDigraphs(<A>digraph</A>, [perm, ()])</C> whe\
re <C>perm</C> is\n    a permutation of the vertices of <A>digraph</A>. If you\
 are only interested\n    in the action of a permutation on the vertices of a \
digraph, then you can\n    use <C>OnDigraphs</C> instead of <C>OnMultiDigraphs\
</C>.\n\n    If <A>digraph</A> belongs to <Ref Filt=\"IsMutableDigraph\"/>, th\
en\n    relabelling of the vertices is performed directly on <A>digraph</A>.\n\
    If <A>digraph</A> belongs to <Ref Filt=\"IsImmutableDigraph\"/>, an immuta\
ble\n    copy of <A>digraph</A> with the vertices relabelled is returned.<P/>\
\n\n    <Example><![CDATA[\ngap> D1 := Digraph([\n> [3, 6, 3], [], [3], [9, 10\
], [9], [],  [], [10, 4, 10], [], []]);\n<immutable multidigraph with 10 verti\
ces, 10 edges>\ngap> p := BlissCanonicalLabelling(D1);\n[ (1,7)(3,6)(4,10)(5,9\
), () ]\ngap> D2 := OnMultiDigraphs(D1, p);\n<immutable multidigraph with 10 v\
ertices, 10 edges>\ngap> OutNeighbours(D2);\n[ [  ], [  ], [  ], [  ], [  ], [\
 6 ], [ 6, 3, 6 ], [ 4, 10, 4 ], \n  [ 5 ], [ 5, 4 ] ]]]></Example>\n  </Descr\
iption>\n</ManSection>\n\n  </Section>\n\n  <Section Label=\"Isomorphisms and \
canonical labellings\">\n    <Heading>Isomorphisms and canonical labellings</H\
eading>\n    From version 0.11.0 of &Digraphs; it is possible to use either &b\
liss; or\n    &nauty; (via &NautyTracesInterface;) to calculate canonical labe\
llings and\n    automorphism groups of digraphs; see <Cite Key=\"JK07\"/> and \
<Cite\n      Key=\"MP14\"/> for more details about &bliss; and &nauty;,\n    r\
espectively. \n\n    <ManSection>\n  <Func Name=\"DigraphsUseNauty\" Arg=\"\"/\
>\n  <Func Name=\"DigraphsUseBliss\" Arg=\"\"/>\n  <Returns>Nothing.</Returns>\
\n  <Description>\n    These functions can be used to specify whether &nauty; \
or &bliss; should be\n    used by default by &Digraphs;. If &NautyTracesInterf\
ace; is not available,\n    then these functions do nothing. Otherwise, by cal\
ling\n    <C>DigraphsUseNauty</C> subsequent computations will default to usin\
g\n    &nauty; rather than &bliss;, where possible.\n    <P/>\n\n    You can c\
all these functions at any point in a &GAP; session, as many\n    times as you\
 like, it is guaranteed that existing digraphs remain\n    valid, and that com\
parison of existing digraphs and newly created digraphs\n    via\n    <Ref Ope\
r=\"IsIsomorphicDigraph\" Label=\"for digraphs\"/>,\n    <Ref Oper=\"IsIsomorp\
hicDigraph\"\n      Label=\"for digraphs and homogeneous lists\"/>,\n    <Ref \
Oper=\"IsomorphismDigraphs\" Label=\"for digraphs\"/>, and\n    <Ref Oper=\"Is\
omorphismDigraphs\"\n      Label=\"for digraphs and homogeneous lists\"/> are \
also valid.<P/>\n\n    It is also possible to compute the automorphism group o\
f a specific digraph\n    using both &nauty; and &bliss; using <Ref Attr=\"Nau\
tyAutomorphismGroup\"/>\n    and <Ref Attr=\"BlissAutomorphismGroup\" Label=\"\
for a digraph\"/>, respectively.\n  </Description>\n</ManSection>\n\n    <ManS\
ection>\n  <Attr Name=\"AutomorphismGroup\" Label=\"for a digraph\" Arg=\"digr\
aph\"/>\n  <Returns>A permutation group.</Returns>\n  <Description>\n    If <A\
>digraph</A> is a digraph, then this attribute contains the group of\n    auto\
morphisms of <A>digraph</A>.  An <E>automorphism</E> of <A>digraph</A>\n    is\
 an isomorphism from <A>digraph</A> to itself. See <Ref\n      Oper=\"Isomorph\
ismDigraphs\" Label=\"for digraphs\" /> for more information\n    about isomor\
phisms of digraphs. <P/>\n\n    If <A>digraph</A> is not a multidigraph then t\
he automorphism group is\n    returned as a group of permutations on the set o\
f vertices of\n    <A>digraph</A>. <P/>\n\n    If <A>digraph</A> is a multidig\
raph then the automorphism group is returned\n    as the direct product of a g\
roup of permutations on the set of vertices of\n    <A>digraph</A> with a grou\
p of permutations on the set of edges of\n    <A>digraph</A>. These groups can\
 be accessed using <Ref Oper=\"Projection\"\n      Label=\"for a domain and a \
positive integer\" BookName=\"ref\"/> on the\n    returned group.<P/>\n\n    B\
y default, the automorphism group is found using &bliss; by Tommi Junttila\n  \
  and Petteri Kaski. If &NautyTracesInterface; is available, then &nauty; by\n\
    Brendan Mckay and Adolfo Piperno can be used instead; see\n    <Ref Attr=\
\"BlissAutomorphismGroup\" Label=\"for a digraph\"/>, \n    <Ref Attr=\"NautyA\
utomorphismGroup\"/>, <Ref Func=\"DigraphsUseBliss\"/>,\n    and <Ref Func=\"D\
igraphsUseNauty\"/>.\n    <P/>\n\n    If the argument <A>digraph</A> is mutabl\
e, then the return value of\n    this attribute is recomputed every time it is\
 called. \n\n    <Example><![CDATA[\ngap> johnson := DigraphFromGraph6String(\
\"E}lw\");\n<immutable digraph with 6 vertices, 24 edges>\ngap> G := Automorph\
ismGroup(johnson);\nGroup([ (3,4), (2,3)(4,5), (1,2)(5,6) ])\ngap> cycle := Cy\
cleDigraph(9);\n<immutable cycle digraph with 9 vertices>\ngap> G := Automorph\
ismGroup(cycle);\nGroup([ (1,2,3,4,5,6,7,8,9) ])\ngap> IsCyclic(G) and Size(G)\
 = 9;\ntrue]]></Example>\n    </Description>\n  </ManSection>\n\n    <ManSecti\
on>\n  <Attr Name=\"BlissAutomorphismGroup\" Arg=\"digraph\" Label=\"for a dig\
raph\"/>\n  <Oper Name=\"BlissAutomorphismGroup\" Arg=\"digraph, vertex_colour\
s\" \n    Label=\"for a digraph and homogenous list\"/>\n  <Oper Name=\"BlissA\
utomorphismGroup\" Arg=\"digraph, vertex_colours, edge_colours\" \n    Label=\
\"for a digraph, homogenous list, and list\"/>\n  <Returns>A permutation group\
.</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph, then this at\
tribute contains the group of\n    automorphisms of <A>digraph</A> as calculat\
ed using &bliss; by Tommi Junttila\n    and Petteri Kaski. <P/>\n\n    The att\
ribute <Ref Attr=\"AutomorphismGroup\" Label=\"for a digraph\"/> and\n    oper\
ation <Ref Oper=\"AutomorphismGroup\" \n      Label=\"for a digraph and a homo\
geneous list\"/> returns\n    the value of either <C>BlissAutomorphismGroup</C\
> or <Ref\n      Attr=\"NautyAutomorphismGroup\"/>. These groups are, of cours\
e, equal but\n    their generating sets may differ. <P/>\n    The attribute <R\
ef Attr=\"AutomorphismGroup\" \n      Label=\"for a digraph, homogeneous list,\
 and list\"/> returns the value of\n    <C>BlissAutomorphismGroup</C> as it is\
 not implemented for &nauty; The \n    requirements for the optional arguments\
 <A>vertex_colours</A> and \n    <A>edge_colours</A> are documented in <Ref At\
tr=\"AutomorphismGroup\" \n      Label=\"for a digraph, homogeneous list, and \
list\"/>.\n\n    See also <Ref Func=\"DigraphsUseBliss\"/>, and <Ref Func=\"Di\
graphsUseNauty\"/>.\n    <P/>\n\n    If the argument <A>digraph</A> is mutable\
, then the return value of\n    this attribute is recomputed every time it is \
called. \n\n    <Example><![CDATA[\ngap> G := BlissAutomorphismGroup(JohnsonDi\
graph(5, 2));;\ngap> IsSymmetricGroup(G);\ntrue\ngap> Size(G);\n120]]></Exampl\
e>\n    </Description>\n  </ManSection>\n\n    <ManSection>\n  <Attr Name=\"Na\
utyAutomorphismGroup\" Arg=\"digraph[, vert_colours]\"/>\n  <Returns>A permuta\
tion group.</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph, th\
en this attribute contains the group of\n    automorphisms of <A>digraph</A> a\
s calculated using &nauty; by\n    Brendan Mckay and Adolfo Piperno via &Nauty\
TracesInterface;.\n\n    <!-- FIXME be more explicit about what the second arg\
 is -->\n\n    The attribute <Ref Attr=\"AutomorphismGroup\" Label=\"for a dig\
raph\"/> and\n    operation <Ref Oper=\"AutomorphismGroup\" \n      Label=\"fo\
r a digraph and a homogeneous list\"/> returns\n    the value of either <C>Nau\
tyAutomorphismGroup</C> or  <Ref\n      Attr=\"BlissAutomorphismGroup\" Label=\
\"for a digraph\"/>.\n    These groups are, of course, equal but their generat\
ing sets may differ.<P/>\n\n    See also <Ref Func=\"DigraphsUseBliss\"/>, and\
 <Ref Func=\"DigraphsUseNauty\"/>.\n    <P/>\n\n    If the argument <A>digraph\
</A> is mutable, then the return value of\n    this attribute is recomputed ev\
ery time it is called. \n\n    <Log><![CDATA[\ngap> NautyAutomorphismGroup(Joh\
nsonDigraph(5, 2));\nGroup([ (3,4)(6,7)(8,9), (2,3)(5,6)(9,10), (2,5)(3,6)(4,7\
),\n (1,2)(6,8)(7,9) ])]]></Log>\n    </Description>\n  </ManSection>\n\n    <\
ManSection>\n  <Oper Name=\"AutomorphismGroup\" Label=\"for a digraph and a ho\
mogeneous list\"\n    Arg=\"digraph, vert_colours\"/>\n  <Returns>A permutatio\
n group.</Returns>\n  <Description>\n\n    This operation computes the automor\
phism group of a vertex-coloured digraph.\n    A vertex-coloured digraph can b\
e specified by its underlying digraph\n    <A>digraph</A> and its colouring <A\
>vert_colours</A>. Let <C>n</C> be the\n    number of vertices of <A>digraph</\
A>. The colouring <A>vert_colours</A> may\n    have one of the following two f\
orms:\n\n    <List>\n      <Item>\n        a list of <C>n</C> integers, where \
<A>vert_colours</A><C>[i]</C> is the\n        colour of vertex <C>i</C>, using\
 the colours <C>[1 .. m]</C> for some\n        <C>m &lt;= n</C>; or\n      </I\
tem>\n      <Item>\n        a list of non-empty disjoint lists whose union is\
\n        <C>DigraphVertices(<A>digraph</A>)</C>, such that\n        <A>vert_c\
olours</A><C>[i]</C> is the list of all vertices with colour\n        <C>i</C>\
.\n      </Item>\n    </List>\n\n    The <E>automorphism group</E> of a colour\
ed digraph <A>digraph</A> with\n    colouring <A>vert_colours</A> is the group\
 consisting of its automorphisms; an\n    <E>automorphism</E> of <A>digraph</A\
> is an isomorphism of coloured\n    digraphs from <A>digraph</A> to itself.  \
This group is equal to the\n    subgroup of <C>AutomorphismGroup(<A>digraph</A\
>)</C> consisting of those\n    automorphisms that preserve the colouring spec\
ified by <A>vert_colours</A>. See\n    <Ref Attr=\"AutomorphismGroup\" Label=\
\"for a digraph\" />, and see <Ref\n      Oper=\"IsomorphismDigraphs\" Label=\
\"for digraphs and homogeneous lists\" />\n    for more information about isom\
orphisms of coloured digraphs. <P/>\n\n    If <A>digraph</A> is not a multidig\
raph then the automorphism group is\n    returned as a group of permutations o\
n the set of vertices of\n    <A>digraph</A>. <P/>\n\n    If <A>digraph</A> is\
 a multidigraph then the automorphism group is returned\n    as the direct pro\
duct of a group of permutations on the set of vertices of\n    <A>digraph</A> \
with a group of permutations on the set of edges of\n    <A>digraph</A>. These\
 groups can be accessed using <Ref Oper=\"Projection\"\n      Label=\"for a do\
main and a positive integer\" BookName=\"ref\"/> on the\n    returned group.<P\
/>\n\n    By default, the automorphism group is found using &bliss; by Tommi J\
unttila\n    and Petteri Kaski. If &NautyTracesInterface; is available, then &\
nauty; by\n    Brendan Mckay and Adolfo Piperno can be used instead; see\n    \
<Ref Attr=\"BlissAutomorphismGroup\"\n      Label=\"for a digraph and homogeno\
us list\"/>,\n    <Ref Attr=\"NautyAutomorphismGroup\"/>, <Ref Func=\"Digraphs\
UseBliss\"/>,\n    and <Ref Func=\"DigraphsUseNauty\"/>.\n\n  <Example><![CDAT\
A[\ngap> cycle := CycleDigraph(9);\n<immutable cycle digraph with 9 vertices>\
\ngap> G := AutomorphismGroup(cycle);;\ngap> IsCyclic(G) and Size(G) = 9;\ntru\
e\ngap> colours := [[1, 4, 7], [2, 5, 8], [3, 6, 9]];;\ngap> H := Automorphism\
Group(cycle, colours);;\ngap> Size(H);\n3\ngap> H = AutomorphismGroup(cycle, [\
1, 2, 3, 1, 2, 3, 1, 2, 3]);\ntrue\ngap> H = SubgroupByProperty(G, p -> OnTupl\
esSets(colours, p) = colours);\ntrue\ngap> IsTrivial(AutomorphismGroup(cycle, \
[1, 1, 2, 2, 2, 2, 2, 2, 2]));\ntrue]]></Example>\n  </Description>\n</ManSect\
ion>\n\n    <ManSection>\n  <Oper Name=\"AutomorphismGroup\"\n    Label=\"for \
a digraph, homogeneous list, and list\"\n    Arg=\"digraph, vert_colours, edge\
_colours\"/>\n  <Returns>A permutation group.</Returns>\n  <Description>\n\n  \
  This operation computes the automorphism group of a vertex- and/or\n    edge\
-coloured digraph.\n    A coloured digraph can be specified by its underlying \
digraph\n    <A>digraph</A> and colourings <A>vert_colours</A>, <A>edge_colour\
s</A>.\n    Let <C>n</C> be the number of vertices of <A>digraph</A>. The colo\
urings\n    must have the following forms:\n\n    <List>\n      <Item>\n      \
  <A>vert_colours</A> must be <K>fail</K> or a list of <C>n</C> integers,\n   \
     where <A>vert_colours</A><C>[i]</C> is the colour of vertex <C>i</C>,\n  \
      using the colours <C>[1 .. m]</C> for some <C>m &lt;= n</C>;\n      </It\
em>\n      <Item>\n        <A>edge_colours</A> must be <K>fail</K> or a list o\
f <C>n</C> lists of\n        integers of the same shape as <C>OutNeighbours(di\
graph)</C>, where\n        <A>edge_colours</A><C>[i][j]</C> is the colour of t\
he edge\n        <C>OutNeighbours(digraph)[i][j]</C>, using the colours <C>[1 \
.. k]</C>\n        for some <C>k &lt;= n</C>;\n      </Item>\n    </List>\n\n \
   Giving <A>vert_colours</A> [<A>edge_colours</A>] as <C>fail</C> is\n    equ\
ivalent to setting all vertices [edges] to be the same colour. <P/>\n\n    Unl\
ike <Ref Attr=\"AutomorphismGroup\" Label=\"for a digraph\"/>, it is\n    poss\
ible to obtain the automorphism group of an edge-coloured multidigraph\n    (s\
ee <Ref Prop=\"IsMultiDigraph\" />) when no two edges share the same\n    sour\
ce, range, and colour.\n\n    The <E>automorphism group</E> of a vertex/edge-c\
oloured digraph\n    <A>digraph</A> with colouring <A>c</A> is the group consi\
sting of its\n    vertex/edge-colour preserving automorphisms; an\n    <E>auto\
morphism</E> of <A>digraph</A> is an isomorphism of vertex/edge-coloured\n    \
digraphs from <A>digraph</A> to itself.  This group is equal to the\n    subgr\
oup of <C>AutomorphismGroup(<A>digraph</A>)</C> consisting of those\n    autom\
orphisms that preserve the colouring specified by <A>colours</A>. See\n    <Re\
f Attr=\"AutomorphismGroup\" Label=\"for a digraph\" />, and see <Ref\n      O\
per=\"IsomorphismDigraphs\" Label=\"for digraphs and homogeneous lists\" />\n \
   for more information about isomorphisms of coloured digraphs. <P/>\n\n    I\
f <A>digraph</A> is not a multidigraph then the automorphism group is\n    ret\
urned as a group of permutations on the set of vertices of\n    <A>digraph</A>\
. <P/>\n\n    If <A>digraph</A> is a multidigraph then the automorphism group \
is returned\n    as the direct product of a group of permutations on the set o\
f vertices of\n    <A>digraph</A> with a group of permutations on the set of e\
dges of\n    <A>digraph</A>. These groups can be accessed using <Ref Oper=\"Pr\
ojection\"\n      Label=\"for a domain and a positive integer\" BookName=\"ref\
\"/> on the\n    returned group.<P/>\n\n    By default, the automorphism group\
 is found using &bliss; by Tommi Junttila\n    and Petteri Kaski. If &NautyTra\
cesInterface; is available, then &nauty; by\n    Brendan Mckay and Adolfo Pipe\
rno can be used instead; see\n     <Ref Attr=\"BlissAutomorphismGroup\"\n     \
  Label=\"for a digraph, homogenous list, and list\"/>,\n     <Ref Attr=\"Naut\
yAutomorphismGroup\"/>, <Ref Func=\"DigraphsUseBliss\"/>, and\n     <Ref Func=\
\"DigraphsUseNauty\"/>.\n\n  <Example><![CDATA[\ngap> cycle := CycleDigraph(12\
);\n<immutable cycle digraph with 12 vertices>\ngap> vert_colours := List([1 .\
. 12], x -> x mod 3 + 1);;\ngap> edge_colours := List([1 .. 12], x -> [x mod 2\
 + 1]);;\ngap> Size(AutomorphismGroup(cycle));\n12\ngap> Size(AutomorphismGrou\
p(cycle, vert_colours));\n4\ngap> Size(AutomorphismGroup(cycle, fail, edge_col\
ours));\n6\ngap> Size(AutomorphismGroup(cycle, vert_colours, edge_colours));\n\
2\ngap> IsTrivial(AutomorphismGroup(cycle,\n> vert_colours, List([1 .. 12], x \
-> [x mod 4 + 1])));\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\n\
    <ManSection>\n  <Attr Name=\"BlissCanonicalLabelling\" Label=\"for a digra\
ph\" Arg=\"digraph\"/>\n  <Attr Name=\"NautyCanonicalLabelling\" Label=\"for a\
 digraph\" Arg=\"digraph\"/>\n  <Returns>A permutation, or a list of two permu\
tations.</Returns>\n  <Description>\n    A function <M>\\rho</M> that maps a d\
igraph to a digraph is a <E>canonical\n      representative map</E> if the fol\
lowing two conditions hold for all\n    digraphs <M>G</M> and <M>H</M>: <P/>\n\
\n    <List>\n      <Item>\n        <M>\\rho(G)</M> and <M>G</M> are isomorphi\
c as digraphs; and\n      </Item>\n      <Item>\n        <M>\\rho(G)=\\rho(H)<\
/M> if and only if <M>G</M> and <M>H</M> are\n        isomorphic as digraphs.\
\n      </Item>\n    </List>\n\n    A <E>canonical labelling</E> of a digraph \
<M>G</M> (under <M>\\rho</M>) is an\n    isomorphism of <M>G</M> onto its <E>c\
anonical representative</E>,\n    <M>\\rho(G)</M>.  See <Ref Oper=\"Isomorphis\
mDigraphs\" Label=\"for digraphs\" />\n    for more information about isomorph\
isms of digraphs. <P/>\n\n    <C>BlissCanonicalLabelling</C> returns a canonic\
al labelling of the digraph\n    <A>digraph</A> found using &bliss; by Tommi J\
unttila and Petteri Kaski.\n    <C>NautyCanonicalLabelling</C> returns a canon\
ical labelling of the digraph\n    <A>digraph</A> found using &nauty; by Brend\
an McKay and Adolfo Piperno.\n    Note that the canonical labellings returned \
by &bliss; and &nauty; are not\n    usually the same (and may depend of the ve\
rsion used).<P/>\n\n    <C>BlissCanonicalLabelling</C> can only be computed if\
 <A>digraph</A> has\n    no multiple edges; see <Ref Prop=\"IsMultiDigraph\" /\
>. <P/>\n\n    <Example><![CDATA[\ngap> digraph1 := DigraphFromDiSparse6String\
(\".ImNS_AiB?qRN\");\n<immutable digraph with 10 vertices, 8 edges>\ngap> Blis\
sCanonicalLabelling(digraph1);\n(1,9,5,7)(3,6,4,10)\ngap> p := (1, 2, 7, 5)(3,\
 9)(6, 10, 8);;\ngap> digraph2 := OnDigraphs(digraph1, p);\n<immutable digraph\
 with 10 vertices, 8 edges>\ngap> digraph1 = digraph2;\nfalse\ngap> OnDigraphs\
(digraph1, BlissCanonicalLabelling(digraph1)) =\n>    OnDigraphs(digraph2, Bli\
ssCanonicalLabelling(digraph2));\ntrue]]></Example>\n  </Description>\n</ManSe\
ction>\n\n    <ManSection>\n  <Oper Name=\"BlissCanonicalLabelling\" Label=\"f\
or a digraph and a list\"\n    Arg=\"digraph, colours\"/>\n  <Oper Name=\"Naut\
yCanonicalLabelling\" Label=\"for a digraph and a list\"\n    Arg=\"digraph, c\
olours\"/>\n  <Returns>A permutation.</Returns>\n  <Description>\n    A functi\
on <M>\\rho</M> that maps a coloured digraph to a coloured digraph is\n    a <\
E>canonical representative map</E> if the following two conditions hold\n    f\
or all coloured digraphs <M>G</M> and <M>H</M>:\n\n    <List>\n      <Item>\n \
       <M>\\rho(G)</M> and <M>G</M> are isomorphic as coloured digraphs; and\n\
      </Item>\n      <Item>\n        <M>\\rho(G)=\\rho(H)</M> if and only if <\
M>G</M> and <M>H</M> are\n        isomorphic as coloured digraphs.\n      </It\
em>\n    </List>\n\n    A <E>canonical labelling</E> of a coloured digraph <M>\
G</M> (under\n    <M>\\rho</M>) is an isomorphism of <M>G</M> onto its <E>cano\
nical\n      representative</E>, <M>\\rho(G)</M>.  See <Ref Oper=\"Isomorphism\
Digraphs\"\n      Label=\"for digraphs and homogeneous lists\" /> for more inf\
ormation about\n    isomorphisms of coloured digraphs. <P/>\n\n    A coloured \
digraph can be specified by its underlying digraph <A>digraph</A>\n    and its\
 colouring <A>colours</A>.  Let <C>n</C> be the number of vertices of\n    <A>\
digraph</A>. The colouring <A>colours</A> may have one of the following\n    t\
wo forms: <P/>\n\n    <List>\n      <Item>\n        a list of <C>n</C> integer\
s, where <A>colours</A><C>[i]</C> is the\n        colour of vertex <C>i</C>, u\
sing the colours <C>[1 .. m]</C> for some\n        <C>m &lt;= n</C>; or\n     \
 </Item>\n      <Item>\n        a list of non-empty disjoint lists whose union\
 is\n        <C>DigraphVertices(<A>digraph</A>)</C>, such that\n        <A>col\
ours</A><C>[i]</C> is the list of all vertices with colour\n        <C>i</C>.\
\n      </Item>\n    </List>\n\n    If <A>digraph</A> and <A>colours</A> toget\
her form a coloured digraph,\n    <C>BlissCanonicalLabelling</C> returns a can\
onical labelling of the digraph\n    <A>digraph</A> found using &bliss; by Tom\
mi Junttila and Petteri Kaski.\n    Similarly, <C>NautyCanonicalLabelling</C> \
returns a canonical labelling of\n    the digraph <A>digraph</A> found using &\
nauty; by Brendan McKay and Adolfo\n    Piperno.  Note that the canonical labe\
llings returned by &bliss; and\n    &nauty; are not usually the same (and may \
depend of the version used).<P/>\n\n    <C>BlissCanonicalLabelling</C> can onl\
y be computed if <A>digraph</A> has\n    no multiple edges; see <Ref Prop=\"Is\
MultiDigraph\" />. The canonical\n    labelling of <A>digraph</A> is given as \
a permutation of its vertices.\n    The canonical representative of <A>digraph\
</A> can be created from\n    <A>digraph</A> and its canonical labelling <C>p<\
/C> by using the\n    operation <Ref Oper=\"OnDigraphs\" Label=\"for a digraph\
 and a perm\" />:\n    <Log>gap> OnDigraphs(digraph, p);</Log>\n\n    The colo\
uring of the canonical representative can easily be\n    constructed. A vertex\
 <C>v</C> (in <A>digraph</A>) has colour <C>i</C> if\n    and only if the vert\
ex <C>v ^ p</C> (in the canonical representative) has\n    colour <C>i</C>, wh\
ere <C>p</C> is the permutation of the canonical\n    labelling that acts on t\
he vertices of <A>digraph</A>. In particular, if\n    <A>colours</A> has the f\
irst form that is described above, then the\n    colouring of the canonical re\
presentative is given by:\n\n    <Log>gap> List(DigraphVertices(digraph), i ->\
 colours[i / p]);</Log>\n\n    On the other hand, if <A>colours</A> has the se\
cond form above, then the\n    canonical representative has colouring:\n\n    \
<Log>gap> OnTuplesSets(colours, p);</Log>\n\n    <P/>\n\n    <Example><![CDATA\
[\ngap> digraph := DigraphFromDiSparse6String(\".ImNS_AiB?qRN\");\n<immutable \
digraph with 10 vertices, 8 edges>\ngap> colours := [[1, 2, 8, 9, 10], [3, 4, \
5, 6, 7]];;\ngap> p := BlissCanonicalLabelling(digraph, colours);\n(1,5,8,4,10\
,3,9)(6,7)\ngap> OnDigraphs(digraph, p);\n<immutable digraph with 10 vertices,\
 8 edges>\ngap> OnTuplesSets(colours, p);\n[ [ 1, 2, 3, 4, 5 ], [ 6, 7, 8, 9, \
10 ] ]\ngap> colours := [1, 1, 1, 1, 2, 3, 1, 3, 2, 1];;\ngap> p := BlissCanon\
icalLabelling(digraph, colours);\n(1,6,9,7)(3,4,5,8,10)\ngap> OnDigraphs(digra\
ph, p);\n<immutable digraph with 10 vertices, 8 edges>\ngap> List(DigraphVerti\
ces(digraph), i -> colours[i / p]);\n[ 1, 1, 1, 1, 1, 1, 2, 2, 3, 3 ]]]></Exam\
ple>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"Blis\
sCanonicalDigraph\" Arg=\"digraph\"/>\n  <Attr Name=\"NautyCanonicalDigraph\" \
Arg=\"digraph\"/>\n  <Returns>A digraph.</Returns>\n  <Description>\n    The a\
ttribute <C>BlissCanonicalLabelling</C> returns the canonical\n    representat\
ive found by applying <Ref Attr=\"BlissCanonicalLabelling\"\n      Label=\"for\
 a digraph\"/>. The digraph returned is canonical in the sense\n    that\n\n  \
  <List>\n      <Item>\n        <C>BlissCanonicalDigraph(<A>digraph</A>)</C> a\
nd <A>digraph</A> are\n        isomorphic as digraphs; and\n      </Item>\n   \
   <Item>\n        If <C>gr</C> is any digraph then <C>BlissCanonicalDigraph(g\
r)</C>\n        and <C>BlissCanonicalDigraph(<A>digraph</A>)</C> are equal if \
and only\n        if <C>gr</C> and <A>digraph</A> are isomorphic as digraphs.\
\n      </Item>\n    </List>\n\n    Analogously, the attribute <C>NautyCanonic\
alLabelling</C> returns the\n    canonical representative found by applying <R\
ef\n      Attr=\"NautyCanonicalLabelling\" Label=\"for a digraph\"/>.\n    <P/\
>\n\n    If the argument <A>digraph</A> is mutable, then the return value of\n\
    this attribute is recomputed every time it is called. \n\n    <Example><![\
CDATA[\ngap> digraph := Digraph([[1], [2, 3], [3], [1, 2, 3]]);\n<immutable di\
graph with 4 vertices, 7 edges>\ngap> canon := BlissCanonicalDigraph(digraph);\
\n<immutable digraph with 4 vertices, 7 edges>\ngap> OutNeighbours(canon);\n[ \
[ 1 ], [ 2 ], [ 3, 2 ], [ 1, 3, 2 ] ]\n]]></Example>\n  </Description>\n</ManS\
ection>\n\n    <ManSection>\n  <Attr Name=\"DigraphGroup\" Arg=\"digraph\"/>\n\
  <Returns>A permutation group.</Returns>\n  <Description>\n    If <A>digraph<\
/A> is immutable and was created knowing a subgroup of\n    its automorphism g\
roup, then this group is stored in the attribute\n    <C>DigraphGroup</C>. If \
<A>digraph</A> is mutable, or was not created\n    knowing a subgroup of its a\
utomorphism group, then <C>DigraphGroup</C>\n    returns the entire automorphi\
sm group of <A>digraph</A>.    \n    Note that if <A>digraph</A> is mutable, t\
hen the automorphism group is\n    recomputed every time this function is call\
ed.\n    <P/>\n\n    Note that certain other constructor operations such as  <\
Ref\n      Oper=\"CayleyDigraph\"/>, <Ref Oper=\"BipartiteDoubleDigraph\"/>, a\
nd <Ref\n      Oper=\"DoubleDigraph\"/>, may not require a group as one of the\
 arguments,\n    but use the standard constructor method using a group, and he\
nce set the\n    <C>DigraphGroup</C> attribute for the resulting digraph.\n\n \
   <Example><![CDATA[\ngap> n := 4;;\ngap> adj := function(x, y)\n>      retur\
n (((x - y) mod n) = 1) or (((x - y) mod n) = n - 1);\n>    end;;\ngap> group \
:= CyclicGroup(IsPermGroup, n);\nGroup([ (1,2,3,4) ])\ngap> D := Digraph(IsMut\
ableDigraph, group, [1 .. n], \\^, adj);\n<mutable digraph with 4 vertices, 8 \
edges>\ngap> HasDigraphGroup(D);\nfalse\ngap> DigraphGroup(D);\nGroup([ (2,4),\
 (1,2)(3,4) ])\ngap> AutomorphismGroup(D);\nGroup([ (2,4), (1,2)(3,4) ])\ngap>\
 D := Digraph(group, [1 .. n], \\^, adj);\n<immutable digraph with 4 vertices,\
 8 edges>\ngap> HasDigraphGroup(D);\ntrue\ngap> DigraphGroup(D);\nGroup([ (1,2\
,3,4) ])\ngap> D := DoubleDigraph(D);\n<immutable digraph with 8 vertices, 32 \
edges>\ngap> HasDigraphGroup(D);\ntrue\ngap> DigraphGroup(D);\nGroup([ (1,2,3,\
4)(5,6,7,8), (1,5)(2,6)(3,7)(4,8) ])\ngap> AutomorphismGroup(D) =\n> Group([(6\
, 8), (5, 7), (4, 6), (3, 5), (2, 4),\n>        (1, 2)(3, 4)(5, 6)(7, 8)]);\nt\
rue\ngap> D := Digraph([[2, 3], [], []]);\n<immutable digraph with 3 vertices,\
 2 edges>\ngap> HasDigraphGroup(D);\nfalse\ngap> HasAutomorphismGroup(D);\nfal\
se\ngap> DigraphGroup(D);\nGroup([ (2,3) ])\ngap> HasAutomorphismGroup(D);\ntr\
ue\ngap> group := DihedralGroup(8);\n<pc group of size 8 with 3 generators>\ng\
ap> D := CayleyDigraph(group);\n<immutable digraph with 8 vertices, 24 edges>\
\ngap> HasDigraphGroup(D);\ntrue\ngap> GeneratorsOfGroup(DigraphGroup(D));\n[ \
(1,2)(3,5)(4,6)(7,8), (1,7,4,3)(2,5,6,8), (1,4)(2,6)(3,7)(5,8) ]]]></Example>\
\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphO\
rbits\" Arg=\"digraph\"/>\n  <Returns>\n    An immutable list of lists of inte\
gers.\n  </Returns>\n  <Description>\n    <C>DigraphOrbits</C> returns the orb\
its of the action of the\n    <Ref Attr=\"DigraphGroup\"/> on the set of verti\
ces of <A>digraph</A>.\n\n    <Example><![CDATA[\ngap> G := Group([(2, 3)(7, 8\
, 9), (1, 2, 3)(4, 5, 6)(8, 9)]);;\ngap> D := EdgeOrbitsDigraph(G, [1, 2]);\n<\
immutable digraph with 9 vertices, 6 edges>\ngap> DigraphOrbits(D);\n[ [ 1, 2,\
 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]\ngap> D := DigraphMutableCopy(D);\n<mutable d\
igraph with 9 vertices, 6 edges>\ngap> DigraphOrbits(D);\n[ [ 1, 2, 3 ], [ 4, \
5, 6, 7, 8, 9 ] ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManS\
ection>\n  <Attr Name=\"DigraphOrbitReps\" Arg=\"digraph\"/>\n  <Returns>\n   \
 An immutable list of integers.\n  </Returns>\n  <Description>\n    <C>Digraph\
OrbitReps</C> returns a list of orbit representatives\n    of the action of th\
e <Ref Attr=\"DigraphGroup\"/> on the set of vertices of\n    <A>digraph</A>.\
\n\n    <Example><![CDATA[\ngap> D := CayleyDigraph(AlternatingGroup(4));\n<im\
mutable digraph with 12 vertices, 24 edges>\ngap> DigraphOrbitReps(D);\n[ 1 ]\
\ngap> D := DigraphMutableCopy(D);\n<mutable digraph with 12 vertices, 24 edge\
s>\ngap> DigraphOrbitReps(D);\n[ 1 ]\ngap> D := DigraphFromDigraph6String(\"&I\
GO??S?`?_@?a?CK?O\");\n<immutable digraph with 10 vertices, 14 edges>\ngap> Di\
graphOrbitReps(D);\n[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]\ngap> DigraphOrbitReps(D\
igraphMutableCopy(D));\n[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ]\n]]></Example>\n  </\
Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"DigraphSchreie\
rVector\" Arg=\"digraph\"/>\n  <Returns>\n    An immutable list of integers.\n\
  </Returns>\n  <Description>\n    <C>DigraphSchreierVector</C> returns the so\
-called <E>Schreier vector</E>\n    of the action of the <Ref Attr=\"DigraphGr\
oup\"/> on the set of vertices of\n    <A>digraph</A>. The Schreier vector is \
a list <C>sch</C> of integers with\n    length <C>DigraphNrVertices(<A>digraph\
</A>)</C> where:\n    <List>\n      <Mark><C>sch[i] &lt; 0:</C></Mark>\n      \
<Item>\n        implies that <C>i</C> is an orbit representative and\n        \
<C>DigraphOrbitReps(<A>digraph</A>)[-sch[i]] = i</C>.\n      </Item>\n\n      \
<Mark><C>sch[i] &gt; 0:</C></Mark>\n      <Item>\n        implies that <C>i / \
gens[sch[i]]</C>\n        is one step closer to the root (or representative) o\
f the tree, where\n        <C>gens</C> is the generators of <C>DigraphGroup(<A\
>digraph</A>)</C>.\n      </Item>\n    </List>\n\n    <Example><![CDATA[\ngap>\
 n := 4;;\ngap> adj := function(x, y)\n>      return (((x - y) mod n) = 1) or \
(((x - y) mod n) = n - 1);\n>    end;;\ngap> group := CyclicGroup(IsPermGroup,\
 n);\nGroup([ (1,2,3,4) ])\ngap> D := Digraph(IsMutableDigraph, group, [1 .. n\
], \\^, adj);\n<mutable digraph with 4 vertices, 8 edges>\ngap> sch := Digraph\
SchreierVector(D);\n[ -1, 2, 2, 1 ]\ngap> D := CayleyDigraph(AlternatingGroup(\
4));\n<immutable digraph with 12 vertices, 24 edges>\ngap> sch := DigraphSchre\
ierVector(D);\n[ -1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1 ]\ngap> DigraphOrbitReps(\
D);\n[ 1 ]\ngap> gens := GeneratorsOfGroup(DigraphGroup(D));\n[ (1,7,5)(2,10,9\
)(3,4,11)(6,8,12), (1,3,2)(4,5,6)(7,9,8)(10,11,12) ]\ngap> 10 / gens[sch[10]];\
\n2\ngap> 7 / gens[sch[7]];\n1\ngap> 5 / gens[sch[5]];\n7]]></Example>\n  </De\
scription>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphStabilize\
r\" Arg=\"digraph, v\"/>\n  <Returns>\n    A permutation group.\n  </Returns>\
\n  <Description>\n    <C>DigraphStabilizer</C> returns the stabilizer of the \
vertex <A>v</A>\n    under of the action of the <Ref Attr=\"DigraphGroup\"/> o\
n the set of\n    vertices of <A>digraph</A>.\n\n    <Example><![CDATA[\ngap> \
D := DigraphFromDigraph6String(\"&GYHPQgWTIIPW\");\n<immutable digraph with 8 \
vertices, 24 edges>\ngap> DigraphStabilizer(D, 8);\nGroup(())\ngap> DigraphSta\
bilizer(D, 2);\nGroup(())\ngap> D := DigraphMutableCopy(D);\n<mutable digraph \
with 8 vertices, 24 edges>\ngap> DigraphStabilizer(D, 8);\nGroup(())\ngap> Dig\
raphStabilizer(D, 2);\nGroup(())\n]]></Example>\n  </Description>\n</ManSectio\
n>\n\n    <ManSection>\n  <Oper Name=\"IsIsomorphicDigraph\" Label=\"for digra\
phs\" Arg=\"digraph1, digraph2\"/>\n  <Returns><K>true</K> or <K>false</K>.</R\
eturns>\n  <Description>\n    This operation returns <K>true</K> if there exis\
ts an isomorphism from the\n    digraph <A>digraph1</A> to the digraph <A>digr\
aph2</A>.  See <Ref\n      Oper=\"IsomorphismDigraphs\" Label=\"for digraphs\"\
 /> for more information\n    about isomorphisms of digraphs. <P/>\n\n    By d\
efault, an isomorphism is found using the canonical labellings of the\n    dig\
raphs obtained from &bliss; by Tommi Junttila\n    and Petteri Kaski. If &Naut\
yTracesInterface; is available, then &nauty; by\n    Brendan Mckay and Adolfo \
Piperno can be used instead; see\n    <Ref Func=\"DigraphsUseBliss\"/>, and <R\
ef Func=\"DigraphsUseNauty\"/>.\n\n    <Example><![CDATA[\ngap> digraph1 := Cy\
cleDigraph(4);\n<immutable cycle digraph with 4 vertices>\ngap> digraph2 := Cy\
cleDigraph(5);\n<immutable cycle digraph with 5 vertices>\ngap> IsIsomorphicDi\
graph(digraph1, digraph2);\nfalse\ngap> digraph2 := DigraphReverse(digraph1);\
\n<immutable digraph with 4 vertices, 4 edges>\ngap> IsIsomorphicDigraph(digra\
ph1, digraph2);\ntrue\ngap> digraph1 := Digraph([[3], [], []]);\n<immutable di\
graph with 3 vertices, 1 edge>\ngap> digraph2 := Digraph([[], [], [2]]);\n<imm\
utable digraph with 3 vertices, 1 edge>\ngap> IsIsomorphicDigraph(digraph1, di\
graph2);\ntrue]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSectio\
n>\n  <Oper Name=\"IsIsomorphicDigraph\" Label=\"for digraphs and homogeneous \
lists\"\n    Arg=\"digraph1, digraph2, colours1, colours2\"/>\n  <Returns><K>t\
rue</K> or <K>false</K>.</Returns>\n  <Description>\n    This operation tests \
for isomorphism of coloured digraphs.  A coloured\n    digraph can be specifie\
d by its underlying digraph <A>digraph1</A> and its\n    colouring <A>colours1\
</A>.  Let <C>n</C> be the number of vertices of\n    <A>digraph1</A>. The col\
ouring <A>colours1</A> may have one of the following\n    two forms:\n\n    <L\
ist>\n      <Item>\n        a list of <C>n</C> integers, where <A>colours</A><\
C>[i]</C> is the\n        colour of vertex <C>i</C>, using the colours <C>[1 .\
. m]</C> for some\n        <C>m &lt;= n</C>; or\n      </Item>\n      <Item>\n\
        a list of non-empty disjoint lists whose union is\n        <C>DigraphV\
ertices(<A>digraph</A>)</C>, such that\n        <A>colours</A><C>[i]</C> is th\
e list of all vertices with colour\n        <C>i</C>.\n      </Item>\n    </Li\
st>\n\n    If <A>digraph1</A> and <A>digraph2</A> are digraphs without multipl\
e edges,\n    and <A>colours1</A> and <A>colours2</A> are colourings of <A>dig\
raph1</A>\n    and <A>digraph2</A>, respectively, then this operation returns \
<K>true</K>\n    if there exists an isomorphism between these two coloured dig\
raphs.  See\n    <Ref Oper=\"IsomorphismDigraphs\" Label=\"for digraphs and ho\
mogeneous lists\"\n      /> for more information about isomorphisms of coloure\
d digraphs. <P/>\n\n    By default, an isomorphism is found using the canonica\
l labellings of the\n    digraphs obtained from &bliss; by Tommi Junttila\n   \
 and Petteri Kaski. If &NautyTracesInterface; is available, then &nauty; by\n \
   Brendan Mckay and Adolfo Piperno can be used instead; see\n    <Ref Func=\"\
DigraphsUseBliss\"/>, and <Ref Func=\"DigraphsUseNauty\"/>.\n\n    <Example><!\
[CDATA[\ngap> digraph1 := ChainDigraph(4);\n<immutable chain digraph with 4 ve\
rtices>\ngap> digraph2 := ChainDigraph(3);\n<immutable chain digraph with 3 ve\
rtices>\ngap> IsIsomorphicDigraph(digraph1, digraph2,\n>  [[1, 4], [2, 3]], [[\
1, 2], [3]]);\nfalse\ngap> digraph2 := DigraphReverse(digraph1);\n<immutable d\
igraph with 4 vertices, 3 edges>\ngap> IsIsomorphicDigraph(digraph1, digraph2,\
\n>  [1, 1, 1, 1], [1, 1, 1, 1]);\ntrue\ngap> IsIsomorphicDigraph(digraph1, di\
graph2,\n>  [1, 2, 2, 1], [1, 2, 2, 1]);\ntrue\ngap> IsIsomorphicDigraph(digra\
ph1, digraph2,\n>  [1, 1, 2, 2], [1, 1, 2, 2]);\nfalse]]></Example>\n  </Descr\
iption>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"IsomorphismDigraphs\
\" Label=\"for digraphs\" Arg=\"digraph1, digraph2\"/>\n  <Returns> A permutat\
ion, or a pair of permutations, or <K>fail</K>.</Returns>\n  <Description>\n  \
  This operation returns an isomorphism between the digraphs <A>digraph1</A>\n\
    and <A>digraph2</A> if one exists, else this operation returns <K>fail</K>\
.\n    <P/>\n\n    An <E>isomorphism</E> from a digraph <A>digraph1</A> to a d\
igraph\n    <A>digraph2</A> is a bijection <C>p</C> from the vertices of\n    \
<A>digraph1</A> to the vertices of <A>digraph2</A> with the following\n    pro\
perty: for all vertices <C>i</C> and <C>j</C> of <A>digraph1</A>,\n    <C>[i, \
j]</C> is an edge of <A>digraph1</A> if and only if <C>[i ^ p, j\n      ^ p]</\
C> is an edge of <A>digraph2</A>. <P/>\n\n    If there exists such an isomorph\
ism, then this operation returns one.\n    The form of this isomorphism is a p\
ermutation <C>p</C> of the vertices of\n    <A>digraph1</A> such that <P/>\n\n\
    <C>OnDigraphs(<A>digraph1</A>, p) = digraph2</C>.\n\n    By default, an is\
omorphism is found using the canonical labellings of the\n    digraphs obtaine\
d from &bliss; by Tommi Junttila\n    and Petteri Kaski. If &NautyTracesInterf\
ace; is available, then &nauty; by\n    Brendan Mckay and Adolfo Piperno can b\
e used instead; see\n    <Ref Func=\"DigraphsUseBliss\"/>, and <Ref Func=\"Dig\
raphsUseNauty\"/>.\n\n    <Example><![CDATA[\ngap> digraph1 := CycleDigraph(4)\
;\n<immutable cycle digraph with 4 vertices>\ngap> digraph2 := CycleDigraph(5)\
;\n<immutable cycle digraph with 5 vertices>\ngap> IsomorphismDigraphs(digraph\
1, digraph2);\nfail\ngap> digraph1 := CompleteBipartiteDigraph(10, 5);\n<immut\
able complete bipartite digraph with bicomponent sizes 10 and 5>\ngap> digraph\
2 := CompleteBipartiteDigraph(5, 10);\n<immutable complete bipartite digraph w\
ith bicomponent sizes 5 and 10>\ngap> p := IsomorphismDigraphs(digraph1, digra\
ph2);\n(1,6,11)(2,7,12)(3,8,13)(4,9,14)(5,10,15)\ngap> OnDigraphs(digraph1, p)\
 = digraph2;\ntrue\n]]></Example>\n  </Description>\n</ManSection>\n\n    <Man\
Section>\n  <Oper Name=\"IsomorphismDigraphs\" Label=\"for digraphs and homoge\
neous lists\"\n    Arg=\"digraph1, digraph2, colours1, colours2\"/>\n  <Return\
s> A permutation, or <K>fail</K>.</Returns>\n  <Description>\n    This operati\
on searches for an isomorphism between coloured digraphs.  A\n    coloured dig\
raph can be specified by its underlying digraph <A>digraph1</A>\n    and its c\
olouring <A>colours1</A>.  Let <C>n</C> be the number of vertices\n    of <A>d\
igraph1</A>. The colouring <A>colours1</A> may have one of the\n    following \
two forms:\n\n    <List>\n      <Item>\n        a list of <C>n</C> integers, w\
here <A>colours</A><C>[i]</C> is the\n        colour of vertex <C>i</C>, using\
 the colours <C>[1 .. m]</C> for some\n        <C>m &lt;= n</C>; or\n      </I\
tem>\n      <Item>\n        a list of non-empty disjoint lists whose union is\
\n        <C>DigraphVertices(<A>digraph</A>)</C>, such that\n        <A>colour\
s</A><C>[i]</C> is the list of all vertices with colour\n        <C>i</C>.\n  \
    </Item>\n    </List>\n\n    An <E>isomorphism</E> between coloured digraph\
s is an isomorphism between\n    the underlying digraphs that preserves the co\
lourings.  See <Ref\n      Oper=\"IsomorphismDigraphs\" Label=\"for digraphs\"\
/> for more information\n    about isomorphisms of digraphs. More precisely, l\
et <C>f</C> be an\n    isomorphism of digraphs from the digraph <A>digraph1</A\
> (with colouring\n    <A>colours1</A>) to the digraph <A>digraph2</A> (with c\
olouring\n    <A>colours2</A>), and let <C>p</C> be the permutation of the ver\
tices of\n    <A>digraph1</A> that corresponds to <C>f</C>.  Then <C>f</C> pre\
serves the\n    colourings of <A>digraph1</A> and <A>digraph2</A> – and henc\
e is an\n    isomorphism of coloured digraphs – if <C><A>colours1</A>[i] =\n\
      <A>colours2</A>[i ^ p]</C> for all vertices <C>i</C> in <A>digraph1</A>.\
\n    <P/>\n\n    This operation returns such an isomorphism if one exists, el\
se it returns\n    <K>fail</K>. <P/>\n\n    By default, an isomorphism is foun\
d using the canonical labellings of the\n    digraphs obtained from &bliss; by\
 Tommi Junttila\n    and Petteri Kaski. If &NautyTracesInterface; is available\
, then &nauty; by\n    Brendan Mckay and Adolfo Piperno can be used instead; s\
ee\n    <Ref Func=\"DigraphsUseBliss\"/>, and <Ref Func=\"DigraphsUseNauty\"/>\
.\n\n    <Example><![CDATA[\ngap> digraph1 := ChainDigraph(4);\n<immutable cha\
in digraph with 4 vertices>\ngap> digraph2 := ChainDigraph(3);\n<immutable cha\
in digraph with 3 vertices>\ngap> IsomorphismDigraphs(digraph1, digraph2,\n>  \
[[1, 4], [2, 3]], [[1, 2], [3]]);\nfail\ngap> digraph2 := DigraphReverse(digra\
ph1);\n<immutable digraph with 4 vertices, 3 edges>\ngap> colours1 := [1, 1, 1\
, 1];;\ngap> colours2 := [1, 1, 1, 1];;\ngap> p := IsomorphismDigraphs(digraph\
1, digraph2, colours1, colours2);\n(1,4)(2,3)\ngap> OnDigraphs(digraph1, p) = \
digraph2;\ntrue\ngap> List(DigraphVertices(digraph1), i -> colours1[i ^ p]) = \
colours2;\ntrue\ngap> colours1 := [1, 1, 2, 2];;\ngap> colours2 := [2, 2, 1, 1\
];;\ngap> p := IsomorphismDigraphs(digraph1, digraph2, colours1, colours2);\n(\
1,4)(2,3)\ngap> OnDigraphs(digraph1, p) = digraph2;\ntrue\ngap> List(DigraphVe\
rtices(digraph1), i -> colours1[i ^ p]) = colours2;\ntrue\ngap> IsomorphismDig\
raphs(digraph1, digraph2,\n>  [1, 1, 2, 2], [1, 1, 2, 2]);\nfail]]></Example>\
\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"Represen\
tativeOutNeighbours\" Arg=\"digraph\"/>\n  <Returns>An immutable list of lists\
.</Returns>\n  <Description>\n    This function returns the list <C>out</C> of\
 <E>out-neighbours</E> of each\n    representative of the orbits of the action\
 of <Ref Attr=\"DigraphGroup\"/> on\n    the vertex set of the digraph <A>digr\
aph</A>. <P/>\n\n    More specifically, if <C>reps</C> is the list of orbit re\
presentatives,\n    then a vertex <C>j</C> appears in <C>out[i]</C> each time\
\n    there exists an edge with source <C>reps[i]</C> and range <C>j</C> in\n \
   <A>digraph</A>.\n    <P/>\n\n    If <Ref Attr=\"DigraphGroup\"/> is trivial\
, then <Ref Attr=\"OutNeighbours\"/>\n    is returned.\n\n    <Example><![CDAT\
A[\ngap> D := Digraph([\n>  [2, 1, 3, 4, 5], [3, 5], [2], [1, 2, 3, 5], [1, 2,\
 3, 4]]);\n<immutable digraph with 5 vertices, 16 edges>\ngap> DigraphGroup(D)\
;\nGroup(())\ngap> RepresentativeOutNeighbours(D);\n[ [ 2, 1, 3, 4, 5 ], [ 3, \
5 ], [ 2 ], [ 1, 2, 3, 5 ], [ 1, 2, 3, 4 ] ]\ngap> D := Digraph(IsMutableDigra\
ph, [\n>  [2, 1, 3, 4, 5], [3, 5], [2], [1, 2, 3, 5], [1, 2, 3, 4]]);\n<mutabl\
e digraph with 5 vertices, 16 edges>\ngap> DigraphGroup(D);\nGroup(())\ngap> R\
epresentativeOutNeighbours(D);\n[ [ 2, 1, 3, 4, 5 ], [ 3, 5 ], [ 2 ], [ 1, 2, \
3, 5 ], [ 1, 2, 3, 4 ] ]\ngap> D := DigraphFromDigraph6String(\"&GYHPQgWTIIPW\
\");\n<immutable digraph with 8 vertices, 24 edges>\ngap> G := DigraphGroup(D)\
;;\ngap> GeneratorsOfGroup(G);\n[ (1,2)(3,4)(5,6)(7,8), (1,3,2,4)(5,7,6,8), (1\
,5)(2,6)(3,8)(4,7) ]\ngap> Set(RepresentativeOutNeighbours(D), Set);\n[ [ 2, 3\
, 5 ] ]]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <\
Oper Name=\"IsDigraphIsomorphism\" Arg=\"src, ran, x\" \n        Label=\"for d\
igraphs and transformation or permutation\"/>\n  <Oper Name=\"IsDigraphIsomorp\
hism\" Arg=\"src, ran, x, col1, col2\"/>\n  <Oper Name=\"IsDigraphAutomorphism\
\" Arg=\"digraph, x\" \n        Label=\"for a digraph and a transformation or \
permutation\"/>\n  <Oper Name=\"IsDigraphAutomorphism\" Arg=\"digraph, x, col\
\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <Description>\n    \
<C>IsDigraphIsomorphism</C> returns <K>true</K> if the permutation or\n    tra\
nsformation <A>x</A> is an isomorphism from the digraph <A>src</A> to\n    the\
 digraph <A>ran</A>.\n    <P/>\n\n    <C>IsDigraphAutomorphism</C> returns <K>\
true</K> if the permutation or\n    transformation <A>x</A> is an automorphism\
 of the digraph <A>digraph</A>.\n    <P/>\n\n    A permutation or transformati\
on <A>x</A> is an <E>isomorphism</E> from a\n    digraph <A>src</A> to a digra\
ph <A>ran</A> if the following hold:\n    <List>\n      <Item>\n        <A>x</\
A> is a bijection from the vertices of <A>src</A> to those of\n        <A>ran<\
/A>;\n      </Item>\n      <Item>\n        <C>[u ^ <A>x</A>, v ^ <A>x</A>]</C>\
 is an edge of\n        <A>ran</A> if and only if <C>[u, v]</C> is an\n       \
 edge of <A>src</A>; and\n      </Item>\n      <Item>\n        <A>x</A> fixes \
every <C>i</C> which is not a vertex of <A>src</A>.\n      </Item>\n    </List\
>\n    See also <Ref Attr=\"AutomorphismGroup\" Label=\"for a digraph\"\n     \
 />.<P/>\n    \n    If <A>col1</A> and <A>col2</A>, or <A>col</A>, are given, \
then they must\n    represent vertex colourings; see \n    <Ref Oper=\"Automor\
phismGroup\" Label=\"for a digraph and a homogeneous list\"/> \n    for detail\
s of the permissible values for\n    these arguments. The homomorphism must th\
en also have the property:\n  \n    <List>\n      <Item>\n        <C>col1[i] =\
 col2[i ^ x]</C> for all vertices <C>i</C> of <A>src</A>,\n        for <C>IsDi\
graphIsomorphism</C>. </Item>\n      <Item>\n        <C>col[i] = col[i ^ x]</C\
> for all vertices <C>i</C> of <A>digraph</A>,\n        for <C>IsDigraphAutomo\
rphism</C>. </Item>\n    </List>\n\n    For some digraphs, it can be faster to\
 use <C>IsDigraphAutomorphism</C>\n    than to test membership in the automorp\
hism group of <A>digraph</A>.\n\n    <Example><![CDATA[\ngap> src := Digraph([\
[1], [1, 2], [1, 3]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> IsD\
igraphAutomorphism(src, (1, 2, 3));\nfalse\ngap> IsDigraphAutomorphism(src, (2\
, 3));\ntrue\ngap> IsDigraphAutomorphism(src, (2, 3), [2, 1, 1]);\ntrue\ngap> \
IsDigraphAutomorphism(src, (2, 3), [2, 2, 1]);\nfalse\ngap> IsDigraphAutomorph\
ism(src, (2, 3)(4, 5));\nfalse\ngap> IsDigraphAutomorphism(src, (1, 4));\nfals\
e\ngap> IsDigraphAutomorphism(src, ());\ntrue\ngap> ran := Digraph([[2, 1], [2\
], [2, 3]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> IsDigraphIsom\
orphism(src, ran, (1, 2));\ntrue\ngap> IsDigraphIsomorphism(ran, src, (1, 2));\
\ntrue\ngap> IsDigraphIsomorphism(ran, src, (1, 2));\ntrue\ngap> IsDigraphIsom\
orphism(src, Digraph([[3], [1, 3], [2]]), (1, 2, 3));\nfalse\ngap> IsDigraphIs\
omorphism(src, ran, (1, 2), [1, 2, 3], [2, 1, 3]);\ntrue\ngap> IsDigraphIsomor\
phism(src, ran, (1, 2), [1, 2, 2], [2, 1, 3]);\nfalse\n]]></Example>\n  </Desc\
ription>\n</ManSection>\n\n      <ManSection>\n    <Oper Name=\"IsDigraphColou\
ring\" Arg=\"digraph, list\"/>\n    <Oper Name=\"IsDigraphColouring\" Arg=\"di\
graph, t\" \n      Label=\"for a transformation\"/>\n    <Returns> <K>true</K>\
 or <K>false</K>. </Returns>\n    <Description>\n      The operation <C>IsDigr\
aphColouring</C> verifies whether or not \n      the list <A>list</A> describe\
s a proper colouring of the digraph \n      <A>digraph</A>. \n      <P/>\n\n  \
    A list <A>list</A> describes a <E>proper colouring</E> of a digraph\n     \
 <A>digraph</A> if <A>list</A> consists of positive integers, the length of\n \
     <A>list</A> equals the number of vertices in <A>digraph</A>, and for any\
\n      vertices <C>u, v</C> of <A>digraph</A> if <C>u</C> and <C>v</C> are ad\
jacent,\n      then <C><A>list</A>[u] &gt;&lt; <A>list</A>[v]</C>.\n      <P/>\
\n\n      A transformation <A>t</A> describes a proper colouring of a digraph\
\n      <A>digraph</A>, if <C>ImageListOfTransformation(<A>t</A>,\n      Digra\
phNrVertices(<A>digraph</A>))</C> is a proper colouring of \n      <A>digraph<\
/A>. <P/>\n\n      See also <Ref Oper=\"IsDigraphHomomorphism\"/>.\n      \n  \
    <Example><![CDATA[\ngap> D := JohnsonDigraph(5, 3);\n<immutable symmetric \
digraph with 10 vertices, 60 edges>\ngap> IsDigraphColouring(D, [1, 2, 3, 3, 2\
, 1, 4, 5, 6, 7]);\ntrue\ngap> IsDigraphColouring(D, [1, 2, 3, 3, 2, 1, 2, 5, \
6, 7]);\nfalse\ngap> IsDigraphColouring(D, [1, 2, 3, 3, 2, 1, 2, 5, 6, -1]);\n\
false\ngap> IsDigraphColouring(D, [1, 2, 3]);\nfalse\ngap> IsDigraphColouring(\
D, IdentityTransformation);\ntrue\n]]></Example>\n    </Description>\n  </ManS\
ection>\n\n  </Section>\n\n  <Section><Heading>Homomorphisms of digraphs</Head\
ing>\n\n    The following methods exist to find homomorphisms between digraphs\
.\n    If an argument to one of these methods is a digraph with multiple edges\
,\n    then the multiplicity of edges will be ignored in order to perform the\
\n    calculation; the digraph will be treated as if it has no multiple edges.\
\n\n    <ManSection>\n  <Func Name=\"HomomorphismDigraphsFinder\" Arg=\"D1, D2\
, hook, user_param, max_results, hint, injective, image, partial_map, colors1,\
 colors2[, order, aut_grp]\"/>\n  <Returns>The argument <A>user_param</A>.</Re\
turns>\n  <Description>\n    This function finds homomorphisms from the digrap\
h <A>D1</A> to the digraph\n    <A>D2</A> subject to the conditions imposed by\
 the other arguments as\n    described below.<P/>\n\n    If <C>f</C> and <C>g<\
/C> are homomorphisms found by\n    <C>HomomorphismDigraphsFinder</C>, then <C\
>f</C> cannot be obtained from\n    <C>g</C> by right multiplying by an automo\
rphism of <A>D2</A> in\n    <A>aut_grp</A>.\n\n    <List>\n      <Mark><A>hook\
</A></Mark>\n      <Item>\n        This argument should be a function or <K>fa\
il</K>.<P/>\n\n        If <A>hook</A> is a function, then it must have two arg\
uments\n        <A>user_param</A> (see below) and a transformation <C>t</C>. T\
he\n        function <C><A>hook</A>(<A>user_param</A>, t)</C> is called every \
time\n        a new homomorphism <C>t</C> is found by\n        <C>Homomorphism\
DigraphsFinder</C>. If the function returns <K>true</K>,\n        then <C>Homo\
morphismDigraphsFinder</C> stops and does not find any\n        further homomo\
rphisms. This feature might be useful if you are\n        searching for a homo\
morphism that satisfies some condition that you\n        cannot specify via th\
e other arguments to\n        <C>HomomorphismDigraphsFinder</C>.\n        <P/>\
\n\n        If <A>hook</A> is <K>fail</K>, then a default function is used whi\
ch\n        simply adds every new homomorphism found by\n        <C>Homomorphi\
smDigraphsFinder</C> to <A>user_param</A>, which must be a\n        mutable li\
st in this case.\n      </Item>\n\n      <Mark><A>user_param</A></Mark>\n     \
 <Item>\n        If <A>hook</A> is a function, then <A>user_param</A> can be a\
ny &GAP;\n        object. The object <A>user_param</A> is used as the first ar\
gument of\n        the function <A>hook</A>. For example, <A>user_param</A> mi\
ght be a\n        transformation semigroup, and <C><A>hook</A>(<A>user_param</\
A>, t)</C>\n        might set <A>user_param</A> to be the closure of <A>user_p\
aram</A> and\n        <C>t</C>. <P/>\n\n        If the value of <A>hook</A> is\
 <K>fail</K>, then the value of\n        <A>user_param</A> must be a mutable l\
ist.\n      </Item>\n\n      <Mark><A>max_results</A></Mark>\n      <Item>\n  \
      This argument should be a positive integer or <K>infinity</K>.\n        \
<C>HomomorphismDigraphsFinder</C> will return after it has found\n        <A>m\
ax_results</A> homomorphisms or the search is complete, whichever\n        hap\
pens first.\n      </Item>\n\n      <Mark><A>hint</A></Mark>\n      <Item>\n  \
      This argument should be a positive integer or <K>fail</K>. <P/>\n\n     \
   If <A>hint</A> is a positive integer, then only homorphisms of rank\n      \
  <A>hint</A> are found.<P/>\n\n        If <A>hint</A> is <K>fail</K>, then no\
 restriction is put on the rank\n        of homomorphisms found.\n      </Item\
>\n\n      <Mark><A>injective</A></Mark>\n      <Item>\n        This argument \
should be <C>0</C>, <C>1</C>, or <C>2</C>.  If it is\n        <C>2</C>, then o\
nly embeddings are found, if it is <C>1</C>, then only\n        injective homo\
morphisms are found, and if it is <C>0</C> there are no\n        restrictions \
imposed by this argument.\n        <P/>\n\n        For backwards compatibility\
, <A>injective</A> can also be <K>false</K>\n        or <K>true</K> which corr\
espond to the values <C>0</C> and <C>1</C>\n        described in the previous \
paragraph, respectively. \n      </Item>\n\n      <Mark><A>image</A></Mark>\n \
     <Item>\n        This argument should be a subset of the vertices of the g\
raph <A>D2</A>.\n        <C>HomomorphismDigraphsFinder</C> only finds homomorp\
hisms from\n        <A>D1</A> to the subgraph of <A>D2</A> induced by the vert\
ices\n        <A>image</A>.\n      </Item>\n\n      <Mark><A>partial_map</A></\
Mark>\n      <Item>\n        This argument should be a partial map from <A>D1<\
/A> to <A>D2</A>,\n        that is, a (not necessarily dense) list of vertices\
 of the digraph\n        <A>D2</A> of length no greater than the number vertic\
es in the digraph\n        <A>D1</A>. <C>HomomorphismDigraphsFinder</C> only f\
inds homomorphisms\n        extending <A>partial_map</A> (if any).\n      </It\
em>\n      \n      <Mark><A>colors1</A></Mark>\n      <Item>\n        This sho\
uld be a list representing possible colours of vertices in the\n        digrap\
h <A>D1</A>; see \n        <Ref Oper=\"AutomorphismGroup\" \n          Label=\
\"for a digraph and a homogeneous list\"/> \n        for details of the permis\
sible values for this argument.\n      </Item>\n      \n      <Mark><A>colors2\
</A></Mark>\n      <Item>\n        This should be a list representing possible\
 colours of vertices in the\n        digraph <A>D2</A>; see \n        <Ref Ope\
r=\"AutomorphismGroup\" \n          Label=\"for a digraph and a homogeneous li\
st\"/> \n        for details of the permissible values for this argument.\n   \
   </Item>\n      <Mark><A>order</A></Mark>\n      <Item>\n        The optiona\
l argument <A>order</A> specifies the order the\n        vertices in <A>D1</A>\
 appear in the search for homomorphisms. \n        The value of this parameter\
 can have a large impact\n        on the runtime of the function. It seems in \
many cases to be a good\n        idea for this to be the <Ref Attr=\"DigraphWe\
lshPowellOrder\"/>, i.e.\n        vertices ordered from highest to lowest degr\
ee.\n      </Item>\n      <Item>\n        The optional argument <A>aut_grp</A>\
 should be a subgroup of the\n        automorphism group of <A>D2</A>. This fu\
nction returns unique\n        representatives of the homomorphisms found up t\
o right multiplication\n        by <A>aut_grp</A>. If this argument is not spe\
cific, it defaults to the\n        full automorphism group of <A>D2</A>, which\
 may be costly to calculate.\n      </Item>\n    </List>\n\n    <Example><![CD\
ATA[\ngap> D := ChainDigraph(10);\n<immutable chain digraph with 10 vertices>\
\ngap> D := DigraphSymmetricClosure(D);\n<immutable symmetric digraph with 10 \
vertices, 18 edges>\ngap> HomomorphismDigraphsFinder(D, D, fail, [], infinity,\
 2, 0,\n> [3, 4], [], fail, fail);\n[ Transformation( [ 3, 4, 3, 4, 3, 4, 3, 4\
, 3, 4 ] ), \n  Transformation( [ 4, 3, 4, 3, 4, 3, 4, 3, 4, 3 ] ) ]\ngap> D2 \
:= CompleteDigraph(6);;\ngap> HomomorphismDigraphsFinder(D, D2, fail, [], 1, f\
ail, 0,\n> [1 .. 6], [1, 2, 1], fail, fail);\n[ Transformation( [ 1, 2, 1, 3, \
4, 5, 6, 1, 2, 1 ] ) ]\ngap> func := function(user_param, t)\n> Add(user_param\
, t * user_param[1]);\n> end;;\ngap> HomomorphismDigraphsFinder(D, D2, func, [\
Transformation([2, 2])],\n> 3, fail, 0, [1 .. 6], [1, 2, 1], fail, fail);\n[ T\
ransformation( [ 2, 2 ] ), \n  Transformation( [ 2, 2, 2, 3, 4, 5, 6, 2, 2, 2 \
] ), \n  Transformation( [ 2, 2, 2, 3, 4, 5, 6, 2, 2, 3 ] ), \n  Transformatio\
n( [ 2, 2, 2, 3, 4, 5, 6, 2, 2, 4 ] ) ]\ngap> HomomorphismDigraphsFinder(NullD\
igraph(2), NullDigraph(3), fail,\n> [], infinity, fail, 1, [1, 2, 3], fail, fa\
il, fail, fail,\n> Group(()));\n[ IdentityTransformation, Transformation( [ 1,\
 3, 3 ] ), \n  Transformation( [ 2, 1 ] ), Transformation( [ 2, 3, 3 ] ), \n  \
Transformation( [ 3, 1, 3 ] ), Transformation( [ 3, 2, 3 ] ) ]\ngap> Homomorph\
ismDigraphsFinder(NullDigraph(2), NullDigraph(3), fail,\n> [], infinity, fail,\
 1, [1, 2, 3], fail, fail, fail, fail,\n> Group((1, 2)));\n[ IdentityTransform\
ation, Transformation( [ 1, 3, 3 ] ), \n  Transformation( [ 3, 1, 3 ] ) ]]]></\
Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"\
DigraphHomomorphism\" Arg=\"digraph1, digraph2\"/>\n  <Returns> A transformati\
on, or <K>fail</K>.</Returns>\n  <Description>\n    A homomorphism from <A>dig\
raph1</A> to <A>digraph2</A> is a mapping from\n    the vertex set of <A>digra\
ph1</A> to a subset of the vertices of\n    <A>digraph2</A>, such that every p\
air of vertices <C>[i,j]</C> which has\n    an edge <C>i->j</C> is mapped to a\
 pair of vertices <C>[a,b]</C> which\n    has an edge <C>a->b</C>.  Note that \
non-adjacent vertices can still be\n    mapped to adjacent vertices. <P/>\n\n \
   <C>DigraphHomomorphism</C> returns a single homomorphism between\n    <A>di\
graph1</A> and <A>digraph2</A> if it exists, otherwise it returns\n    <K>fail\
</K>.\n<Example><![CDATA[\ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph(\
[[3, 5], [2], [3, 1], [], [4]]);\n<immutable digraph with 5 vertices, 6 edges>\
\ngap> DigraphHomomorphism(gr1, gr1);\nIdentityTransformation\ngap> map := Dig\
raphHomomorphism(gr1, gr2);\nTransformation( [ 3, 1, 5, 4, 5 ] )\ngap> IsDigra\
phHomomorphism(gr1, gr2, map);\ntrue\n]]></Example>\n  </Description>\n</ManSe\
ction>\n\n    <ManSection>\n  <Oper Name=\"HomomorphismsDigraphs\" Arg=\"digra\
ph1, digraph2\"/>\n  <Oper Name=\"HomomorphismsDigraphsRepresentatives\" Arg=\
\"digraph1, digraph2\"/>\n  <Returns> A list of transformations.</Returns>\n  \
<Description>\n    <C>HomomorphismsDigraphsRepresentatives</C> finds every\n  \
  <Ref Oper=\"DigraphHomomorphism\"/> between <A>digraph1</A> and\n    <A>digr\
aph2</A>, up to right multiplication by an element of the\n    <Ref Attr=\"Aut\
omorphismGroup\" Label=\"for a digraph\"/> of <A>digraph2</A>.\n    In other w\
ords, every homomorphism <C>f</C> between <A>digraph1</A> and\n    <A>digraph2\
</A> can be written as the composition <C>f = g * x</C>,\n    where <C>g</C> i\
s one of the <C>HomomorphismsDigraphsRepresentatives</C>\n    and <C>x</C> is \
an automorphism of <A>digraph2</A>.\n    <P/>\n\n    <C>HomomorphismsDigraphs<\
/C> returns all homomorphisms between\n    <A>digraph1</A> and <A>digraph2</A>\
.\n    <Example><![CDATA[\ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digraph(\
[[3, 5], [2], [3, 1], [], [4]]);\n<immutable digraph with 5 vertices, 6 edges>\
\ngap> HomomorphismsDigraphs(gr1, gr2);\n[ Transformation( [ 1, 3, 1 ] ), Tran\
sformation( [ 1, 3, 3 ] ), \n  Transformation( [ 1, 5, 4, 4, 5 ] ), Transforma\
tion( [ 2, 2, 2 ] ), \n  Transformation( [ 3, 1, 3 ] ), Transformation( [ 3, 1\
, 5, 4, 5 ] ), \n  Transformation( [ 3, 3, 1 ] ), Transformation( [ 3, 3, 3 ] \
) ]\ngap> HomomorphismsDigraphsRepresentatives(gr1, CompleteDigraph(3));\n[ Tr\
ansformation( [ 2, 1 ] ), Transformation( [ 2, 1, 2 ] ) ]\n]]></Example>\n  </\
Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphMonomor\
phism\" Arg=\"digraph1, digraph2\"/>\n  <Returns>A transformation, or <K>fail<\
/K>.</Returns>\n  <Description>\n    <C>DigraphMonomorphism</C> returns a sing\
le <E>injective</E> <Ref\n      Oper=\"DigraphHomomorphism\"/> between <A>digr\
aph1</A> and <A>digraph2</A>\n    if one exists, otherwise it returns <K>fail<\
/K>.\n    <Example><![CDATA[\ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digra\
ph([[3, 5], [2], [3, 1], [], [4]]);\n<immutable digraph with 5 vertices, 6 edg\
es>\ngap> DigraphMonomorphism(gr1, gr1);\nIdentityTransformation\ngap> Digraph\
Monomorphism(gr1, gr2);\nTransformation( [ 3, 1, 5, 4, 5 ] )\n]]></Example>\n \
 </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"Monomorphis\
msDigraphs\" Arg=\"digraph1, digraph2\"/>\n  <Oper Name=\"MonomorphismsDigraph\
sRepresentatives\" Arg=\"digraph1, digraph2\"/>\n  <Returns>A list of transfor\
mations.</Returns>\n  <Description>\n    These operations behave the same as <\
Ref Oper=\"HomomorphismsDigraphs\"/> and\n    <Ref Oper=\"HomomorphismsDigraph\
sRepresentatives\"/>, except they only return\n    <E>injective</E> homomorphi\
sms.\n    <Example><![CDATA[\ngap> gr1 := ChainDigraph(3);;\ngap> gr2 := Digra\
ph([[3, 5], [2], [3, 1], [], [4]]);\n<immutable digraph with 5 vertices, 6 edg\
es>\ngap> MonomorphismsDigraphs(gr1, gr2);\n[ Transformation( [ 1, 5, 4, 4, 5 \
] ), \n  Transformation( [ 3, 1, 5, 4, 5 ] ) ]\ngap> MonomorphismsDigraphsRepr\
esentatives(gr1, CompleteDigraph(3));\n[ Transformation( [ 2, 1 ] ) ]\n]]></Ex\
ample>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"Di\
graphEpimorphism\" Arg=\"digraph1, digraph2\"/>\n  <Returns>A transformation, \
or <K>fail</K>.</Returns>\n  <Description>\n    <C>DigraphEpimorphism</C> retu\
rns a single <E>surjective</E> <Ref\n      Oper=\"DigraphHomomorphism\"/> betw\
een <A>digraph1</A> and <A>digraph2</A>\n    if one exists, otherwise it retur\
ns <K>fail</K>.\n    <Example><![CDATA[\ngap> gr1 := DigraphReverse(ChainDigra\
ph(4));\n<immutable digraph with 4 vertices, 3 edges>\ngap> gr2 := DigraphRemo\
veEdge(CompleteDigraph(3), [1, 2]);\n<immutable digraph with 3 vertices, 5 edg\
es>\ngap> DigraphEpimorphism(gr2, gr1);\nfail\ngap> DigraphEpimorphism(gr1, gr\
2);\nTransformation( [ 3, 1, 2, 3 ] )\n]]></Example>\n  </Description>\n</ManS\
ection>\n\n    <ManSection>\n  <Oper Name=\"EpimorphismsDigraphs\" Arg=\"digra\
ph1, digraph2\"/>\n  <Oper Name=\"EpimorphismsDigraphsRepresentatives\" Arg=\"\
digraph1, digraph2\"/>\n  <Returns>A list of transformations.</Returns>\n  <De\
scription>\n    These operations behave the same as <Ref Oper=\"HomomorphismsD\
igraphs\"/> and\n    <Ref Oper=\"HomomorphismsDigraphsRepresentatives\"/>, exc\
ept they only return\n    <E>surjective</E> homomorphisms.\n    <Example><![CD\
ATA[\ngap> gr1 := DigraphReverse(ChainDigraph(4));\n<immutable digraph with 4 \
vertices, 3 edges>\ngap> gr2 := DigraphSymmetricClosure(CycleDigraph(3));\n<im\
mutable symmetric digraph with 3 vertices, 6 edges>\ngap> EpimorphismsDigraphs\
Representatives(gr1, gr2);\n[ Transformation( [ 3, 1, 2, 1 ] ), Transformation\
( [ 3, 1, 2, 3 ] ), \n  Transformation( [ 2, 1, 2, 3 ] ) ]\ngap> EpimorphismsD\
igraphs(gr1, gr2);\n[ Transformation( [ 1, 2, 1, 3 ] ), Transformation( [ 1, 2\
, 3, 1 ] ), \n  Transformation( [ 1, 2, 3, 2 ] ), Transformation( [ 1, 3, 1, 2\
 ] ), \n  Transformation( [ 1, 3, 2, 1 ] ), Transformation( [ 1, 3, 2, 3 ] ), \
\n  Transformation( [ 2, 1, 2, 3 ] ), Transformation( [ 2, 1, 3, 1 ] ), \n  Tr\
ansformation( [ 2, 1, 3, 2 ] ), Transformation( [ 2, 3, 1, 2 ] ), \n  Transfor\
mation( [ 2, 3, 1, 3 ] ), Transformation( [ 2, 3, 2, 1 ] ), \n  Transformation\
( [ 3, 1, 2, 1 ] ), Transformation( [ 3, 1, 2, 3 ] ), \n  Transformation( [ 3,\
 1, 3, 2 ] ), Transformation( [ 3, 2, 1, 2 ] ), \n  Transformation( [ 3, 2, 1,\
 3 ] ), Transformation( [ 3, 2, 3, 1 ] ) ]\n]]></Example>\n  </Description>\n<\
/ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphEmbedding\" Arg=\"digr\
aph1, digraph2\"/>\n  <Returns> A transformation, or <K>fail</K>.</Returns>\n \
 <Description>\n    An embedding of a digraph <A>digraph1</A> into another dig\
raph\n    <A>digraph2</A> is a <Ref Oper=\"DigraphMonomorphism\"/> from <A>dig\
raph1</A>\n    to <A>digraph2</A> which has the additional property that a pai\
r of\n    vertices <C>[i, j]</C> which have no edge <C>i -> j</C> in <A>digrap\
h1</A> are\n\n    mapped to a pair of vertices <C>[a, b]</C> which have no edg\
e <C>a->b</C> in\n    <A>digraph2</A>.<P/>\n\n    In other words, an embedding\
 <C>t</C> is an isomorphism from\n    <A>digraph1</A> to the <Ref Oper=\"Induc\
edSubdigraph\"/> of <A>digraph2</A>\n    on the image of <C>t</C>. <P/>\n\n   \
 <C>DigraphEmbedding</C> returns a single embedding if one exists, otherwise\n\
    it returns <K>fail</K>.\n    <Example><![CDATA[\ngap> gr := ChainDigraph(3\
);\n<immutable chain digraph with 3 vertices>\ngap> DigraphEmbedding(gr, Compl\
eteDigraph(4));\nfail\ngap> DigraphEmbedding(gr, Digraph([[3], [1, 4], [1], [3\
]]));\nTransformation( [ 2, 4, 3, 4 ] )\n]]></Example>\n  </Description>\n</Ma\
nSection>\n\n    <ManSection>\n  <Oper Name=\"EmbeddingsDigraphs\" Arg=\"D1, D\
2\"/>\n  <Oper Name=\"EmbeddingsDigraphsRepresentatives\" Arg=\"D1, D2\"/>\n  \
<Returns>A list of transformations.</Returns>\n  <Description>\n    These oper\
ations behave the same as <Ref Oper=\"HomomorphismsDigraphs\"/> and\n    <Ref \
Oper=\"HomomorphismsDigraphsRepresentatives\"/>, except they only return\n    \
embeddings of <A>D1</A> into <A>D2</A>.<P/>\n\n    See also <Ref Oper=\"IsDigr\
aphEmbedding\"/>.\n    <Example><![CDATA[\ngap> D1 := NullDigraph(2);\n<immuta\
ble empty digraph with 2 vertices>\ngap> D2 := CycleDigraph(5);\n<immutable cy\
cle digraph with 5 vertices>\ngap> EmbeddingsDigraphsRepresentatives(D1, D2);\
\n[ Transformation( [ 1, 3, 3 ] ), Transformation( [ 1, 4, 3, 4 ] ) ]\ngap> Em\
beddingsDigraphs(D1, D2);\n[ Transformation( [ 1, 3, 3 ] ), Transformation( [ \
1, 4, 3, 4 ] ), \n  Transformation( [ 2, 4, 4, 5, 1 ] ), \n  Transformation( [\
 2, 5, 4, 5, 1 ] ), \n  Transformation( [ 3, 1, 5, 1, 2 ] ), \n  Transformatio\
n( [ 3, 5, 5, 1, 2 ] ), \n  Transformation( [ 4, 1, 1, 2, 3 ] ), \n  Transform\
ation( [ 4, 2, 1, 2, 3 ] ), \n  Transformation( [ 5, 2, 2, 3, 4 ] ), \n  Trans\
formation( [ 5, 3, 2, 3, 4 ] ) ]\n]]></Example>\n  </Description>\n</ManSectio\
n>\n\n    <ManSection>\n  <Oper Name=\"IsDigraphHomomorphism\" Arg=\"src, ran,\
 x\" \n        Label=\"for digraphs and a permutation or transformation\"/>\n \
 <Oper Name=\"IsDigraphHomomorphism\" Arg=\"src, ran, x, col1, col2\"/>\n  <Op\
er Name=\"IsDigraphEpimorphism\" Arg=\"src, ran, x\"\n        Label=\"for digr\
aphs and a permutation or transformation\"/>\n  <Oper Name=\"IsDigraphEpimorph\
ism\" Arg=\"src, ran, x, col1, col2\"/>\n  <Oper Name=\"IsDigraphMonomorphism\
\" Arg=\"src, ran, x\"\n        Label=\"for digraphs and a permutation or tran\
sformation\"/>\n  <Oper Name=\"IsDigraphMonomorphism\" Arg=\"src, ran, x, col1\
, col2\"/>\n  <Oper Name=\"IsDigraphEndomorphism\" Arg=\"digraph, x\"\n       \
 Label=\"for digraphs and a permutation or transformation\"/>\n  <Oper Name=\"\
IsDigraphEndomorphism\" Arg=\"digraph, x, col\"/>\n  <Returns><K>true</K> or <\
K>false</K>.</Returns>\n  <Description>\n    <C>IsDigraphHomomorphism</C> retu\
rns <K>true</K> if the permutation\n    or transformation <A>x</A> is a homomo\
rphism from the digraph\n    <A>src</A> to the digraph <A>ran</A>.\n    <P/>\n\
\n    <C>IsDigraphEpimorphism</C> returns <K>true</K> if the permutation\n    \
or transformation <A>x</A> is a surjective homomorphism from the digraph\n    \
<A>src</A> to the digraph <A>ran</A>.\n    <P/>\n\n    <C>IsDigraphMonomorphis\
m</C> returns <K>true</K> if the permutation\n    or transformation <A>x</A> i\
s an injective homomorphism from the digraph\n    <A>src</A> to the digraph <A\
>ran</A>.\n    <P/>\n\n    <C>IsDigraphEndomorphism</C> returns <K>true</K> if\
 the permutation\n    or transformation <A>x</A> is an endomorphism of the dig\
raph\n    <A>digraph</A>.\n    <P/>\n\n    A permutation or transformation <A>\
x</A> is a <E>homomorphism</E> from a\n    digraph <A>src</A> to a digraph <A>\
ran</A> if the following hold:\n    <List>\n      <Item>\n        <C>[u ^ <A>x\
</A>, v ^ <A>x</A>]</C> is an edge of\n        <A>ran</A> whenever <C>[u, v]</\
C> is an\n        edge of <A>src</A>; and </Item>\n      <Item>\n        <A>x<\
/A> fixes every <C>i</C> which is not a vertex of <A>src</A>.\n      </Item>\n\
    </List>\n    See also <Ref Func=\"GeneratorsOfEndomorphismMonoid\"/>.<P/>\
\n\n\n    If <A>col1</A> and <A>col2</A>, or <A>col</A>, are given, then they \
must\n    represent vertex colourings; see \n    <Ref Oper=\"AutomorphismGroup\
\" Label=\"for a digraph and a homogeneous list\"/> \n    for details of the p\
ermissible values for these argument. The\n    homomorphism must then also hav\
e the property:\n  \n    <List>\n      <Item>\n        <C>col[i] = col[i ^ x]<\
/C> for all vertices <C>i</C> of <A>digraph</A>,\n        in the case of <C>Is\
DigraphEndomorphism</C>.</Item>\n      <Item>\n        <C>col1[i] = col2[i ^ x\
]</C> for all vertices <C>i</C> of <A>src</A>,\n        in the cases of the ot\
her operations.</Item>\n    </List>\n\n    See also <Ref Oper=\"DigraphsRespec\
tsColouring\"/>.\n    \n    <Example><![CDATA[\ngap> src := Digraph([[1], [1, \
2], [1, 3]]);\n<immutable digraph with 3 vertices, 5 edges>\ngap> ran := Digra\
ph([[1], [1, 2]]);\n<immutable digraph with 2 vertices, 3 edges>\ngap> IsDigra\
phHomomorphism(src, ran, Transformation([1, 2, 2]));\ntrue\ngap> IsDigraphHomo\
morphism(src, ran, Transformation([2, 1, 2]));\nfalse\ngap> IsDigraphHomomorph\
ism(src, ran, Transformation([3, 3, 3]));\nfalse\ngap> IsDigraphHomomorphism(s\
rc, src, Transformation([3, 3, 3]));\ntrue\ngap> IsDigraphHomomorphism(src, ra\
n, Transformation([1, 2, 2]),\n>                          [1, 2, 2], [1, 2]);\
\ntrue\ngap> IsDigraphHomomorphism(src, ran, Transformation([1, 2, 2]),\n>    \
                      [2, 1, 1], [1, 2]);\nfalse\ngap> IsDigraphEndomorphism(s\
rc, Transformation([3, 3, 3]));\ntrue\ngap> IsDigraphEndomorphism(src, Transfo\
rmation([3, 3, 3]), [1, 1, 1]);\ntrue\ngap> IsDigraphEndomorphism(src, Transfo\
rmation([3, 3, 3]), [1, 1, 2]);\nfalse\ngap> IsDigraphEpimorphism(src, ran, Tr\
ansformation([3, 3, 3]));\nfalse\ngap> IsDigraphMonomorphism(src, ran, Transfo\
rmation([1, 2, 2]));\nfalse\ngap> IsDigraphEpimorphism(src, ran, Transformatio\
n([1, 2, 2]));\ntrue\ngap> IsDigraphMonomorphism(ran, src, ());\ntrue]]></Exam\
ple>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"IsDi\
graphEmbedding\" Arg=\"src, ran, x\"\n        Label=\"for digraphs and a permu\
tation or transformation\"/>\n  <Oper Name=\"IsDigraphEmbedding\" Arg=\"src, r\
an, x, col1, col2\"/>\n  <Returns><K>true</K> or <K>false</K>.</Returns>\n  <D\
escription>\n    <C>IsDigraphEmbedding</C> returns <K>true</K> if the permutat\
ion\n    or transformation <A>x</A> is a embedding of the digraph\n    <A>src<\
/A> into the digraph <A>ran</A>, while respecting the colourings\n    <A>col1<\
/A> and <A>col2</A> if given.\n    <P/>\n\n    A permutation or transformation\
 <A>x</A> is a <E>embedding</E> of a digraph\n    <A>src</A> into a digraph <A\
>ran</A> if <A>x</A> is a monomorphism from\n    <A>src</A> to <A>ran</A> and \
the inverse of <A>x</A> is a monomorphism from\n    the subdigraph of <A>ran</\
A> induced by the image of <A>x</A> to\n    <A>src</A>.\n\n    See also <Ref O\
per=\"IsDigraphHomomorphism\"/>.<P/>\n\n    <Example><![CDATA[\ngap> src := Di\
graph([[1], [1, 2]]);\n<immutable digraph with 2 vertices, 3 edges>\ngap> ran \
:= Digraph([[1], [1, 2], [1, 3]]);\n<immutable digraph with 3 vertices, 5 edge\
s>\ngap> IsDigraphMonomorphism(src, ran, ());\ntrue\ngap> IsDigraphEmbedding(s\
rc, ran, ());\ntrue\ngap> IsDigraphEmbedding(src, ran, (), [2, 1], [2, 1, 1]);\
\ntrue\ngap> IsDigraphEmbedding(src, ran, (), [2, 1], [1, 2, 1]);\nfalse\ngap>\
 ran := Digraph([[1, 2], [1, 2], [1, 3]]);\n<immutable digraph with 3 vertices\
, 6 edges>\ngap> IsDigraphMonomorphism(src, ran, IdentityTransformation);\ntru\
e\ngap> IsDigraphEmbedding(src, ran, IdentityTransformation);\nfalse]]></Examp\
le>\n  </Description>\n</ManSection>\n\n      <ManSection>\n    <Oper Name=\"D\
igraphsRespectsColouring\" Arg=\"src, ran, x, col1, col2\"/>\n    <Returns> <K\
>true</K> or <K>false</K>. </Returns>\n    <Description>\n      The operation \
<C>DigraphsRespectsColouring</C> verifies whether or not \n      the permutati\
on or transformation <A>x</A> respects the vertex colourings\n      <A>col1</A\
> and <A>col2</A> of the digraphs <A>src</A> and <A>range</A>.\n      That is,\
 <C>DigraphsRespectsColouring</C> returns <K>true</K> if and only if for\n    \
  all vertices <C>i</C> of <A>src</A>, <C>col1[i] = col2[i ^ x]</C>.\n      <P\
/>\n\n      <Example><![CDATA[\ngap> src := Digraph([[1], [1, 2]]);\n<immutabl\
e digraph with 2 vertices, 3 edges>\ngap> ran := Digraph([[1], [1, 2], [1, 3]]\
);\n<immutable digraph with 3 vertices, 5 edges>\ngap> DigraphsRespectsColouri\
ng(src, ran, (1, 2), [2, 1], [1, 2, 1]);\ntrue\ngap> DigraphsRespectsColouring\
(src, ran, (1, 2), [2, 1], [2, 1, 1]);\nfalse\n]]></Example>\n    </Descriptio\
n>\n  </ManSection>\n\n    <ManSection>\n  <Func Name=\"GeneratorsOfEndomorphi\
smMonoid\" Arg=\"digraph[, colors][, limit]\"/>\n  <Attr Name=\"GeneratorsOfEn\
domorphismMonoidAttr\" Arg=\"digraph\"/>\n  <Returns> A list of transformation\
s.</Returns>\n  <Description>\n    An endomorphism of <A>digraph</A> is a homo\
morphism\n    <Ref Oper=\"DigraphHomomorphism\"/> from <A>digraph</A> back to \
itself.\n\n    <C>GeneratorsOfEndomorphismMonoid</C>, called with a single arg\
ument,\n    returns a generating set for the monoid of all endomorphisms of\n \
   <A>digraph</A>. If <A>digraph</A>  belongs to <Ref\n      Filt=\"IsImmutabl\
eDigraph\"/>, then the value of\n    <C>GeneratorsOfEndomorphismMonoid</C> wil\
l not be recomputed on future\n    calls.<P/>\n\n    If the <A>colors</A> argu\
ment is specified, then\n    <C>GeneratorsOfEndomorphismMonoid</C> will return\
 a generating\n    set for the monoid of endomorphisms which respect the given\
 colouring.\n    The colouring <A>colors</A> can be in one of two forms: <P/>\
\n\n    <List>\n      <Item>\n        A list of positive integers of size the \
number of vertices of\n        <A>digraph</A>, where <A>colors</A><C>[i]</C> i\
s the colour of vertex\n        <C>i</C>.\n      </Item>\n      <Item>\n      \
  A list of lists, such that <A>colors</A><C>[i]</C> is a list of all\n       \
 vertices with colour <C>i</C>.\n      </Item>\n    </List>\n\n    If the <A>l\
imit</A> argument is specified, then it will return only the\n    first <A>lim\
it</A> homomorphisms, where <A>limit</A> must be a positive\n    integer or <C\
>infinity</C>. <P/>\n\n    <Example><![CDATA[\ngap> gr := Digraph(List([1 .. 3\
], x -> [1 .. 3]));;\ngap> GeneratorsOfEndomorphismMonoid(gr);\n[ Transformati\
on( [ 1, 3, 2 ] ), Transformation( [ 2, 1 ] ), \n  IdentityTransformation, Tra\
nsformation( [ 1, 2, 1 ] ), \n  Transformation( [ 1, 2, 2 ] ), Transformation(\
 [ 1, 1, 2 ] ), \n  Transformation( [ 1, 1, 1 ] ) ]\ngap> GeneratorsOfEndomorp\
hismMonoid(gr, 3);\n[ Transformation( [ 1, 3, 2 ] ), Transformation( [ 2, 1 ] \
), \n  IdentityTransformation ]\ngap> gr := CompleteDigraph(3);;\ngap> Generat\
orsOfEndomorphismMonoid(gr);\n[ Transformation( [ 2, 3, 1 ] ), Transformation(\
 [ 2, 1 ] ), \n  IdentityTransformation ]\ngap> GeneratorsOfEndomorphismMonoid\
(gr, [1, 2, 2]);\n[ Transformation( [ 1, 3, 2 ] ), IdentityTransformation ]\ng\
ap> GeneratorsOfEndomorphismMonoid(gr, [[1], [2, 3]]);\n[ Transformation( [ 1,\
 3, 2 ] ), IdentityTransformation ]\n]]></Example>\n  </Description>\n</ManSec\
tion>\n\n    <ManSection>\n  <Oper Name=\"DigraphColouring\" Arg=\"digraph, n\
\"\n    Label=\"for a digraph and a number of colours\"/>\n  <Returns> A trans\
formation, or <K>fail</K>.</Returns>\n  <Description>\n    A <E>proper colouri\
ng</E> of a digraph is a labelling of its vertices in\n    such a way that adj\
acent vertices have different labels. A <E>proper\n      <C>n</C>-colouring</E\
> is a proper colouring that uses exactly <C>n</C>\n    colours.  Equivalently\
, a proper (<C>n</C>-)colouring of a digraph can be\n    defined to be a <Ref \
Oper=\"DigraphEpimorphism\"/> from a digraph onto the\n    complete digraph (w\
ith <C>n</C> vertices); see <Ref\n      Oper=\"CompleteDigraph\"/>.  Note that\
 a digraph with loops (<Ref\n      Prop=\"DigraphHasLoops\"/>) does not have a\
 proper <C>n</C>-colouring for\n    any value <C>n</C>.\n    <P/>\n\n    If <A\
>digraph</A> is a digraph and <A>n</A> is a non-negative integer, then\n    <C\
>DigraphColouring(<A>digraph</A>, <A>n</A>)</C> returns an epimorphism\n    fr\
om <A>digraph</A> onto the complete digraph with <A>n</A> vertices if one\n   \
 exists, else it returns <K>fail</K>. <P/>\n\n    See also <Ref Attr=\"Digraph\
GreedyColouring\" Label=\"for a digraph\"/> and \n    <P/>\n\n    Note that a \
digraph with at least two vertices has a 2-colouring if and only\n    if it is\
 bipartite, see <Ref Prop=\"IsBipartiteDigraph\"/>.\n\n    <Example><![CDATA[\
\ngap> DigraphColouring(CompleteDigraph(5), 4);\nfail\ngap> DigraphColouring(C\
hainDigraph(10), 1);\nfail\ngap> D := ChainDigraph(10);;\ngap> t := DigraphCol\
ouring(D, 2);\nTransformation( [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ] )\ngap> IsDigr\
aphColouring(D, t); \ntrue\ngap> DigraphGreedyColouring(D);\nTransformation( [\
 2, 1, 2, 1, 2, 1, 2, 1, 2, 1 ] )\n]]></Example>\n  </Description>\n</ManSecti\
on>\n\n    <ManSection>\n  <Oper Name=\"DigraphGreedyColouring\" \n        Arg\
=\"digraph, order\" \n        Label=\"for a digraph and vertex order\"/>\n  <O\
per Name=\"DigraphGreedyColouring\" \n        Arg=\"digraph, func\" \n        \
Label=\"for a digraph and vertex order function\"/>\n  <Attr Name=\"DigraphGre\
edyColouring\" \n        Arg=\"digraph\" \n        Label=\"for a digraph\"/>\n\
  <Returns> A transformation, or <K>fail</K>.</Returns>\n  <Description>\n    \
A <E>proper colouring</E> of a digraph is a labelling of its vertices in\n    \
such a way that adjacent vertices have different labels. Note that a digraph \
\n    with loops (<Ref Prop=\"DigraphHasLoops\"/>) does not have any proper \n\
    colouring.\n    <P/>\n    \n    If <A>digraph</A> is a digraph and <A>orde\
r</A> is a dense list consisting \n    of all of the vertices of <A>digraph</A\
> (in any order), then  \n    <C>DigraphGreedyColouring</C>\n    uses a greedy\
 algorithm with the specified order to obtain some proper\n    colouring of <A\
>digraph</A>, which may not use the minimal number of\n    colours. <P/>\n    \
\n    If <A>digraph</A> is a digraph and <A>func</A> is a function whose argum\
ent \n    is a digraph, and that returns a dense list <A>order</A>, then \n   \
 <C>DigraphGreedyColouring(<A>digraph</A>, <A>func</A>)</C> returns\n    <C>Di\
graphGreedyColouring(<A>digraph</A>, <A>func</A>(<A>digraph</A>))</C>.\n    <P\
/>\n\n    If the optional second argument (either a list or a function), is no\
t \n    specified, then <Ref Attr=\"DigraphWelshPowellOrder\"/> is used by def\
ault. \n    <P/>\n    \n    See also\n    <Ref Oper=\"DigraphColouring\" \n   \
      Label=\"for a digraph and a number of colours\"/>.\n    <P/>\n\n    <Exa\
mple><![CDATA[\ngap> DigraphGreedyColouring(ChainDigraph(10));\nTransformation\
( [ 2, 1, 2, 1, 2, 1, 2, 1, 2, 1 ] )\ngap> DigraphGreedyColouring(ChainDigraph\
(10), [1 .. 10]);\nTransformation( [ 1, 2, 1, 2, 1, 2, 1, 2, 1, 2 ] )\n]]></Ex\
ample>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"Di\
graphWelshPowellOrder\" Arg=\"digraph\"/>\n  <Returns> A list of the vertices.\
</Returns>\n  <Description>\n    <C>DigraphWelshPowellOrder</C> returns a list\
 of all of the vertices of \n    the digraph <A>digraph</A> ordered according \
to the sum of the number of \n    out- and in-neighbours, from highest to lowe\
st. \n    <P/>\n\n    <Example><![CDATA[\ngap> DigraphWelshPowellOrder(Digraph\
([[4], [9], [9], [], \n>                                     [4, 6, 9], [1], [\
], [], \n>                                     [4, 5], [4, 5]]));\n[ 5, 9, 4, \
1, 6, 10, 2, 3, 7, 8 ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    \
<ManSection>\n  <Attr Name=\"ChromaticNumber\" Arg=\"digraph\"/>\n  <Returns> \
A non-negative integer.</Returns>\n  <Description>\n    A <E>proper colouring<\
/E> of a digraph is a labelling of its\n    vertices in such a way that adjace\
nt vertices have different labels.\n    Equivalently, a proper digraph colouri\
ng can be defined to be a <Ref\n      Oper=\"DigraphEpimorphism\"/> from a dig\
raph onto a complete digraph. <P/>\n\n    If <A>digraph</A> is a digraph witho\
ut loops (see <Ref\n      Prop=\"DigraphHasLoops\"/>, then <C>ChromaticNumber<\
/C> returns the least\n    non-negative integer <C>n</C> such that there is a \
proper colouring of\n    <A>digraph</A> with <C>n</C> colours.  In other words\
, for a digraph with at\n    least one vertex, <C>ChromaticNumber</C> returns \
the least number <C>n</C>\n    such that <C>DigraphColouring(<A>digraph</A>, n\
)</C> does not return\n    <K>fail</K>. See <Ref Oper=\"DigraphColouring\"\n  \
    Label=\"for a digraph and a number of colours\"/>.\n\n    <Example><![CDAT\
A[\ngap> ChromaticNumber(NullDigraph(10));\n1\ngap> ChromaticNumber(CompleteDi\
graph(10));\n10\ngap> ChromaticNumber(CompleteBipartiteDigraph(5, 5));\n2\ngap\
> ChromaticNumber(Digraph([[], [3], [5], [2, 3], [4]]));\n3\ngap> ChromaticNum\
ber(NullDigraph(0));\n0\ngap> D := PetersenGraph(IsMutableDigraph);\n<mutable \
digraph with 10 vertices, 30 edges>\ngap> ChromaticNumber(D);\n3\n]]></Example\
>\n  </Description>\n</ManSection>\n\n      <ManSection>\n    <Attr Name = \"D\
igraphCore\" Arg = \"D\"/>\n    <Returns>A list of positive integers.</Returns\
>\n    <Description>\n      If <A>D</A> is a digraph, then <C>DigraphCore</C> \
returns a list of vertices\n      corresponding to the <C>core</C> of <A>D</A>\
. In particular, the subdigraph\n      of <A>D</A> induced by this list is iso\
morphic to the core of <A>D</A>.<P/>\n\n    The <E>core</E> of a digraph <C>D<\
/C> is the minimal subdigraph <A>C</A> of\n    <C>D</C> which is a homomorphic\
 image of <C>D</C>. The core of a digraph \n    is unique up to isomorphism.\n\
      <Example><![CDATA[\ngap> D := DigraphSymmetricClosure(CycleDigraph(8));\
\n<immutable symmetric digraph with 8 vertices, 16 edges>\ngap> DigraphCore(D)\
;\n[ 1, 2 ]\ngap> D := PetersenGraph();\n<immutable digraph with 10 vertices, \
30 edges>\ngap> DigraphCore(D);\n[ 1 .. 10 ]\ngap> D := Digraph(IsMutableDigra\
ph, [[3], [3], [4], [5], [2]]);\n<mutable digraph with 5 vertices, 5 edges>\ng\
ap> DigraphCore(D);\n[ 2, 3, 4, 5 ]\n]]></Example>\n    </Description>\n  </Ma\
nSection>\n\n  </Section>\n\n</Chapter>\n <!-- homomorphisms -->\n  <Chapter L\
abel=\"Finding cliques and independent sets\">\n  <Heading>Finding cliques and\
 independent sets</Heading>\n\n    In &Digraphs;, a <E>clique</E> of a digraph\
 is a set of mutually adjacent\n    vertices of the digraph, and an <E>indepen\
dent set</E> is a set of mutually\n    non-adjacent vertices of the digraph. A\
 <E>maximal clique</E> is a clique\n    which is not properly contained in ano\
ther clique, and a <E>maximal\n      independent set</E> is an independent set\
 which is not properly contained\n    in another independent set.  Using this \
definition in &Digraphs;, cliques\n    and independent sets are both permitted\
, but not required, to contain vertices\n    at which there is a loop.  Anothe\
r name for a clique is a <E>complete\n      subgraph</E>.\n    <P/>\n\n    &Di\
graphs; provides extensive functionality for computing cliques and\n    indepe\
ndent sets of a digraph, whether maximal or not.  The fundamental\n    algorit\
hm used in most of the methods in &Digraphs; to calculate cliques\n    and ind\
ependent sets is a version of the Bron-Kerbosch algorithm.\n    Calculating th\
e cliques and independent sets of a digraph is a well-known\n    and hard prob\
lem, and searching for cliques or independent sets in a\n    digraph can be ve\
ry lengthy, even for a digraph with a small number of\n    vertices.  &Digraph\
s; uses several strategies to increase the performance\n    of these calculati\
ons.\n    <P/>\n\n    From the definition of cliques and independent sets, it \
follows that the\n    presence of loops and multiple edges in a digraph is irr\
elevant to the\n    existence of cliques and independent sets in the digraph. \
 See <Ref\n      Prop=\"DigraphHasLoops\"/> and <Ref Prop=\"IsMultiDigraph\"/>\
 for more\n    information about these properties.  Therefore given a digraph\
\n    <A>digraph</A>, the cliques and independent sets of <A>digraph</A> are\n\
    equal to the cliques and independent sets of the digraph:\n\n    <List>\n \
     <Item>\n        <C>DigraphRemoveLoops(DigraphRemoveAllMultipleEdges(</C><\
A>digraph</A><C>))</C>.\n      </Item>\n    </List>\n\n    See <Ref Oper=\"Dig\
raphRemoveLoops\"/> and <Ref\n      Oper=\"DigraphRemoveAllMultipleEdges\"/> f\
or more information about these\n    attributes.  Furthermore, the cliques of \
this digraph are equal to the\n    cliques of the digraph formed by removing a\
ny edge <C>[u,v]</C> for which\n    the corresponding reverse edge <C>[v,u]</C\
> is not present.  Therefore,\n    overall, the cliques of <A>digraph</A> are \
equal to the cliques of the\n    symmetric digraph:\n\n    <List>\n      <Item\
>\n        <C>MaximalSymmetricSubdigraphWithoutLoops(</C><A>digraph</A><C>)</C\
>.\n      </Item>\n    </List>\n\n    See <Ref Oper=\"MaximalSymmetricSubdigra\
phWithoutLoops\"/> for more\n    information about this. The <Ref Attr=\"Autom\
orphismGroup\"\n      Label=\"for a digraph\" /> of this symmetric digraph con\
tains the\n    automorphism group of <A>digraph</A> as a subgroup.  By perform\
ing the\n    search for maximal cliques with the help of this larger automorph\
ism group\n    to reduce the search space, the computation time may be reduced\
.  The\n    functions and attributes which return representatives of cliques o\
f\n    <A>digraph</A> will return orbit representatives of cliques under the\n\
    action of the automorphism group of the <E>maximal symmetric subdigraph\n \
     without loops</E> on sets of vertices.<P/>\n\n    The independent sets of\
 a digraph are equal to the independent sets of the\n    <Ref Oper=\"DigraphSy\
mmetricClosure\"/>.  Therefore, overall, the independent\n    sets of <A>digra\
ph</A> are equal to the independent sets of the symmetric\n    digraph:\n\n   \
 <List>\n      <Item>\n        <C>DigraphSymmetricClosure(DigraphRemoveLoops(D\
igraphRemoveAllMultipleEdges(\n        </C><A>digraph</A><C>)))</C>.\n      </\
Item>\n    </List>\n\n    Again, the automorphism group of this symmetric digr\
aph contains the\n    automorphism group of <A>digraph</A>. Since a search for\
 independent sets\n    is equal to a search for cliques in the <Ref Oper=\"Dig\
raphDual\"/>, the\n    methods used in &Digraphs; usually transform a search f\
or independent sets\n    into a search for cliques, as described above.  The f\
unctions and\n    attributes which return representatives of independent sets \
of\n    <A>digraph</A> will return orbit representatives of independent sets u\
nder\n    the action of the automorphism group of the <E>symmetric closure</E>\
 of the\n    digraph formed by removing loops and multiple edges.<P/>\n\n    P\
lease note that in &Digraphs;, cliques and independent sets are not\n    requi\
red to be maximal. Some authors use the word clique to mean\n    <E>maximal</E\
> clique, and some authors use the phrase independent set to\n    mean <E>maxi\
mal</E> independent set, but please note that &Digraphs; does\n    not use thi\
s definition.\n    <P/>\n\n  <Section><Heading>Finding cliques</Heading>\n    \
<ManSection>\n<Oper Name=\"IsClique\" Arg=\"digraph, l\"/>\n<Oper Name=\"IsMax\
imalClique\" Arg=\"digraph, l\"/>\n<Returns><K>true</K> or <K>false</K>.</Retu\
rns>\n<Description>\n  If <A>digraph</A> is a digraph and <A>l</A> is a duplic\
ate-free list of\n  vertices of <A>digraph</A>, then\n  <C>IsClique(</C><A>dig\
raph</A><C>,</C><A>l</A><C>)</C> returns <K>true</K>\n    if <A>l</A> is a <E>\
clique</E> of <A>digraph</A> and <K>false</K> if it is\n    not.  Similarly,\n\
    <C>IsMaximalClique(</C><A>digraph</A><C>,</C><A>l</A><C>)</C> returns\n   \
 <K>true</K> if <A>l</A> is a <E>maximal clique</E> of <A>digraph</A> and\n   \
 <K>false</K> if it is not.  <P/>\n\n    A <E>clique</E> of a digraph is a set\
 of mutually adjacent vertices of the\n    digraph. A <E>maximal clique</E> is\
 a clique that is not properly\n    contained in another clique. A clique is p\
ermitted, but not required, to\n    contain vertices at which there is a loop.\
\n    <Example><![CDATA[\ngap> D := CompleteDigraph(4);;\ngap> IsClique(D, [1,\
 3, 2]);\ntrue\ngap> IsMaximalClique(D, [1, 3, 2]);\nfalse\ngap> IsMaximalCliq\
ue(D, DigraphVertices(D));\ntrue\ngap> D := Digraph([[1, 2, 4, 4], [1, 3, 4], \
[2, 1], [1, 2]]);\n<immutable multidigraph with 4 vertices, 11 edges>\ngap> Is\
Clique(D, [2, 3, 4]);\nfalse\ngap> IsMaximalClique(D, [1, 2, 4]);\ntrue\ngap> \
D := CompleteDigraph(IsMutableDigraph, 4);;\ngap> IsClique(D, [1, 3, 2]);\ntru\
e]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Func N\
ame=\"CliquesFinder\" Arg=\"digraph, hook, user_param, limit, include,\n    ex\
clude, max, size, reps\"/>\n  <Returns>The argument <A>user_param</A>.</Return\
s>\n  <Description>\n    This function finds cliques of the digraph <A>digraph\
</A> subject to the\n    conditions imposed by the other arguments as describe\
d below. Note\n    that a clique is represented by the immutable list of the v\
ertices that\n    it contains.\n    <P/>\n\n    Let <C>G</C> denote the automo\
rphism group of the maximal symmetric\n    subdigraph of <A>digraph</A> withou\
t loops (see <Ref\n      Attr=\"AutomorphismGroup\" Label=\"for a digraph\"/> \
and <Ref\n      Oper=\"MaximalSymmetricSubdigraphWithoutLoops\"/>).\n\n    <Li\
st>\n      <Mark><A>hook</A></Mark>\n      <Item>\n        This argument shoul\
d be a function or <K>fail</K>.<P/>\n\n        If <A>hook</A> is a function, t\
hen it should have two arguments\n        <A>user_param</A> (see below) and a \
clique <C>c</C>. The function\n        <C><A>hook</A>(<A>user_param</A>, c)</C\
> is called every time a new\n        clique <C>c</C> is found by <C>CliquesFi\
nder</C>.<P/>\n\n        If <A>hook</A> is <K>fail</K>, then a default functio\
n is used that\n        simply adds every new clique found by <C>CliquesFinder\
</C> to\n        <A>user_param</A>, which must be a list in this case.\n      \
</Item>\n\n      <Mark><A>user_param</A></Mark>\n      <Item>\n        If <A>h\
ook</A> is a function, then <A>user_param</A> can be any &GAP;\n        object\
. The object <A>user_param</A> is used as the first argument for\n        the \
function <A>hook</A>. For example, <A>user_param</A> might be a\n        list,\
 and <C><A>hook</A>(<A>user_param</A>, c)</C> might add the size\n        of t\
he clique <C>c</C> to the list <A>user_param</A>. <P/>\n\n        If the value\
 of <A>hook</A> is <K>fail</K>, then the value of\n        <A>user_param</A> m\
ust be a list.\n      </Item>\n\n      <Mark><A>limit</A></Mark>\n      <Item>\
\n        This argument should be a positive integer or <K>infinity</K>.\n    \
    <C>CliquesFinder</C> will return after it has found\n        <A>limit</A> \
cliques or the search is complete.\n      </Item>\n\n      <Mark><A>include</A\
> and <A>exclude</A></Mark>\n      <Item>\n        These arguments should each\
 be a (possibly empty) duplicate-free list\n        of vertices of <A>digraph<\
/A> (i.e. positive integers less than the\n        number of vertices of <A>di\
graph</A>). <P/>\n\n        <C>CliquesFinder</C> will only look for cliques co\
ntaining all of the\n        vertices in <A>include</A> and containing none of\
 the vertices in\n        <A>exclude</A>. <P/>\n\n        Note that the search\
 may be much more efficient if each of these lists\n        is invariant under\
 the action of <C>G</C> on sets of vertices.\n      </Item>\n\n      <Mark><A>\
max</A></Mark>\n      <Item>\n        This argument should be <K>true</K> or <\
K>false</K>.  If <A>max</A> is\n        true then <C>CliquesFinder</C> will on\
ly search for <E>maximal</E>\n        cliques. If <K>max</K> is <K>false</K> t\
hen non-maximal cliques may be\n        found.\n      </Item>\n\n      <Mark><\
A>size</A></Mark>\n      <Item>\n        This argument should be <K>fail</K> o\
r a positive integer.\n        If <A>size</A> is a positive integer then <C>Cl\
iquesFinder</C> will\n        only search for cliques that contain precisely <\
A>size</A> vertices.\n        If <A>size</A> is <K>fail</K> then cliques of an\
y size may be found.\n      </Item>\n\n      <Mark><A>reps</A></Mark>\n      <\
Item>\n        This argument should be <K>true</K> or <K>false</K>.<P/>\n\n   \
     If <A>reps</A> is <K>true</K> then the arguments <A>include</A> and\n    \
    <A>exclude</A> are each required to be invariant under the action of\n    \
    <C>G</C> on sets of vertices.  In this case, <C>CliquesFinder</C> will\n  \
      find representatives of the orbits of the desired cliques under the\n   \
     action of <C>G</C>, <E>although representatives may be returned that\n   \
       are in the same orbit</E>.\n        If <A>reps</A> is false then <C>Cli\
quesFinder</C> will not take this into\n        consideration.<P/>\n\n        \
For a digraph such that <C>G</C> is non-trivial, the search for\n        cliqu\
e representatives can be much more efficient than the search for\n        all \
cliques.\n      </Item>\n    </List>\n\n    This function uses a version of th\
e Bron-Kerbosch algorithm.\n    <Example><![CDATA[\ngap> D := CompleteDigraph(\
5);\n<immutable complete digraph with 5 vertices>\ngap> user_param := [];;\nga\
p> f := function(a, b)  # Calculate size of clique\n>   AddSet(user_param, Siz\
e(b));\n> end;;\ngap> CliquesFinder(D, f, user_param, infinity, [], [], false,\
 fail,\n>                  true);\n[ 1, 2, 3, 4, 5 ]\ngap> CliquesFinder(D, fa\
il, [], 5, [2, 4], [3], false, fail, false);\n[ [ 2, 4 ], [ 1, 2, 4 ], [ 2, 4,\
 5 ], [ 1, 2, 4, 5 ] ]\ngap> CliquesFinder(D, fail, [], 2, [2, 4], [3], false,\
 fail, false);\n[ [ 2, 4 ], [ 1, 2, 4 ] ]\ngap> CliquesFinder(D, fail, [], inf\
inity, [], [], true, 5, false);\n[ [ 1, 2, 3, 4, 5 ] ]\ngap> CliquesFinder(D, \
fail, [], infinity, [1, 3], [], false, 3, false);\n[ [ 1, 2, 3 ], [ 1, 3, 4 ],\
 [ 1, 3, 5 ] ]\ngap> CliquesFinder(D, fail, [], infinity, [1, 3], [], true, 3,\
 false);\n[  ]\ngap> D := CompleteDigraph(IsMutableDigraph, 5);\n<mutable digr\
aph with 5 vertices, 20 edges>\ngap> user_param := [];;\ngap> f := function(a,\
 b)  # Calculate size of clique\n>   AddSet(user_param, Size(b));\n> end;;\nga\
p> CliquesFinder(D, f, user_param, infinity, [], [], false, fail,\n>          \
        true);\n[ 1, 2, 3, 4, 5 ]\ngap> CliquesFinder(D, fail, [], 5, [2, 4], \
[3], false, fail, false);\n[ [ 2, 4 ], [ 1, 2, 4 ], [ 2, 4, 5 ], [ 1, 2, 4, 5 \
] ]\ngap> CliquesFinder(D, fail, [], 2, [2, 4], [3], false, fail, false);\n[ [\
 2, 4 ], [ 1, 2, 4 ] ]\ngap> CliquesFinder(D, fail, [], infinity, [], [], true\
, 5, false);\n[ [ 1, 2, 3, 4, 5 ] ]\ngap> CliquesFinder(D, fail, [], infinity,\
 [1, 3], [], false, 3, false);\n[ [ 1, 2, 3 ], [ 1, 3, 4 ], [ 1, 3, 5 ] ]\ngap\
> CliquesFinder(D, fail, [], infinity, [1, 3], [], true, 3, false);\n[  ]]]></\
Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Func Name=\"\
DigraphClique\" Arg=\"digraph[, include[, exclude[, size]]]\"/>\n  <Func Name=\
\"DigraphMaximalClique\" Arg=\"digraph[, include[, exclude[,\n    size]]]\"/>\
\n  <Returns>An immutable list of positive integers, or <K>fail</K>.</Returns>\
\n  <Description>\n    If <A>digraph</A> is a digraph, then these functions re\
turns a clique\n    of <A>digraph</A> if one exists that satisfies the argumen\
ts, else it\n    returns <K>fail</K>.  A clique is defined by the set of verti\
ces that it\n    contains; see <Ref Oper=\"IsClique\"/> and <Ref Oper=\"IsMaxi\
malClique\"/>.<P/>\n\n    The optional arguments <A>include</A> and <A>exclude\
</A> must each be a\n    (possibly empty) duplicate-free list of vertices of <\
A>digraph</A>, and\n    the optional argument <A>size</A> must be a positive i\
nteger.  By default,\n    <A>include</A> and <A>exclude</A> are empty. These f\
unctions will search for\n    a clique of <A>digraph</A> that includes the ver\
tices of <A>include</A>\n    but does not include any vertices in <A>exclude</\
A>; if the argument\n    <A>size</A> is supplied, then additionally the clique\
 will be required to\n    contain precisely <A>size</A> vertices.<P/>\n\n    I\
f <A>include</A> is not a clique, then these functions return <K>fail</K>.\n  \
  Otherwise, the functions behave in the following way, depending on the\n    \
number of arguments:\n\n    <List>\n      <Mark>One or two arguments</Mark>\n \
     <Item>\n        If one or two arguments are supplied, then <C>DigraphCliq\
ue</C> and\n        <C>DigraphMaximalClique</C> greedily enlarge the clique <A\
>include</A>\n        until it can not continue.  The result is guaranteed to \
be a maximal\n        clique. This may or may not return an answer more quickl\
y than using\n        <Ref Func=\"DigraphMaximalCliques\"/>.  with a limit of \
1.\n      </Item>\n      <Mark>Three arguments</Mark>\n      <Item>\n        I\
f three arguments are supplied, then <C>DigraphClique</C> greedily\n        en\
larges the clique <A>include</A> until it can not continue, although\n        \
this clique may not be maximal.<P/>\n\n        Given three arguments, <C>Digra\
phMaximalClique</C> returns the maximal\n        clique returned by <C>Digraph\
MaximalCliques(</C><A>digraph</A><C>,\n        </C><A>include</A><C>, </C><A>e\
xclude</A><C>, 1)</C> if one exists,\n        else <K>fail</K>.\n      </Item>\
\n      <Mark>Four arguments</Mark>\n      <Item>\n        If four arguments a\
re supplied, then <C>DigraphClique</C> returns the\n        clique returned by\
 <C>DigraphCliques(</C><A>digraph</A><C>,\n          </C><A>include</A><C>, </\
C><A>exclude</A><C>, 1,\n        </C><A>size</A><C>)</C> if one exists, else <\
K>fail</K>. This clique may\n        not be maximal.<P/> Given four arguments,\
 <C>DigraphMaximalClique</C>\n        returns the maximal clique returned by\n\
        <C>DigraphMaximalCliques(</C><A>digraph</A><C>, </C><A>include</A><C>,\
\n        </C><A>exclude</A><C>, 1, </C><A>size</A><C>)</C> if one exists, els\
e\n        <K>fail</K>.\n      </Item>\n    </List>\n\n    <Example><![CDATA[\
\ngap> D := Digraph([[2, 3, 4], [1, 3], [1, 2], [1, 5], []]);\n<immutable digr\
aph with 5 vertices, 9 edges>\ngap> IsSymmetricDigraph(D);\nfalse\ngap> Digrap\
hClique(D);\n[ 5 ]\ngap> DigraphMaximalClique(D);\n[ 5 ]\ngap> DigraphClique(D\
, [1, 2]);\n[ 1, 2, 3 ]\ngap> DigraphMaximalClique(D, [1, 3]);\n[ 1, 3, 2 ]\ng\
ap> DigraphClique(D, [1], [2]);\n[ 1, 4 ]\ngap> DigraphMaximalClique(D, [1], [\
3, 4]);\nfail\ngap> DigraphClique(D, [1, 5]);\nfail\ngap> DigraphClique(D, [],\
 [], 2);\n[ 1, 2 ]\ngap> D := Digraph(IsMutableDigraph,\n>                 [[2\
, 3, 4], [1, 3], [1, 2], [1, 5], []]);\n<mutable digraph with 5 vertices, 9 ed\
ges>\ngap> IsSymmetricDigraph(D);\nfalse\ngap> DigraphClique(D);\n[ 5 ]]]></Ex\
ample>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Func Name=\"Di\
graphMaximalCliques\" Arg=\"digraph[, include[, exclude[, limit[, size]]]]\"/>\
\n  <Func Name=\"DigraphMaximalCliquesReps\" Arg=\"digraph[, include[, exclude\
[,\n    limit[, size]]]]\"/>\n  <Func Name=\"DigraphCliques\" Arg=\"digraph[, \
include[, exclude[,\n    limit[, size]]]]\"/>\n  <Func Name=\"DigraphCliquesRe\
ps\" Arg=\"digraph[, include[,\n    exclude[, limit[, size]]]]\"/>\n  <Attr Na\
me=\"DigraphMaximalCliquesAttr\" Arg=\"digraph\"/>\n  <Attr Name=\"DigraphMaxi\
malCliquesRepsAttr\" Arg=\"digraph\"/>\n  <Returns>An immutable list of lists \
of positive integers.</Returns>\n  <Description>\n    If <A>digraph</A> is dig\
raph, then these functions and attributes use <Ref\n      Func=\"CliquesFinder\
\"/> to return cliques of <A>digraph</A>. A\n    clique is defined by the set \
of vertices that it contains; see <Ref\n      Oper=\"IsClique\"/> and <Ref Ope\
r=\"IsMaximalClique\"/>.<P/>\n\n    The optional arguments <A>include</A> and \
<A>exclude</A> must each be a\n    (possibly empty) list of vertices of <A>dig\
raph</A>, the optional argument\n    <A>limit</A> must be either a positive in\
teger or <C>infinity</C>, and the\n    optional argument <A>size</A> must be a\
 positive integer.  If not\n    specified, then <A>include</A> and <A>exclude<\
/A> are chosen to be empty\n    lists, and <A>limit</A> is set to <C>infinity<\
/C>. <P/>\n\n    The functions will return as many suitable cliques as possibl\
e, up to the\n    number <A>limit</A>.  These functions will find cliques that\
 contain all\n    of the vertices of <A>include</A> but do not contain any of \
the\n    vertices of <A>exclude</A>.  The argument <A>size</A> restricts the s\
earch\n    to those cliques that contain precisely <A>size</A> vertices.\n    \
If the function or attribute has <C>Maximal</C> in its name, then only\n    ma\
ximal cliques will be returned; otherwise non-maximal cliques may be\n    retu\
rned. <P/>\n\n    Let <C>G</C> denote the automorphism group of maximal symmet\
ric subdigraph\n    of <A>digraph</A> without loops (see <Ref Attr=\"Automorph\
ismGroup\"\n      Label=\"for a digraph\"/> and <Ref\n      Oper=\"MaximalSymm\
etricSubdigraphWithoutLoops\"/>).\n\n    <List>\n      <Mark>Distinct cliques<\
/Mark>\n      <Item>\n        <C>DigraphMaximalCliques</C> and <C>DigraphCliqu\
es</C> each return a\n        duplicate-free list of at most <A>limit</A> cliq\
ues of <A>digraph</A>\n        that satisfy the arguments.<P/>\n\n        The \
computation may be significantly faster if <A>include</A> and\n        <A>excl\
ude</A> are invariant under the action of <C>G</C>\n        on sets of vertice\
s.\n      </Item>\n\n      <Mark>Orbit representatives of cliques</Mark>\n    \
  <Item>\n        To use <C>DigraphMaximalCliquesReps</C> or <C>DigraphCliques\
Reps</C>,\n        the arguments <A>include</A> and <A>exclude</A> must each b\
e invariant\n        under the action of <C>G</C> on sets of vertices.<P/>\n\n\
        If this is the case, then <C>DigraphMaximalCliquesReps</C> and\n      \
  <C>DigraphCliquesReps</C> each return a duplicate-free list of at most\n    \
    <A>limit</A> orbits representatives (under the action of <C>G</C> on\n    \
    sets vertices) of cliques of <A>digraph</A> that satisfy the\n        argu\
ments.<P/>\n\n        The representatives are not guaranteed to be in distinct\
 orbits.\n        However, if fewer than <A>lim</A> results are returned, then\
 there\n        will be at least one representative from each orbit of maximal\
 cliques.\n      </Item>\n    </List>\n\n    <Example><![CDATA[\ngap> D := Dig\
raph([\n> [2, 3], [1, 3], [1, 2, 4], [3, 5, 6], [4, 6], [4, 5]]);\n<immutable \
digraph with 6 vertices, 14 edges>\ngap> IsSymmetricDigraph(D);\ntrue\ngap> G \
:= AutomorphismGroup(D);\nGroup([ (5,6), (1,2), (1,5)(2,6)(3,4) ])\ngap> Digra\
phMaximalCliques(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 3, 4 ] ]\ngap> DigraphMaxi\
malCliquesReps(D);\n[ [ 1, 2, 3 ], [ 3, 4 ] ]\ngap> Orbit(G, [1, 2, 3], OnSets\
);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ] ]\ngap> Orbit(G, [3, 4], OnSets);\n[ [ 3, 4 ] ]\
\ngap> DigraphMaximalCliquesReps(D, [3, 4], [], 1);\n[ [ 3, 4 ] ]\ngap> Digrap\
hMaximalCliques(D, [1, 2], [5, 6], 1, 2);\n[  ]\ngap> DigraphCliques(D, [1], [\
5, 6], infinity, 2);\n[ [ 1, 2 ], [ 1, 3 ] ]\ngap> D := Digraph(IsMutableDigra\
ph, [\n> [2, 3], [1, 3], [1, 2, 4], [3, 5, 6], [4, 6], [4, 5]]);\n<mutable dig\
raph with 6 vertices, 14 edges>\ngap> IsSymmetricDigraph(D);\ntrue\ngap> G := \
AutomorphismGroup(D);\nGroup([ (5,6), (1,2), (1,5)(2,6)(3,4) ])\ngap> DigraphM\
aximalCliques(D);\n[ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 3, 4 ] ]]]></Example>\n  </De\
scription>\n</ManSection>\n\n    <ManSection>\n  <Attr Name=\"CliqueNumber\" A\
rg=\"digraph\"/>\n  <Returns>A non-negative integer.</Returns>\n  <Description\
>\n    If <A>digraph</A> is a digraph, then <C>CliqueNumber(<A>digraph</A>)</C\
>\n    returns the largest integer <C>n</C> such that <A>digraph</A> contains \
a\n    clique with <C>n</C> vertices as an induced subdigraph.\n    <P/>\n\n  \
  A <E>clique</E> of a digraph is a set of mutually adjacent vertices of the\n\
    digraph. Loops and multiple edges are ignored for the purpose of\n    dete\
rmining the clique number of a digraph. \n    <Example><![CDATA[\ngap> D := Co\
mpleteDigraph(4);;\ngap> CliqueNumber(D);\n4\ngap> D := Digraph([[1, 2, 4, 4],\
 [1, 3, 4], [2, 1], [1, 2]]);\n<immutable multidigraph with 4 vertices, 11 edg\
es>\ngap> CliqueNumber(D);\n3\ngap> D := CompleteDigraph(IsMutableDigraph, 4);\
;\ngap> CliqueNumber(D);\n4]]></Example>\n</Description>\n</ManSection>\n\n  <\
/Section>\n\n  <Section><Heading>Finding independent sets</Heading>\n    <ManS\
ection>\n  <Oper Name=\"IsIndependentSet\" Arg=\"digraph, l\"/>\n  <Oper Name=\
\"IsMaximalIndependentSet\" Arg=\"digraph, l\"/>\n  <Returns><K>true</K> or <K\
>false</K>.</Returns>\n  <Description>\n    If <A>digraph</A> is a digraph and\
 <A>l</A> is a duplicate-free list of\n    vertices of <A>digraph</A>, then\n \
   <C>IsIndependentSet(</C><A>digraph</A><C>,</C><A>l</A><C>)</C> returns\n   \
 <K>true</K> if <A>l</A> is an <E>independent set</E> of <A>digraph</A> and\n \
   <K>false</K> if it is not.  Similarly,\n    <C>IsMaximalIndependentSet(</C>\
<A>digraph</A><C>,</C><A>l</A><C>)</C>\n    returns <K>true</K> if <A>l</A> is\
 a <E>maximal independent set</E> of\n    <A>digraph</A> and <K>false</K> if i\
t is not.  <P/>\n\n    An <E>independent set</E> of a digraph is a set of mutu\
ally non-adjacent\n    vertices of the digraph. A <E>maximal independent set</\
E> is an independent\n    set that is not properly contained in another indepe\
ndent set. An\n    independent set is permitted, but not required, to contain \
vertices at\n    which there is a loop.\n    <Example><![CDATA[\ngap> D := Cyc\
leDigraph(4);;\ngap> IsIndependentSet(D, [1]);\ntrue\ngap> IsMaximalIndependen\
tSet(D, [1]);\nfalse\ngap> IsIndependentSet(D, [1, 4, 3]);\nfalse\ngap> IsInde\
pendentSet(D, [2, 4]);\ntrue\ngap> IsMaximalIndependentSet(D, [2, 4]);\ntrue\n\
gap> D := CycleDigraph(IsMutableDigraph, 4);;\ngap> IsIndependentSet(D, [1]);\
\ntrue]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <F\
unc Name=\"DigraphIndependentSet\"\n    Arg=\"digraph[, include[, exclude[, si\
ze]]]\"/>\n  <Func Name=\"DigraphMaximalIndependentSet\"\n    Arg=\"digraph[, \
include[, exclude[,\n    size]]]\"/>\n  <Returns>An immutable list of positive\
 integers, or <K>fail</K>.</Returns>\n  <Description>\n    If <A>digraph</A> i\
s a digraph, then these functions returns an independent\n    set of <A>digrap\
h</A> if one exists that satisfies the arguments, else it\n    returns <K>fail\
</K>.  An independent set is defined by the set of vertices\n    that it conta\
ins; see <Ref Oper=\"IsIndependentSet\"/> and <Ref\n      Oper=\"IsMaximalInde\
pendentSet\"/>.<P/>\n\n    The optional arguments <A>include</A> and <A>exclud\
e</A> must each be a\n    (possibly empty) duplicate-free list of vertices of \
<A>digraph</A>, and the\n    optional argument <A>size</A> must be a positive \
integer.  By default,\n    <A>include</A> and <A>exclude</A> are empty. These \
functions will search\n    for an independent set of <A>digraph</A> that inclu\
des the vertices of\n    <A>include</A> but does not include any vertices in <\
A>exclude</A>;\n    if the argument <A>size</A> is supplied, then additionally\
 the independent\n    set will be required to contain precisely <A>size</A> ve\
rtices.<P/>\n\n    If <A>include</A> is not an independent set, then these fun\
ctions return\n    <K>fail</K>.  Otherwise, the functions behave in the follow\
ing way,\n    depending on the number of arguments:\n\n    <List>\n      <Mark\
>One or two arguments</Mark>\n      <Item>\n        If one or two arguments ar\
e supplied, then <C>DigraphIndependentSet</C>\n        and <C>DigraphMaximalIn\
dependentSet</C> greedily enlarge the\n        independent set <A>include</A> \
until it can not continue.  The result\n        is guaranteed to be a maximal \
independent set. This may or may not\n        return an answer more quickly th\
an using <Ref\n          Func=\"DigraphMaximalIndependentSets\"/>.  with a lim\
it of 1.\n      </Item>\n      <Mark>Three arguments</Mark>\n      <Item>\n   \
     If three arguments are supplied, then <C>DigraphIndependentSet</C>\n     \
   greedily enlarges the independent set <A>include</A> until it can not\n    \
    continue, although this independent set may not be maximal.<P/>\n\n       \
 Given three arguments, <C>DigraphMaximalIndependentSet</C> returns the\n     \
   maximal independent set returned by\n        <C>DigraphMaximalIndependentSe\
ts(</C><A>digraph</A><C>,\n        </C><A>include</A><C>, </C><A>exclude</A><C\
>, 1)</C> if one exists,\n        else <K>fail</K>.\n      </Item>\n      <Mar\
k>Four arguments</Mark>\n      <Item>\n        If four arguments are supplied,\
 then <C>DigraphIndependentSet</C>\n        returns the independent set return\
ed by\n        <C>DigraphIndependentSets(</C><A>digraph</A><C>, </C><A>include\
</A><C>,\n        </C><A>exclude</A><C>, 1, </C><A>size</A><C>)</C> if one exi\
sts, else\n        <K>fail</K>. This independent set may not be maximal.<P/> G\
iven four\n        arguments, <C>DigraphMaximalIndependentSet</C> returns the \
maximal\n        independent set returned by\n        <C>DigraphMaximalIndepen\
dentSets(</C><A>digraph</A><C>,\n          </C><A>include</A><C>, </C><A>exclu\
de</A><C>, 1,\n        </C><A>size</A><C>)</C> if one exists, else <K>fail</K>\
.\n      </Item>\n    </List>\n    <Example><![CDATA[\ngap> D := ChainDigraph(\
6);\n<immutable chain digraph with 6 vertices>\ngap> DigraphIndependentSet(D);\
\n[ 6, 4, 2 ]\ngap> DigraphMaximalIndependentSet(D);\n[ 6, 4, 2 ]\ngap> Digrap\
hIndependentSet(D, [2, 4]);\n[ 2, 4, 6 ]\ngap> DigraphMaximalIndependentSet(D,\
 [1, 3]);\n[ 1, 3, 6 ]\ngap> DigraphIndependentSet(D, [2, 4], [6]);\n[ 2, 4 ]\
\ngap> DigraphMaximalIndependentSet(D, [2, 4], [6]);\nfail\ngap> DigraphIndepe\
ndentSet(D, [1], [], 2);\n[ 1, 3 ]\ngap> DigraphMaximalIndependentSet(D, [1], \
[], 2);\nfail\ngap> DigraphMaximalIndependentSet(D, [1], [], 3);\n[ 1, 3, 5 ]\
\ngap> D := ChainDigraph(IsMutableDigraph, 6);\n<mutable digraph with 6 vertic\
es, 5 edges>\ngap> DigraphIndependentSet(D);\n[ 6, 4, 2 ]\ngap> DigraphMaximal\
IndependentSet(D);\n[ 6, 4, 2 ]\ngap> DigraphIndependentSet(D, [2, 4]);\n[ 2, \
4, 6 ]\ngap> DigraphMaximalIndependentSet(D, [1, 3]);\n[ 1, 3, 6 ]\ngap> Digra\
phIndependentSet(D, [2, 4], [6]);\n[ 2, 4 ]\ngap> DigraphMaximalIndependentSet\
(D, [2, 4], [6]);\nfail\ngap> DigraphIndependentSet(D, [1], [], 2);\n[ 1, 3 ]\
\ngap> DigraphMaximalIndependentSet(D, [1], [], 2);\nfail\ngap> DigraphMaximal\
IndependentSet(D, [1], [], 3);\n[ 1, 3, 5 ]]]></Example>\n  </Description>\n</\
ManSection>\n\n    <ManSection>\n  <Func Name=\"DigraphMaximalIndependentSets\
\" Arg=\"digraph[, include[, exclude[,\n    limit[, size]]]]\"/>\n  <Func Name\
=\"DigraphMaximalIndependentSetsReps\" Arg=\"digraph[, include[,\n    exclude[\
, limit[, size]]]]\"/>\n  <Func Name=\"DigraphIndependentSets\" Arg=\"digraph[\
, include[,\n    exclude[, limit[, size]]]]\"/>\n  <Func Name=\"DigraphIndepen\
dentSetsReps\" Arg=\"digraph[, include[,\n    exclude[, limit[, size]]]]\"/>\n\
  <Attr Name=\"DigraphMaximalIndependentSetsAttr\" Arg=\"digraph\"/>\n  <Attr \
Name=\"DigraphMaximalIndependentSetsRepsAttr\" Arg=\"digraph\"/>\n  <Returns>A\
n immutable list of lists of positive integers.</Returns>\n  <Description>\n  \
  If <A>digraph</A> is digraph, then these functions and attributes use <Ref\n\
      Func=\"CliquesFinder\"/> to return independent sets of <A>digraph</A>. A\
n\n    independent set is defined by the set of vertices that it contains; see\
\n    <Ref Oper=\"IsMaximalIndependentSet\"/> and <Ref\n      Oper=\"IsIndepen\
dentSet\"/>.<P/>\n\n    The optional arguments <A>include</A> and <A>exclude</\
A> must each be a\n    (possibly empty) list of vertices of <A>digraph</A>, th\
e optional argument\n    <A>limit</A> must be either a positive integer or <C>\
infinity</C>, and the\n    optional argument <A>size</A> must be a positive in\
teger.  If not\n    specified, then <A>include</A> and <A>exclude</A> are chos\
en to be empty\n    lists, and <A>limit</A> is set to <C>infinity</C>. <P/>\n\
\n    The functions will return as many suitable independent sets as possible,\
 up\n    to the number <A>limit</A>.  These functions will find independent se\
ts\n    that contain all of the vertices of <A>include</A> but do not\n    con\
tain any of the vertices of <A>exclude</A> The argument <A>size</A>\n    restr\
icts the search to those cliques that contain precisely <A>size</A>\n    verti\
ces.  If the function or attribute has <C>Maximal</C> in its name,\n    then o\
nly maximal independent sets will be returned; otherwise non-maximal\n    inde\
pendent sets may be returned.\n    <P/>\n\n    Let <C>G</C> denote the <Ref At\
tr=\"AutomorphismGroup\" Label=\"for a digraph\"/>\n    of the <Ref Oper=\"Dig\
raphSymmetricClosure\"/> of the digraph formed from\n    <A>digraph</A> by rem\
oving loops and ignoring the multiplicity of edges.\n\n    <List>\n      <Mark\
>Distinct independent sets</Mark>\n      <Item>\n        <C>DigraphMaximalInde\
pendentSets</C> and <C>DigraphIndependentSets</C>\n        each return a dupli\
cate-free list of at most <A>limit</A> independent\n        sets of <A>digraph\
</A> that satisfy the arguments.<P/>\n\n        The computation may be signifi\
cantly faster if <A>include</A> and\n        <A>exclude</A> are invariant unde\
r the action of <C>G</C> on sets of\n        vertices.\n      </Item>\n\n     \
 <Mark>Representatives of distinct orbits of independent sets</Mark>\n      <I\
tem>\n        To use <C>DigraphMaximalIndependentSetsReps</C> or\n        <C>D\
igraphIndependentSetsReps</C>, the arguments <A>include</A> and\n        <A>ex\
clude</A> must each be invariant under the action of <C>G</C> on\n        sets\
 of vertices.<P/>\n\n        If this is the case, then <C>DigraphMaximalIndepe\
ndentSetsReps</C> and\n        <C>DigraphIndependentSetsReps</C> each return a\
 list of\n        at most <A>limit</A> orbits representatives (under the actio\
n of\n        <C>G</C> on sets of vertices) of independent sets of <A>digraph<\
/A>\n        that satisfy the arguments. <P/>\n\n        The representatives a\
re not guaranteed to be in distinct orbits.\n        However, if <A>lim</A> is\
 not specified, or fewer than <A>lim</A>\n        results are returned, then t\
here will be at least one representative\n        from each orbit of maximal i\
ndependent sets.\n      </Item>\n    </List>\n\n    <Example><![CDATA[\ngap> D\
 := CycleDigraph(5);\n<immutable cycle digraph with 5 vertices>\ngap> DigraphM\
aximalIndependentSetsReps(D);\n[ [ 1, 3 ] ]\ngap> DigraphIndependentSetsReps(D\
);\n[ [ 1 ], [ 1, 3 ] ]\ngap> Set(DigraphMaximalIndependentSets(D));\n[ [ 1, 3\
 ], [ 1, 4 ], [ 2, 4 ], [ 2, 5 ], [ 3, 5 ] ]\ngap> DigraphMaximalIndependentSe\
ts(D, [1]);\n[ [ 1, 3 ], [ 1, 4 ] ]\ngap> DigraphIndependentSets(D, [], [4, 5]\
);\n[ [ 1 ], [ 2 ], [ 3 ], [ 1, 3 ] ]\ngap> DigraphIndependentSets(D, [], [4, \
5], 1, 2);\n[ [ 1, 3 ] ]\ngap> D := CycleDigraph(IsMutableDigraph, 5);\n<mutab\
le digraph with 5 vertices, 5 edges>\ngap> DigraphMaximalIndependentSetsReps(D\
);\n[ [ 1, 3 ] ]\ngap> DigraphIndependentSetsReps(D);\n[ [ 1 ], [ 1, 3 ] ]\nga\
p> Set(DigraphMaximalIndependentSets(D));\n[ [ 1, 3 ], [ 1, 4 ], [ 2, 4 ], [ 2\
, 5 ], [ 3, 5 ] ]\ngap> DigraphMaximalIndependentSets(D, [1]);\n[ [ 1, 3 ], [ \
1, 4 ] ]\ngap> DigraphIndependentSets(D, [], [4, 5]);\n[ [ 1 ], [ 2 ], [ 3 ], \
[ 1, 3 ] ]\ngap> DigraphIndependentSets(D, [], [4, 5], 1, 2);\n[ [ 1, 3 ] ]]]>\
</Example>\n  </Description>\n</ManSection>\n\n  </Section>\n</Chapter>\n <!--\
 cliques -->\n  <Chapter Label=\"Visualising and IO\"><Heading>Visualising and\
 IO</Heading>\n\n  <Section><Heading>Visualising a digraph</Heading>\n      <M\
anSection>\n    <Func Name=\"Splash\" Arg=\"str, [opts]\"/>\n    <Returns>Noth\
ing.</Returns>\n    <Description>\n      This function attempts to convert the\
 string <A>str</A> into a pdf\n      document and open this document, i.e. to \
splash it all over your monitor.<P/>\n\n      The string <A>str</A> must corre\
spond to a valid <C>dot</C> or\n      <C>LaTeX</C> text file and you must have\
 have <C>GraphViz</C> and\n      <C>pdflatex</C> installed on your computer.  \
For details about these file\n      formats, see <URL>http://www.latex-project\
.org</URL> and\n      <URL>http://www.graphviz.org</URL>.<P/>\n\n      This fu\
nction is provided to allow convenient, immediate viewing of the\n      pictur\
es produced by the function <Ref Attr=\"DotDigraph\"/>.<P/>\n\n      The optio\
nal second argument <A>opts</A> should be a record with\n      components corr\
esponding to various options, given below.\n\n      <List>\n        <Mark>path\
</Mark>\n        <Item>\n          this should be a string representing the pa\
th to the directory where\n          you want <C>Splash</C> to do its work. Th\
e default value of this\n          option is <C>\"~/\"</C>.\n        </Item>\n\
\n        <Mark>directory</Mark>\n        <Item>\n          this should be a s\
tring representing the name of the directory in\n          <C>path</C> where y\
ou want <C>Splash</C> to do its work. This function\n          will create thi\
s directory if does not already exist. <P/>\n\n          The default value of \
this option is <C>\"tmp.viz\"</C> if the option\n          <C>path</C> is pres\
ent, and the result of\n          <Ref Func=\"DirectoryTemporary\" BookName=\"\
ref\"/> is used otherwise.\n        </Item>\n\n        <Mark>filename</Mark>\n\
        <Item>\n          this should be a string representing the name of the\
 file where\n          <A>str</A> will be written.  The default value of this \
option is\n          <C>\"vizpicture\"</C>.\n        </Item>\n\n        <Mark>\
viewer</Mark>\n        <Item>\n          this should be a string representing \
the name of the program which\n          should open the files produced by <C>\
GraphViz</C> or <C>pdflatex</C>.\n        </Item>\n\n        <Mark>type</Mark>\
\n        <Item>\n          this option can be used to specify that the string\
 <A>str</A> contains\n          a &LaTeX; or <C>dot</C> document. You can spec\
ify this option in\n          <A>str</A> directly by making the first line <C>\
\"%latex\"</C> or\n          <C>\"//dot\"</C>.  There is no default value for \
this option, this\n          option must be specified in <A>str</A> or in <A>o\
pt.type</A>.\n        </Item>\n\n        <Mark>engine</Mark>\n        <Item>\n\
          this option can be used to specify the GraphViz engine to use\n     \
     to render a <C>dot</C> document. The valid choices are <C>\"dot\"</C>,\n \
         <C>\"neato\"</C>, <C>\"circo\"</C>, <C>\"twopi\"</C>, <C>\"fdp\"</C>,\
\n          <C>\"sfdp\"</C>, and <C>\"patchwork\"</C>. Please refer to the\n  \
        GraphViz documentation for details on these engines.\n          The de\
fault value for this option is <C>\"dot\"</C>, and it\n          must be speci\
fied in <A>opt.engine</A>.\n        </Item>\n\n        <Mark>filetype</Mark>\n\
        <Item>\n          this should be a string representing the type of fil\
e which\n          <C>Splash</C> should produce. For &LaTeX; files, this optio\
n is\n          ignored and the default value <C>\"pdf\"</C> is used.\n       \
 </Item>\n      </List>\n\n      This function was written by Attila Egri-Nagy\
 and Manuel Delgado with some\n      minor changes by J. D. Mitchell.<P/>\n   \
   <Log><![CDATA[\ngap> Splash(DotDigraph(RandomDigraph(4)));\n]]></Log>\n    \
</Description>\n  </ManSection>\n\n      <ManSection>\n    <Attr Name=\"DotDig\
raph\" Arg=\"digraph\"/>\n    <Oper Name=\"DotColoredDigraph\" Arg=\"digraph, \
vert, edge\"/>\n    <Oper Name=\"DotVertexLabelledDigraph\" Arg=\"digraph\"/>\
\n    <Oper Name=\"DotVertexColoredDigraph\" Arg=\"digraph, vert\"/>\n    <Ope\
r Name=\"DotEdgeColoredDigraph\" Arg=\"digraph, edge\"/>\n    <Returns>A strin\
g.</Returns>\n    <Description>\n      <C>DotDigraph</C> produces a graphical \
representation of the digraph\n      <A>digraph</A>. Vertices are displayed as\
 circles, numbered consistently\n      with <A>digraph</A>. Edges are displaye\
d as arrowed lines between\n      vertices, with the arrowhead of each line po\
inting towards the range\n      of the edge.<P/>\n\n      <C>DotColoredDigraph\
</C> differs from <C>DotDigraph</C> only in\n      that the values in given in\
 the two lists are used to color the vertices and\n      edges of the graph wh\
en displayed. The list for vertex colours should be\n      a list of length eq\
ual to the number of vertices, containing strings that\n      are accepted by \
the graphviz software, which is the one used for graph\n      representation. \
The list for edge colours should be a list of lists\n      with the same shape\
 of the outneighbours of the digraph that contains strings \n      that corres\
pond to colours accepted by the graphviz software. If the lists \n      are no\
t the appropriate size, or have holes then the function will return\n      an \
error.<P/>\n\n      <C>DotVertexColoredDigraph</C> differs from <C>DotDigraph<\
/C> only in\n      that the values in given in the list are used to color the \
vertices\n      of the graph when displayed. The list for vertex colours shoul\
d be\n      a list of length equal to the number of vertices, containing strin\
gs that\n      are accepted by the graphviz software, which is the one used fo\
r graph\n      representation. If the list is not the appropriate size, or has\
 holes \n      then the function will return an error.<P/>\n\n      <C>DotEdge\
ColoredDigraph</C> differs from <C>DotDigraph</C> only in\n      that the valu\
es in given in the list are used to color the vertices and\n      edges of the\
 graph when displayed. The list for edge colours should be a list\n      of li\
sts with the same shape of the outneighbours of the digraph that contains\n   \
   strings that correspond to colours accepted by the graphviz software. If th\
e \n      list is not the appropriate size, or has holes then the function wil\
l return\n      an error.<P/>\n\n      <C>DotVertexLabelledDigraph</C> differs\
 from <C>DotDigraph</C> only in\n      that the values in <Ref Oper=\"DigraphV\
ertexLabels\"/> are used to label\n      the vertices in the produced picture \
rather than the numbers <C>1</C> to\n      the number of vertices of the digra\
ph. <P/>\n\n      The output is in <C>dot</C> format (also known as <C>GraphVi\
z</C>)\n      format. For details about this file format, and information abou\
t how to\n      display or edit this format see <URL>http://www.graphviz.org</\
URL>. <P/>\n\n      The string returned by <C>DotDigraph</C> or\n      <C>DotV\
ertexLabelledDigraph</C> can be written to a file using\n      the command <Re\
f Func=\"FileString\" BookName=\"GAPDoc\"/>.<P/>\n      <Log><![CDATA[\ngap> a\
dj := List([1 .. 4], x -> [1, 1, 1, 1]);\n[ [ 1, 1, 1, 1 ], [ 1, 1, 1, 1 ], [ \
1, 1, 1, 1 ], [ 1, 1, 1, 1 ] ]\ngap> adj[1][3] := 0;\n0\ngap> gr := DigraphByA\
djacencyMatrix(adj);\n<immutable digraph with 4 vertices, 15 edges>\ngap> D :=\
 CompleteDigraph(4);\n<immutable complete digraph with 4 vertices>\ngap> vertc\
olors := [];;\ngap> vertcolors[1] := \"blue\";; vertcolors[2] := \"red\";; \ng\
ap> vertcolors[3] := \"green\";; vertcolors[4] := \"yellow\";;\ngap> edgecolor\
s := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [];;\ngap> edgecolors[3\
] := [];; edgecolors[4] := [];; \ngap> edgecolors[1][2] := \"lightblue\";;\nga\
p> edgecolors[1][3] := \"pink\";;\ngap> edgecolors[1][4] := \"purple\";;\ngap>\
 edgecolors[2][1] := \"lightblue\";;\ngap> edgecolors[2][3] := \"pink\";; \nga\
p> edgecolors[2][4] := \"purple\";; \ngap> edgecolors[3][1] := \"lightblue\";;\
 \ngap> edgecolors[3][2] := \"pink\";; \ngap> edgecolors[3][4] := \"purple\";;\
\ngap> edgecolors[4][1] := \"lightblue\";; \ngap> edgecolors[4][2] := \"pink\"\
;;\ngap> edgecolors[4][3] := \"purple\";;\ngap> Print(DotColoredDigraph(D, ver\
tcolors, edgecolors));\n//dot\ndigraph hgn{\nnode [shape=circle]\n1[color=blue\
, style=filled]\n2[color=red, style=filled]\n3[color=green, style=filled]\n4[c\
olor=yellow, style=filled]\n1 -> 2[color=lightblue]\n1 -> 3[color=pink]\n1 -> \
4[color=purple]\n2 -> 1[color=lightblue]\n2 -> 3[color=pink]\n2 -> 4[color=pur\
ple]\n3 -> 1[color=lightblue]\n3 -> 2[color=pink]\n3 -> 4[color=purple]\n4 -> \
1[color=lightblue]\n4 -> 2[color=pink]\n4 -> 3[color=purple]\n}\ngap> D := Emp\
tyDigraph(3);\n<immutable empty digraph with 3 vertices>\ngap> vertcolors := [\
];;\ngap> vertcolors[1] := \"blue\";; vertcolors[2] := \"red\";;\ngap> vertcol\
ors[3] := \"green\";;\ngap> edgecolors := [];;\ngap> edgecolors[1] := [];; edg\
ecolors[2] := [];; \ngap> edgecolors[3] := [];;\ngap> Print(DotColoredDigraph(\
D, vertcolors, edgecolors));\n//dot\ndigraph hgn{\nnode [shape=circle]\n1[colo\
r=blue, style=filled]\n2[color=red, style=filled]\n3[color=green, style=filled\
]\n}\ngap> D := Digraph([[2], [1, 3], [2]]);\n<immutable digraph with 3 vertic\
es, 4 edges>\ngap> vertcolors := [];;\ngap> vertcolors[1] := \"blue\";;\ngap> \
vertcolors[2] := \"pink\";;\ngap> vertcolors[3] := \"purple\";;\ngap> edgecolo\
rs := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [];;\ngap> edgecolors[\
3] := [];;\ngap> edgecolors[1][2] := \"green\";; edgecolors[2][1] := \"green\"\
;;\ngap> edgecolors[2][3] := \"red\";; edgecolors[3][2] := \"red\";;\ngap> Pri\
nt(DotSymmetricColoredDigraph(D, vertcolors, edgecolors));\n//dot\ngraph hgn{\
\nnode [shape=circle]\n\n1[color=blue, style=filled]\n2[color=pink, style=fill\
ed]\n3[color=purple, style=filled]\n1 -- 2[color=green]\n2 -- 3[color=red]\n}\
\ngap> D := Digraph([[2, 3], [1, 3], [1]]);\n<immutable digraph with 3 vertice\
s, 5 edges>\ngap> vertcolors := [];;\ngap> vertcolors[1] := \"blue\";; vertcol\
ors[2] := \"red\";;\ngap> vertcolors[3] := \"green\";;\ngap> edgecolors := [];\
;\ngap> edgecolors[1] := [];; edgecolors[2] := [];;\ngap> edgecolors[3] := [];\
;\ngap> edgecolors[1][2] := \"orange\";; edgecolors[1][3] := \"yellow\";;\ngap\
> edgecolors[2][1] := \"orange\";; edgecolors[2][3] := \"pink\";;\ngap> edgeco\
lors[3][1] := \"yellow\";;\ngap> Print(DotColoredDigraph(D, vertcolors, edgeco\
lors));;\n//dot\ndigraph hgn{\nnode [shape=circle]\n1[color=blue, style=filled\
]\n2[color=red, style=filled]\n3[color=green, style=filled]\n1 -> 2[color=oran\
ge]\n1 -> 3[color=yellow]\n2 -> 1[color=orange]\n2 -> 3[color=pink]\n3 -> 1[co\
lor=yellow]\n}\ngap> D := Digraph(IsMutableDigraph, [[2, 3], [1, 3], [1]]);\n<\
mutable digraph with 3 vertices, 5 edges>\ngap> vertcolors := [];;\ngap> vertc\
olors[1] := \"blue\";; vertcolors[2] := \"red\";;\ngap> vertcolors[3] := \"gre\
en\";;\ngap> edgecolors := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [\
];;\ngap> edgecolors[3] := [];;\ngap> edgecolors[1][2] := \"orange\";; edgecol\
ors[1][3] := \"yellow\";;\ngap> edgecolors[2][1] := \"orange\";; edgecolors[2]\
[3] := \"pink\";;\ngap> edgecolors[3][1] := \"yellow\";;\ngap> Print(DotColore\
dDigraph(D, vertcolors, edgecolors));;\n//dot\ndigraph hgn{\nnode [shape=circl\
e]\n1[color=blue, style=filled]\n2[color=red, style=filled]\n3[color=green, st\
yle=filled]\n1 -> 2[color=orange]\n1 -> 3[color=yellow]\n2 -> 1[color=orange]\
\n2 -> 3[color=pink]\n3 -> 1[color=yellow]\n}\ngap> D;\n<mutable digraph with \
3 vertices, 5 edges>\ngap> DotSymmetricDigraph(gr2){[12 .. 70]};\n\" hgn{\\nno\
de [shape=circle]\\n\\n1\\n2\\n3\\n4\\n1 -- 2\\n2 -- 3\\n3 -- 3\\n3 -\"\ngap> \
DotSymmetricDigraph(gr1);\nError, the argument <D> must be a symmetric digraph\
,\ngap> D := CompleteDigraph(4);\n<immutable complete digraph with 4 vertices>\
\ngap> vertcolors := [];;\ngap> vertcolors[1] := \"blue\";; vertcolors[2] := \
\"red\";; \ngap> vertcolors[3] := \"green\";; vertcolors[4] := \"yellow\";;\ng\
ap> Print(DotVertexColoredDigraph(D, vertcolors));\n//dot\ndigraph hgn{\nnode \
[shape=circle]\n1[color=blue, style=filled]\n2[color=red, style=filled]\n3[col\
or=green, style=filled]\n4[color=yellow, style=filled]\n1 -> 2\n1 -> 3\n1 -> 4\
\n2 -> 1\n2 -> 3\n2 -> 4\n3 -> 1\n3 -> 2\n3 -> 4\n4 -> 1\n4 -> 2\n4 -> 3\n}\ng\
ap> D := CompleteDigraph(4);\n<immutable complete digraph with 4 vertices>\nga\
p> edgecolors := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [];;\ngap> \
edgecolors[3] := [];; edgecolors[4] := [];; \ngap> edgecolors[1][2] := \"light\
blue\";;\ngap> edgecolors[1][3] := \"pink\";;\ngap> edgecolors[1][4] := \"purp\
le\";;\ngap> edgecolors[2][1] := \"lightblue\";;\ngap> edgecolors[2][3] := \"p\
ink\";; \ngap> edgecolors[2][4] := \"purple\";; \ngap> edgecolors[3][1] := \"l\
ightblue\";; \ngap> edgecolors[3][2] := \"pink\";; \ngap> edgecolors[3][4] := \
\"purple\";;\ngap> edgecolors[4][1] := \"lightblue\";; \ngap> edgecolors[4][2]\
 := \"pink\";;\ngap> edgecolors[4][3] := \"purple\";;\ngap> Print(DotEdgeColor\
edDigraph(D, edgecolors));\n//dot\ndigraph hgn{\nnode [shape=circle]\n1\n2\n3\
\n4\n1 -> 2[color=lightblue]\n1 -> 3[color=pink]\n1 -> 4[color=purple]\n2 -> 1\
[color=lightblue]\n2 -> 3[color=pink]\n2 -> 4[color=purple]\n3 -> 1[color=ligh\
tblue]\n3 -> 2[color=pink]\n3 -> 4[color=purple]\n4 -> 1[color=lightblue]\n4 -\
> 2[color=pink]\n4 -> 3[color=purple]\n}\ngap> FileString(\"dot/k4.dot\", DotD\
igraph(gr));\n154]]></Log>\n    </Description>\n  </ManSection>\n\n      <ManS\
ection>\n    <Attr Name=\"DotSymmetricDigraph\" Arg=\"digraph\"/>\n    <Oper N\
ame=\"DotSymmetricColoredDigraph\" Arg=\"digraph, vert, edge\"/>\n    <Oper Na\
me=\"DotSymmetricVertexColoredDigraph\" Arg=\"digraph, vert\"/>\n    <Oper Nam\
e=\"DotSymmetricEdgeColoredDigraph\" Arg=\"digraph, edge\"/>\n    <Returns>A s\
tring.</Returns>\n    <Description>\n      This function produces a graphical \
representation of the symmetric\n      digraph <A>digraph</A>. <C>DotSymmetric\
Digraph</C> will return an\n      error if <A>digraph</A> is not a symmetric d\
igraph. See\n      <Ref Prop=\"IsSymmetricDigraph\"/>.<P/>\n\n      The functi\
on <C>DotSymmetricColoredDigraph</C> differs from <C>DotDigraph</C>\n      onl\
y in that the values given in the two lists are used to color the vertices\n  \
    and edges of the graph when displayed. The list for vertex colours should \
be\n      a list of length equal to the number of vertices, containing strings\
 that\n      are accepted by the graphviz software, which is the one used for \
graph\n      representation.  The list for edge colours should be a list of li\
sts\n      with the same shape of the outneighbours of the digraph that contai\
ns strings \n      that correspond to colours accepted by the graphviz softwar\
e.\n      If the list is not the appropriate size, or has holes then the funct\
ion\n      will return an error.  <P/>\n\n      The function <C>DotSymmetricVe\
rtexColoredDigraph</C> differs from <C>DotDigraph</C>\n      only in that the \
values in given in the list is used to color the vertices\n      of the graph \
when displayed. The list for vertex colours should be\n      a list of length \
equal to the number of vertices, containing strings that\n      are accepted b\
y the graphviz software, which is the one used for graph\n      representation\
. If the list is not the appropriate size, or has holes \n      then the funct\
ion will return an error.  <P/>\n\n      The function <C>DotSymmetricEdgeColor\
edDigraph</C> differs from <C>DotDigraph</C>\n      only in that the values gi\
ven in the list are used to color the edges\n      of the graph when displayed\
. The list for edge colours should be\n      a list of lists with the same sha\
pe of the outneighbours, containing strings that\n      are accepted by the gr\
aphviz software, which is the one used for graph\n      representation. If the\
 list is not the appropriate size, or has holes \n      then the function will\
 return an error.  <P/>\n\n      Vertices are displayed as circles, numbered c\
onsistently with\n      <A>digraph</A>. Since <A>digraph</A> is symmetric, for\
 every non-loop\n      edge there is a complementary edge with opposite source\
 and range.\n      <C>DotSymmetricDigraph</C> displays each pair of complement\
ary edges\n      as a single line between the relevant vertices, with no arrow\
head.<P/>\n\n      The output is in <C>dot</C> format (also known as <C>GraphV\
iz</C>)\n      format. For details about this file format, and information abo\
ut how\n      to display or edit this format see\n      <URL>http://www.graphv\
iz.org</URL>. <P/>\n\n      The string returned by <C>DotSymmetricDigraph</C> \
can be written to a\n      file using the command <Ref Func=\"FileString\" Boo\
kName=\"GAPDoc\"/>.<P/>\n\n      <Log><![CDATA[\ngap> star := Digraph([[2, 2, \
3, 4], [1, 1], [1], [1, 4]]);\n<immutable multidigraph with 4 vertices, 9 edge\
s>\ngap> IsSymmetricDigraph(star);\ntrue\ngap> FileString(\"dot/star.dot\", Do\
tSymmetricDigraph(gr));\ngap> D := Digraph([[2], [1, 3], [2]]);\n<immutable di\
graph with 3 vertices, 4 edges>\ngap> vertcolors := [];;\ngap> vertcolors[1] :\
= \"blue\";;\ngap> vertcolors[2] := \"pink\";;\ngap> vertcolors[3] := \"purple\
\";;\ngap> edgecolors := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [];\
;\ngap> edgecolors[3] := [];;\ngap> edgecolors[1][2] := \"green\";; edgecolors\
[2][1] := \"green\";;\ngap> edgecolors[2][3] := \"red\";; edgecolors[3][2] := \
\"red\";;\ngap> Print(DotSymmetricColoredDigraph(D, vertcolors, edgecolors));\
\n//dot\ngraph hgn{\nnode [shape=circle]\n\n1[color=blue, style=filled]\n2[col\
or=pink, style=filled]\n3[color=purple, style=filled]\n1 -- 2[color=green]\n2 \
-- 3[color=red]\n}\ngap> D := Digraph([[2], [1, 3], [2]]);\n<immutable digraph\
 with 3 vertices, 4 edges>\ngap> vertcolors := [];;\ngap> vertcolors[1] := \"b\
lue\";;\ngap> vertcolors[2] := \"pink\";;\ngap> vertcolors[3] := \"purple\";;\
\ngap> Print(DotSymmetricVertexColoredDigraph(D, vertcolors));\n//dot\ngraph h\
gn{\nnode [shape=circle]\n\n1[color=blue, style=filled]\n2[color=pink, style=f\
illed]\n3[color=purple, style=filled]\n1 -- 2\n2 -- 3\n}\ngap> D := Digraph([[\
2], [1, 3], [2]]);\n<immutable digraph with 3 vertices, 4 edges>\ngap> edgecol\
ors := [];;\ngap> edgecolors[1] := [];; edgecolors[2] := [];;\ngap> edgecolors\
[3] := [];;\ngap> edgecolors[1][2] := \"green\";; edgecolors[2][1] := \"green\
\";;\ngap> edgecolors[2][3] := \"red\";; edgecolors[3][2] := \"red\";;\ngap> P\
rint(DotSymmetricEdgeColoredDigraph(D, edgecolors));\n//dot\ngraph hgn{\nnode \
[shape=circle]\n\n1\n2\n3\n1 -- 2[color=green]\n2 -- 3[color=red]\n}\n83]]></L\
og>\n    </Description>\n  </ManSection>\n\n      <ManSection>\n    <Attr Name\
=\"DotPartialOrderDigraph\" Arg=\"digraph\"/>\n    <Returns>A string.</Returns\
>\n    <Description>\n      This function produces a graphical representation \
of a partial order\n      digraph <A>digraph</A>. <C>DotPartialOrderDigraph</C\
> will return an error\n      if <A>digraph</A> is not a partial order digraph\
. See <Ref\n        Prop=\"IsPartialOrderDigraph\"/>.<P/>\n\n      Since <A>di\
graph</A> is a partial order, it is both reflexive and\n      transitive. The \
output of <C>DotPartialOrderDigraph</C> is the\n      <Ref Attr=\"DotDigraph\"\
/> of the\n      <Ref Oper=\"DigraphReflexiveTransitiveReduction\"/> of <A>dig\
raph</A>.<P/>\n\n      The output is in <C>dot</C> format (also known as <C>Gr\
aphViz</C>)\n      format. For details about this file format, and information\
 about how\n      to display or edit this format see\n      <URL>http://www.gr\
aphviz.org</URL>. <P/>\n\n      The string returned by <C>DotPartialOrderDigra\
ph</C> can be written to a\n      file using the command <Ref Func=\"FileStrin\
g\" BookName=\"GAPDoc\"/>.<P/>\n\n      <Log><![CDATA[\ngap> poset := Digraph(\
[[1, 4], [2], [2, 3, 4], [4]);\ngap> IsPartialOrderDigraph(gr);\ntrue\ngap> Fi\
leString(\"dot/poset.dot\", DotPartialOrderDigraph(gr));\n83]]></Log>\n    </D\
escription>\n  </ManSection>\n\n      <ManSection>\n    <Attr Name=\"DotPreord\
erDigraph\" Arg=\"digraph\"/>\n    <Attr Name=\"DotQuasiorderDigraph\" Arg=\"d\
igraph\"/>\n    <Returns>A string.</Returns>\n    <Description>\n      This fu\
nction produces a graphical representation of a preorder\n      digraph <A>dig\
raph</A>. <C>DotPreorderDigraph</C> will return an error\n      if <A>digraph<\
/A> is not a preorder digraph. See <Ref\n        Prop=\"IsPreorderDigraph\"/>.\
<P/>\n\n      A preorder digraph is reflexive and transitive but in general it\
 is\n      not anti-symmetric and may have strongly connected components\n    \
  containing more than one vertex. The <Ref Oper=\"QuotientDigraph\"/>\n      \
<A>Q</A> obtained by forming the quotient of <A>digraph</A> by the\n      part\
ition of its vertices into the strongly connected components\n      satisfies \
<Ref Prop=\"IsPartialOrderDigraph\"/>. Thus every vertex of\n      <A>Q</A> co\
rresponds to a strongly connected component of <A>digraph</A>.\n      The outp\
ut of <C>DotPreorderDigraph</C> displays the \n      <Ref Oper=\"DigraphReflex\
iveTransitiveReduction\"/> of <A>Q</A> with\n      vertices displayed as round\
ed rectangles labelled by all of the vertices\n      of <A>digraph</A> in the \
corresponding strongly connected component. <P/>\n\n      The output is in <C>\
dot</C> format (also known as <C>GraphViz</C>)\n      format. For details abou\
t this file format, and information about how\n      to display or edit this f\
ormat see\n      <URL>http://www.graphviz.org</URL>. <P/>\n\n      The string \
returned by <C>DotPreorderDigraph</C> can be written to a\n      file using th\
e command <Ref Func=\"FileString\" BookName=\"GAPDoc\"/>.<P/>\n\n      <Log><!\
[CDATA[\ngap> preset := Digraph([[1, 2, 4, 5], [1, 2, 4, 5], [3, 4], [4], [1, \
2, 4, 5]);\ngap> IsPreorderDigraph(gr);\ntrue\ngap> FileString(\"dot/preset.do\
t\", DotProrderDigraph(gr));\n83]]></Log>\n    </Description>\n  </ManSection>\
\n\n      <ManSection>\n    <Oper Name=\"DotHighlightedDigraph\" Arg=\"digraph\
, verts [, colour1, colour2]\"/>\n    <Returns>A string.</Returns>\n    <Descr\
iption>\n      <C>DotHighlightedDigraph</C> produces a graphical represenation\
 of the\n      digraph <A>digraph</A>, where the vertices in the list <A>verts\
</A>, and\n      edges between them, are drawn with colour <A>colour1</A> and \
all other\n      vertices and edges in <A>digraph</A> are drawn with colour <A\
>colour2</A>.\n      If <A>colour1</A> and <A>colour2</A> are not given then\n\
      <C>DotHighlightedDigraph</C> uses black and grey respectively. <P/>\n\n \
     Note that <C>DotHighlightedDigraph</C> does not validate the colours\n   \
   <A>colour1</A> and <A>colour2</A> - consult the GraphViz documentation to\n\
      see what is available.\n\n      See <Ref Attr=\"DotDigraph\"/> for more \
details on the output.<P/>\n\n      <Log><![CDATA[\ngap> digraph := Digraph([[\
2, 3], [2], [1, 3]]);\n<digraph with 3 vertices, 5 edges>\ngap> FileString(\"d\
ot/my_digraph.dot\",\n> DotHighlightedDigraph(digraph, [1, 2], \"red\", \"blac\
k\"));\n264]]></Log>\n    </Description>\n  </ManSection>\n\n  </Section>\n\n \
 <Section><Heading>Reading and writing digraphs to a file</Heading>\n    This \
section describes different ways to store and read graphs\n    from a file in \
the &Digraphs; package.\n    <List>\n      <Mark> Graph6 </Mark>\n      <Item>\
\n\t<E> Graph6 </E> is a graph data format for storing undirected graphs\n\twi\
th no multiple edges nor loops of size up to <M> 2^{36} - 1 </M> in\n\tprintab\
le chracters. The format consists of two parts. The first part\n\tuses one to \
eight bytes to store the number of vertices. And the second\n\tpart is the upp\
er half of the adjacency matrix converted into ASCII\n\tcharacters. For a more\
 detail description see <URL Text='Graph6'>\n\thttp://cs.anu.edu.au/~bdm/data/\
formats.txt</URL>.\n      </Item>\n\n      <Mark> Sparse6 </Mark>\n      <Item\
>\n\t<E> Sparse6 </E> is a graph data format for storing undirected graphs\n\t\
with possibly multiple edges or loops. The maximal number of vertices\n\tallow\
ed is <M> 2^{36} - 1 </M>. The format consists of two parts. The\n\tfirst part\
 uses one to eight bytes to store the number of vertices.\n\tAnd the second pa\
rt only stores information about the edges.\n\tTherefore, the <E> Sparse6 </E>\
 format return a more compact encoding\n\tthen <E> Graph6 </E> for sparse grap\
h, i.e.  graphs where the number\n\tof edges is much less than the number of v\
ertices squared.  For a more\n\tdetail description see <URL Text='Sparse6'>\n \
       http://cs.anu.edu.au/~bdm/data/formats.txt</URL>.\n      </Item>\n\n   \
   <Mark> Digraph6 </Mark>\n      <Item>\n\t<E>Digraph6</E> is a new format ba\
sed on <E> Graph6 </E>, but designed\n\tfor digraphs. The entire adjacency mat\
rix is stored, and\n\ttherefore there is support for directed edges and single\
-vertex loops.\n\tHowever, multiple edges are not supported.\n      </Item>\n\
\n      <Mark> DiSparse6 </Mark>\n      <Item>\n\t<E>DiSparse6</E> is a new fo\
rmat based on <E> Sparse6 </E>, but\n\tdesigned for digraphs. In this format t\
he list of edges is\n\tpartitioned into inceasing and decreasing edges, depend\
ing whether the\n\tedge has its source bigger than the range. Then both sets o\
f edges are\n\twritten separetly in <E> Sparse6 </E> format with a separation \
symbol\n\tin between.\n      </Item>\n    </List>\n    <ManSection>\n  <Attr N\
ame=\"String\" Arg=\"digraph\"/>\n  <Oper Name=\"PrintString\" Arg=\"digraph\"\
/>\n  <Returns>A string.</Returns>\n  <Description>\n    Returns a string <C>s\
tring</C> such that <C>EvalString(string)</C>\n    is equal to <A>digraph</A>,\
 and has the same mutability.\n    See <Ref Func=\"EvalString\" BookName=\"ref\
\" />.\n    <P/>\n\n    The methods installed for <C>String</C> make some atte\
mpts to\n    ensure that <C>string</C> has as short a length as possible, but\
\n    there may exist shorter strings that also evaluate to <A>digraph</A>.\n \
   <P/>\n\n    It is possible that <C>string</C> may contain escaped special\n\
    characters. To obtain a representation of <A>digraph</A> that\n    can be \
entered as GAP input, please use\n    <Ref Func=\"Print\" BookName=\"ref\" />.\
\n    Note that <C>Print</C> for a digraph  delegates to\n    <C>PrintString</\
C>, which delegates to <C>String</C>.\n    <Log><![CDATA[\ngap> D := CycleDigr\
aph(3);\n<immutable cycle digraph with 3 vertices>\ngap> Print(D);\nCycleDigra\
ph(3);\ngap> G := PetersenGraph(IsMutableDigraph);\n<mutable digraph with 10 v\
ertices, 30 edges>\ngap> String(G);\n\"DigraphFromGraph6String(IsMutableDigrap\
h, \\\"IheA@GUAo\\\");\"\ngap> Print(last);\nDigraphFromGraph6String(IsMutable\
Digraph, \"IheA@GUAo\");\ngap> DigraphFromGraph6String(IsMutableDigraph, \"Ihe\
A@GUAo\");\n<mutable digraph with 10 vertices, 30 edges>\n]]></Log>\n  </Descr\
iption>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"DigraphFromGraph6St\
ring\"    Arg=\"[filt, ]str\"/>\n  <Oper Name=\"DigraphFromDigraph6String\"  A\
rg=\"[filt, ]str\"/>\n  <Oper Name=\"DigraphFromSparse6String\"   Arg=\"[filt,\
 ]str\"/>\n  <Oper Name=\"DigraphFromDiSparse6String\" Arg=\"[filt, ]str\"/>\n\
  <Returns>A digraph.</Returns>\n  <Description>\n    If <A>str</A> is a strin\
g encoding a graph in Graph6, Digraph6, Sparse6 or\n    DiSparse6 format, then\
 the corresponding function returns a digraph. In the\n    case of either Grap\
h6 or Sparse6, formats which do not support directed\n    edges, this will be \
a digraph such that for every edge, the edge going in\n    the opposite direct\
ion is also present.<P/>\n\n    Each of these functions takes an optional firs\
t argument <A>filt</A>,\n    which should be either <Ref Filt=\"IsMutableDigra\
ph\"/>\n    or <Ref Filt=\"IsImmutableDigraph\"/>,\n    and which specifies wh\
ether the output digraph shall\n    be mutable or immutable.\n    If no first \
argument is provided, then an immutable\n    digraph is returned by default.\n\
    <Example><![CDATA[\ngap> DigraphFromGraph6String(\"?\");\n<immutable empty\
 digraph with 0 vertices>\ngap> DigraphFromGraph6String(\"C]\");\n<immutable d\
igraph with 4 vertices, 8 edges>\ngap> DigraphFromGraph6String(\"H?AAEM{\");\n\
<immutable digraph with 9 vertices, 22 edges>\ngap> DigraphFromDigraph6String(\
\"&?\");\n<immutable empty digraph with 0 vertices>\ngap> DigraphFromDigraph6S\
tring(IsMutableDigraph, \"&DOOOW?\");\n<mutable digraph with 5 vertices, 5 edg\
es>\ngap> DigraphFromDigraph6String(\"&CQFG\");\n<immutable digraph with 4 ver\
tices, 6 edges>\ngap> DigraphFromDigraph6String(\"&IM[SrKLc~lhesbU[F_\");\n<im\
mutable digraph with 10 vertices, 51 edges>\ngap> DigraphFromDiSparse6String(\
\".CaWBGA?b\");\n<immutable multidigraph with 4 vertices, 9 edges>\n]]></Examp\
le>\n    </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"Gra\
ph6String\" Arg=\"digraph\"/>\n  <Oper Name=\"Digraph6String\" Arg=\"digraph\"\
/>\n  <Oper Name=\"Sparse6String\" Arg=\"digraph\"/>\n  <Oper Name=\"DiSparse6\
String\" Arg=\"digraph\"/>\n  <Returns>A string.</Returns>\n  <Description>\n \
   These four functions return a highly compressed string fully describing the\
\n    digraph <A>digraph</A>. <P/>\n\n    Graph6 and Digraph6 are formats best\
 used on small, dense graphs, if\n    applicable. For larger, sparse graphs us\
e <E>Sparse6</E> and\n    <E>Disparse6</E> (this latter also preserves multipl\
e edges). <P/>\n\n    See <Ref Func=\"WriteDigraphs\"/>.\n    <Example><![CDAT\
A[\ngap> gr := Digraph([[2, 3], [1], [1]]);\n<immutable digraph with 3 vertice\
s, 4 edges>\ngap> Sparse6String(gr);\n\":Bc\"\ngap> DiSparse6String(gr);\n\".B\
c{f\"\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <\
Func Name=\"DigraphFile\" Arg=\"filename [, coder][, mode]\"/>\n  <Returns>An \
IO file object.</Returns>\n  <Description>\n    If <A>filename</A> is a string\
 representing the name of a file, then\n    <C>DigraphFile</C> returns an &IO;\
 package file object for that file.\n    <P/>\n\n    If the optional argument \
<A>coder</A> is specified\n    and is a function which either encodes a digrap\
h as a string, or decodes a\n    string into a digraph, then this function wil\
l be used when reading or\n    writing to the returned file object. If the opt\
ional argument <A>coder</A>\n    is not specified, then the encoding of the di\
graphs in the returned file\n    object must be specified in the the file exte\
nsion. The file extension must\n    be one of: <C>.g6</C>, <C>.s6</C>, <C>.d6<\
/C>, <C>.ds6</C>, <C>.txt</C>,\n    <C>.p</C>, or <C>.pickle</C>; more details\
 of these file formats is given\n    below. <P/>\n\n    If the optional argume\
nt <A>mode</A> is specified, then it must be one of:\n    <C>\"w\"</C> (for wr\
ite), <C>\"a\"</C> (for append), or <C>\"r\"</C> (for read).\n    If <A>mode</\
A> is not specified, then <C>\"r\"</C> is used by default. <P/>\n\n    If <A>f\
ilename</A> ends in one of: <C>.gz</C>, <C>.bz2</C>, or\n    <C>.xz</C>, then \
the digraphs which are read from, or written to, the\n    returned file object\
 are decompressed, or compressed, appropriately.\n    <P/>\n\n    The file obj\
ect returned by <C>DigraphFile</C> can be given as the first\n    argument for\
 either of the functions <Ref Func=\"ReadDigraphs\"/> or <Ref\n      Func=\"Wr\
iteDigraphs\"/>. The purpose of this is to reduce the overhead of\n    recreat\
ing the file object inside the functions <Ref Func=\"ReadDigraphs\"/>\n    or \
<Ref Func=\"WriteDigraphs\"/> when, for example, reading or writing many\n    \
digraphs in a loop.\n    <P/>\n\n    The currently supported file formats, and\
 associated filename extensions,\n    are:\n    <List>\n      <Mark>graph6 (.g\
6)</Mark>\n      <Item>\n\tA standard and widely-used format for undirected gr\
aphs, with no support\n\tfor loops or multiple edges.  Only symmetric graphs a\
re allowed -- each\n\tedge is combined with its converse edge to produce a sin\
gle undirected\n\tedge.  This format is best used for \"dense\" graphs -- thos\
e with many\n\tedges per vertex.\n      </Item>\n      <Mark>sparse6 (.s6)</Ma\
rk>\n      <Item>\n\tUnlike graph6, sparse6 has support for loops and multiple\
 edges.\n\tHowever, its use is still limited to symmetric graphs.  This format\
 is\n\tbetter-suited to \"sparse\" graphs -- those with few edges per vertex.\
\n      </Item>\n      <Mark>digraph6 (.d6)</Mark>\n      <Item>\n\tThis forma\
t is based on graph6, but stores direction information -\n\ttherefore is not l\
imited to symmetric graphs.  Loops are allowed, but\n\tmultiple edges are not.\
  Best compression with \"dense\" graphs.\n      </Item>\n      <Mark>disparse\
6 (.ds6)</Mark>\n      <Item>\n\tAny type of digraph can be encoded in dispars\
e6: directions, loops, and\n\tmultiple edges are all allowed.  Similar to spar\
se6, this has the best\n\tcompression rate with \"sparse\" graphs.\n      </It\
em>\n      <Mark>plain text (.txt)</Mark>\n      <Item>\n\tThis is a human-rea\
dable format which stores graphs in the form\n        <C>0 7  0 8  1 7  2 8  3\
 8  4 8  5 8  6 8</C> i.e. pairs of vertices\n        describing edges in a gr\
aph. More specifically, the vertices making up\n        one edge must be separ\
ated by a single space, and pairs of vertices must\n        be separated by tw\
o spaces. <P/>\n\n        See <Ref Oper=\"ReadPlainTextDigraph\"/> for a more \
flexible way to store\n        digraphs in a plain text file. <P/>\n      </It\
em>\n\n      <Mark>pickled (<F>.p</F> or <F>.pickle</F>)</Mark>\n      <Item>\
\n        Digraphs are pickled using the &IO; package. This is particularly go\
od\n        when the <Ref Attr=\"DigraphGroup\"/> is non-trivial.\n      </Ite\
m>\n    </List>\n\n    <Example><![CDATA[\ngap> filename := Concatenation(DIGR\
APHS_Dir(), \"/tst/out/man.d6.gz\");;\ngap> file := DigraphFile(filename, \"w\
\");;\ngap> for i in [1 .. 10] do\n> WriteDigraphs(file, Digraph([[1, 3], [2],\
 [1, 2]]));\n> od;\ngap> IO_Close(file);;\ngap> file := DigraphFile(filename, \
\"r\");;\ngap> ReadDigraphs(file, 9);\n<immutable digraph with 3 vertices, 5 e\
dges>\ngap> IO_Close(file);;\n]]></Example>\n    </Description>\n</ManSection>\
\n\n    <ManSection>\n  <Func Name=\"ReadDigraphs\" Arg=\"filename[, decoder][\
, n]\"/>\n  <Returns>A digraph, or a list of digraphs.</Returns>\n  <Descripti\
on>\n    If <A>filename</A> is a string containing the name of a file containi\
ng\n    encoded digraphs or an &IO; file object created using <Ref\n      Func\
=\"DigraphFile\"/>, then <C>ReadDigraphs</C> returns the digraphs\n    encoded\
 in the file as a list.  Note that if <A>filename</A> is a\n    compressed fil\
e, which has been compressed appropriately to give a filename\n    extension o\
f <C>.gz</C>, <C>.bz2</C>, or <C>.xz</C>, then\n    <C>ReadDigraphs</C> can re\
ad <A>filename</A> without it first needing to be\n    decompressed.\n    <P/>\
\n\n    If the optional argument <A>decoder</A> is specified\n    and is a fun\
ction which decodes a string into a digraph,\n    then <C>ReadDigraphs</C> wil\
l use <A>decoder</A> to decode the digraphs\n    contained in <A>filename</A>.\
<P/>\n\n    If the optional argument <A>n</A> is specified, then <C>ReadDigrap\
hs</C>\n    returns the <A>n</A>th digraph encoded in the file <A>filename</A>\
.\n    <P/>\n\n    If the optional argument <A>decoder</A> is not specified, t\
hen\n    <C>ReadDigraphs</C> will deduce which decoder to use based on the fil\
ename\n    extension of <A>filename</A> (after removing the compression-relate\
d\n    filename extensions <C>.gz</C>, <C>.bz2</C>, and <C>.xz</C>).  For exam\
ple,\n    if the filename extension is <C>.g6</C>, then <C>ReadDigraphs</C> wi\
ll use\n    the graph6 decoder <Ref Oper=\"DigraphFromGraph6String\"/>.\n    <\
P/>\n\n    The currently supported file formats, and associated filename exten\
sions,\n    are:\n    <List>\n      <Mark>graph6 (.g6)</Mark>\n      <Item>\n\
\tA standard and widely-used format for undirected graphs, with no support\n\t\
for loops or multiple edges.  Only symmetric graphs are allowed -- each\n\tedg\
e is combined with its converse edge to produce a single undirected\n\tedge.  \
This format is best used for \"dense\" graphs -- those with many\n\tedges per \
vertex.\n      </Item>\n      <Mark>sparse6 (.s6)</Mark>\n      <Item>\n\tUnli\
ke graph6, sparse6 has support for loops and multiple edges.\n\tHowever, its u\
se is still limited to symmetric graphs.  This format is\n\tbetter-suited to \
\"sparse\" graphs -- those with few edges per vertex.\n      </Item>\n      <M\
ark>digraph6 (.d6)</Mark>\n      <Item>\n\tThis format is based on graph6, but\
 stores direction information -\n\ttherefore is not limited to symmetric graph\
s.  Loops are allowed, but\n\tmultiple edges are not.  Best compression with \
\"dense\" graphs.\n      </Item>\n      <Mark>disparse6 (.ds6)</Mark>\n      <\
Item>\n\tAny type of digraph can be encoded in disparse6: directions, loops, a\
nd\n\tmultiple edges are all allowed.  Similar to sparse6, this has the best\n\
\tcompression rate with \"sparse\" graphs.\n      </Item>\n      <Mark>plain t\
ext (.txt)</Mark>\n      <Item>\n\tThis is a human-readable format which store\
s graphs in the form\n        <C>0 7  0 8  1 7  2 8  3 8  4 8  5 8  6 8</C> i.\
e. pairs of vertices\n        describing edges in a graph. More specifically, \
the vertices making up\n        one edge must be separated by a single space, \
and pairs of vertices must\n        be separated by two spaces. <P/>\n\n      \
  See <Ref Oper=\"ReadPlainTextDigraph\"/> for a more flexible way to store\n \
       digraphs in a plain text file. <P/>\n<!--\n        Just so I remember:\
\n        <C>ReadPlainTextDigraph(\"data-local/soc-Epinions1.txt.gz\", \"\\t\"\
, 1,\n        '#');</C>\n-->\n      </Item>\n\n      <Mark>pickled (<F>.p</F> \
or <F>.pickle</F>)</Mark>\n      <Item>\n        Digraphs are pickled using th\
e &IO; package. This is particularly good\n        when the <Ref Attr=\"Digrap\
hGroup\"/> is non-trivial.\n      </Item>\n    </List>\n\n    <Example><![CDAT\
A[\ngap> ReadDigraphs(\n> Concatenation(DIGRAPHS_Dir(), \"/data/graph5.g6.gz\"\
), 10);\n<immutable digraph with 5 vertices, 8 edges>\ngap> ReadDigraphs(\n> C\
oncatenation(DIGRAPHS_Dir(), \"/data/graph5.g6.gz\"), 17);\n<immutable digraph\
 with 5 vertices, 12 edges>\ngap> ReadDigraphs(\n> Concatenation(DIGRAPHS_Dir(\
), \"/data/tree9.4.txt\"));\n[ <immutable digraph with 9 vertices, 8 edges>, \
\n  <immutable digraph with 9 vertices, 8 edges>, \n  <immutable digraph with \
9 vertices, 8 edges>, \n  <immutable digraph with 9 vertices, 8 edges>, \n  <i\
mmutable digraph with 9 vertices, 8 edges>, \n  <immutable digraph with 9 vert\
ices, 8 edges>, \n  <immutable digraph with 9 vertices, 8 edges>, \n  <immutab\
le digraph with 9 vertices, 8 edges>, \n  <immutable digraph with 9 vertices, \
8 edges>, \n  <immutable digraph with 9 vertices, 8 edges>, \n  <immutable dig\
raph with 9 vertices, 8 edges>, \n  <immutable digraph with 9 vertices, 8 edge\
s>, \n  <immutable digraph with 9 vertices, 8 edges>, \n  <immutable digraph w\
ith 9 vertices, 8 edges> ]]]></Example>\n    </Description>\n</ManSection>\n\n\
    <ManSection>\n  <Func Name=\"WriteDigraphs\" Arg=\"filename, digraphs[, en\
coder] [, mode]\"/>\n  <Description>\n    If <A>digraphs</A> is a list of digr\
aphs or a digraph and <A>filename</A>\n    is a string or an &IO; file object \
created using <Ref Func=\"DigraphFile\"/>,\n    then <C>WriteDigraphs</C> writ\
es the digraphs to the file represented by\n    <A>filename</A>.  If the suppl\
ied filename ends in one of the extensions\n    <C>.gz</C>, <C>.bz2</C>, or <C\
>.xz</C>, then the file will be compressed\n    appropriately.  Excluding thes\
e extensions, if the file ends with an\n    extension in the list below, the c\
orresponding graph format will be used to\n    encode it.  If such an extensio\
n is not included, an appropriate format\n    will be chosen intelligently, an\
d an extension appended, to minimise file\n    size.\n    <P/>\n\n    <!-- TOD\
O: encode and mode. -->\n\n    For more verbose information on the progress of\
 the function, set the info\n    level of <A>InfoDigraphs</A> to 1 or higher, \
using <C>SetInfoLevel</C>.<P/>\n\n    The currently supported file formats are\
:\n    <List>\n      <Mark>graph6 (.g6)</Mark>\n      <Item>\n\tA standard and\
 widely-used format for undirected graphs, with no support\n\tfor loops or mul\
tiple edges.  Only symmetric graphs are allowed -- each\n\tedge is combined wi\
th its converse edge to produce a single undirected\n\tedge.  This format is b\
est used for \"dense\" graphs -- those with many\n\tedges per vertex.\n      <\
/Item>\n      <Mark>sparse6 (.s6)</Mark>\n      <Item>\n\tUnlike graph6, spars\
e6 has support for loops and multiple edges.\n\tHowever, its use is still limi\
ted to symmetric graphs.  This format is\n\tbetter-suited to \"sparse\" graphs\
 -- those with few edges per vertex.\n      </Item>\n      <Mark>digraph6 (.d6\
)</Mark>\n      <Item>\n\tThis format is based on graph6, but stores direction\
 information -\n\ttherefore is not limited to symmetric graphs.  Loops are all\
owed, but\n\tmultiple edges are not.  Best compression with \"dense\" graphs.\
\n      </Item>\n      <Mark>disparse6 (.ds6)</Mark>\n      <Item>\n\tAny type\
 of digraph can be encoded in disparse6: directions, loops, and\n\tmultiple ed\
ges are all allowed.  Similar to sparse6, this has the best\n\tcompression rat\
e with \"sparse\" graphs.\n      </Item>\n\n      <Mark>plain text (.txt)</Mar\
k>\n      <Item>\n\tThis is a human-readable format which stores graphs in the\
 form\n        <C>0 7  0 8  1 7  2 8  3 8  4 8  5 8  6 8</C> i.e. pairs of ver\
tices\n        describing edges in a graph. More specifically, the vertices ma\
king up\n        one edge must be separated by a single space, and pairs of ve\
rtices must\n        be separated by two spaces. <P/>\n\n        See <Ref Oper\
=\"ReadPlainTextDigraph\"/> for a more flexible way to store\n        digraphs\
 in a plain text file. <P/>\n<!--\n        Just so I remember:\n        <C>Rea\
dPlainTextDigraph(\"data-local/soc-Epinions1.txt.gz\", \"\\t\", 1, '#');</C>\n\
-->\n      </Item>\n      <Mark>pickled (<F>.p</F> or <F>.pickle</F>)</Mark>\n\
      <Item>\n        Digraphs are pickled using the &IO; package. This is par\
ticularly good\n        when the <Ref Attr=\"DigraphGroup\"/> is non-trivial.\
\n      </Item>\n    </List>\n\n    <Example><![CDATA[\ngap> grs := [];;\ngap>\
 grs[1] := Digraph([]);\n<immutable empty digraph with 0 vertices>\ngap> grs[2\
] := Digraph([[1, 3], [2], [1, 2]]);\n<immutable digraph with 3 vertices, 5 ed\
ges>\ngap> grs[3] := Digraph([\n> [6, 7], [6, 9], [1, 3, 4, 5, 8, 9],\n> [1, 2\
, 3, 4, 5, 6, 7, 10], [1, 5, 6, 7, 10], [2, 4, 5, 9, 10],\n> [3, 4, 5, 6, 7, 8\
, 9, 10], [1, 3, 5, 7, 8, 9], [1, 2, 5],\n> [1, 2, 4, 6, 7, 8]]);\n<immutable \
digraph with 10 vertices, 51 edges>\ngap> filename := Concatenation(DIGRAPHS_D\
ir(), \"/tst/out/man.d6.gz\");;\ngap> WriteDigraphs(filename, grs, \"w\");\nIO\
_OK\ngap> ReadDigraphs(filename);\n[ <immutable empty digraph with 0 vertices>\
, \n  <immutable digraph with 3 vertices, 5 edges>, \n  <immutable digraph wit\
h 10 vertices, 51 edges> ]]]></Example>\n    </Description>\n</ManSection>\n\n\
    <ManSection>\n  <Func Name=\"IteratorFromDigraphFile\" Arg=\"filename [, d\
ecoder]\"/>\n  <Returns>An iterator.</Returns>\n  <Description>\n    If <A>fil\
ename</A> is a string representing the name of a file containing\n    encoded \
digraphs, then <C>IteratorFromDigraphFile</C> returns an iterator\n    for whi\
ch the value of <Ref Oper=\"NextIterator\" BookName=\"ref\"/> is the\n    next\
 digraph encoded in the file.\n    <P/>\n\n    If the optional argument <A>dec\
oder</A> is specified and is a function\n    which decodes a string into a dig\
raph, then <C>IteratorFromDigraphFile</C>\n    will use <A>decoder</A> to deco\
de the digraphs contained in <A>filename</A>.\n    <P/>\n\n    The purpose of \
this function is to easily allow looping over digraphs\n    encoded in a file \
when loading all of the encoded digraphs would require\n    too much memory. <\
P/>\n\n    To see what file types are available, see <Ref Func=\"WriteDigraphs\
\"/>.\n\n    <Example><![CDATA[\ngap> filename := Concatenation(DIGRAPHS_Dir()\
, \"/tst/out/man.d6.gz\");;\ngap> file := DigraphFile(filename, \"w\");;\ngap>\
 for i in [1 .. 10] do\n>   WriteDigraphs(file, Digraph([[1, 3], [2], [1, 2]])\
);\n> od;\ngap> IO_Close(file);;\ngap> iter := IteratorFromDigraphFile(filenam\
e);\n<iterator>\ngap> for x in iter do od;\n]]></Example>\n  </Description>\n<\
/ManSection>\n\n    <ManSection>\n  <Func Name=\"DigraphPlainTextLineEncoder\"\
 Arg=\"delimiter1, [delimiter2,] offset\"/>\n  <Oper Name=\"DigraphPlainTextLi\
neDecoder\" Arg=\"delimiter1, [delimiter2,] offset\"/>\n  <Returns>A string.</\
Returns>\n  <Description>\n    These two functions return a function which enc\
odes or decodes a digraph in\n    a plain text format.<P/>\n\n    <A>DigraphPl\
ainTextLineEncoder</A> returns a function which takes a single\n    digraph as\
 an argument.  The function returns a string describing the edges\n    of that\
 digraph; each edge is written as a pair of integers separated by the\n    str\
ing <A>delimiter2</A>, and the edges themselves are separated by the\n    stri\
ng <A>delimiter1</A>.  <A>DigraphPlainTextLineDecoder</A> returns the\n    cor\
responding decoder function, which takes a string argument in this format\n   \
 and returns a digraph.<P/>\n\n    If only one delimiter is passed as an argum\
ent to\n    <A>DigraphPlainTextLineDecoder</A>, it will return a function whic\
h decodes\n    a single edge, returning its contents as a list of integers.<P/\
>\n\n    The argument <A>offset</A> should be an integer, which will describe \
a\n    number to be added to each vertex before it is encoded, or after it is\
\n    decoded.  This may be used, for example, to label vertices starting at 0\
\n    instead of 1.<P/>\n\n    Note that the number of vertices of a digraph i\
s not stored, and so vertices\n    which are not connected to any edge may be \
lost.\n\n    <Example><![CDATA[\ngap> gr := Digraph([[2, 3], [1], [1]]);\n<imm\
utable digraph with 3 vertices, 4 edges>\ngap> enc := DigraphPlainTextLineEnco\
der(\"  \", \" \", -1);;\ngap> dec := DigraphPlainTextLineDecoder(\"  \", \" \
\", 1);;\ngap> enc(gr);\n\"0 1  0 2  1 0  2 0\"\ngap> dec(last);\n<immutable d\
igraph with 3 vertices, 4 edges>\n]]></Example>\n  </Description>\n</ManSectio\
n>\n\n    <ManSection>\n  <Oper Name=\"TournamentLineDecoder\" Arg=\"str\"/>\n\
  <Returns>A digraph.</Returns>\n  <Description>\n    This function takes a st\
ring <A>str</A>, decodes it, and then returns the\n    tournament [see <Ref Pr\
op=\"IsTournament\"/>] which it defines, according to\n    the following rules\
. <P/>\n\n    The characters of the string <A>str</A> represent the entries in\
 the upper\n    triangle of a tournament's adjacency matrix. The number of ver\
tices\n    <C>n</C> will be detected from the length of the string and will be\
 as\n    large as possible.  <P/>\n\n    The first character represents the po\
ssible edge <C>1 -> 2</C>, the second\n    represents <C>1 -> 3</C> and so on \
until <C>1 -> n</C>; then the following\n    character represents <C>2 -> 3</C\
>, and so on up to the character which\n    represents the edge <C>n-1 -> n</C\
>. <P/>\n\n    If a character of the string with corresponding edge <C>i -> j<\
/C> is equal\n    to <C>1</C>, then the edge <C>i -> j</C> is present in the t\
ournament.\n    Otherwise, the edge <C>i -> j</C> is present instead.  In this\
 way, all the\n    possible edges are encoded one-by-one.\n\n    <Example><![C\
DATA[\ngap> gr := TournamentLineDecoder(\"100001\");\n<immutable digraph with \
4 vertices, 6 edges>\ngap> OutNeighbours(gr);\n[ [ 2 ], [  ], [ 1, 2, 4 ], [ 1\
, 2 ] ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    <ManSection>\n \
 <Oper Name=\"AdjacencyMatrixUpperTriangleLineDecoder\" Arg=\"str\"/>\n  <Retu\
rns>A digraph.</Returns>\n  <Description>\n    This function takes a string <A\
>str</A>, decodes it, and then returns the\n    topologically sorted digraph [\
see <Ref Attr=\"DigraphTopologicalSort\"/>]\n    which it defines, according t\
o the following rules. <P/>\n\n    The characters of the string <A>str</A> rep\
resent the entries in the upper\n    triangle of a digraph's adjacency matrix.\
 The number of vertices <C>n</C>\n    will be detected from the length of the \
string and will be as large as\n    possible.  <P/>\n\n    The first character\
 represents the possible edge <C>1 -> 2</C>, the second\n    represents <C>1 -\
> 3</C> and so on until <C>1 -> n</C>; then the following\n    character repre\
sents <C>2 -> 3</C>, and so on up to the character which\n    represents the e\
dge <C>n-1 -> n</C>.  If a character of the string with\n    corresponding edg\
e <C>i -> j</C> is equal to <C>1</C>, then this edge is\n    present in the di\
graph. Otherwise, it is not present.  In this way, all the\n    possible edges\
 are encoded one-by-one. <P/>\n\n    In particular, note that there exists no \
edge <C>[i, j]</C> if <M>j \\leq\n      i</M>.  In order words, the digraph wi\
ll be topologically sorted.\n\n    <Example><![CDATA[\ngap> gr := AdjacencyMat\
rixUpperTriangleLineDecoder(\"100001\");\n<immutable digraph with 4 vertices, \
2 edges>\ngap> OutNeighbours(gr);\n[ [ 2 ], [  ], [ 4 ], [  ] ]\ngap> gr := Ad\
jacencyMatrixUpperTriangleLineDecoder(\"111111x111\");\n<immutable digraph wit\
h 5 vertices, 9 edges>\ngap> OutNeighbours(gr);\n[ [ 2, 3, 4, 5 ], [ 3, 4 ], [\
 4, 5 ], [ 5 ], [  ] ]\n]]></Example>\n  </Description>\n</ManSection>\n\n    \
<ManSection>\n  <Oper Name=\"TCodeDecoder\" Arg=\"str\"/>\n  <Returns>A digrap\
h.</Returns>\n  <Description>\n    If <A>str</A> is a string consisting of at \
least two non-negative integers\n    separated by spaces, then this function w\
ill attempt to return the digraph\n    which it defines as a TCode string. <P/\
>\n\n    The first integer of the string defines the number of vertices <C>v</\
C> in\n    the digraph, and the second defines the number of edges <C>e</C>.  \
The\n    following <C>2e</C> integers should be vertex numbers in the range <C\
>[0 ..\n      v-1]</C>. These integers are read in pairs and define the digrap\
h's\n    edges.  This function will return an error if <A>str</A> has fewer th\
an\n    <C>2e+2</C> entries. <P/>\n\n    Note that the vertex numbers will be \
incremented by 1 in the digraph\n    returned.  Hence the string fragment <C>0\
 6</C> will describe the edge\n    <C>[1,7]</C>.\n    <Example><![CDATA[\ngap>\
 gr := TCodeDecoder(\"3 2 0 2 2 1\");\n<immutable digraph with 3 vertices, 2 e\
dges>\ngap> OutNeighbours(gr);\n[ [ 3 ], [  ], [ 2 ] ]\ngap> gr := TCodeDecode\
r(\"12 3 0 10 5 2 8 8\");\n<immutable digraph with 12 vertices, 3 edges>\ngap>\
 OutNeighbours(gr);\n[ [ 11 ], [  ], [  ], [  ], [  ], [ 3 ], [  ], [  ], [ 9 \
], [  ], \n  [  ], [  ] ]\n]]></Example>\n  </Description>\n</ManSection>\n\n \
   <ManSection>\n  <Oper Name=\"PlainTextString\" Arg=\"digraph\"/>\n  <Oper N\
ame=\"DigraphFromPlainTextString\" Arg=\"s\"/>\n  <Returns>A string.</Returns>\
\n  <Description>\n    <A>PlainTextString</A> takes a single digraph, and retu\
rns a string\n    describing the edges of that digraph.  <A>DigraphFromPlainTe\
xtString</A>\n    takes such a string and returns the digraph which it describ\
es.  Each edge\n    is written as a pair of integers separated by a single spa\
ce.  The edges\n    themselves are separated by a double space.  Vertex number\
s are reduced by\n    1 when they are encoded, so that vertices in the string \
are labelled\n    starting at 0.<P/>\n\n    Note that the number of vertices o\
f a digraph is not stored, and so vertices\n    which are not connected to any\
 edge may be lost.<P/>\n\n    \n    The operation <C>DigraphFromPlainTextStrin\
g</C>\n    takes an optional first argument <Ref Filt=\"IsMutableDigraph\"/>\n\
    or <Ref Filt=\"IsImmutableDigraph\"/>, which specifies whether the output \
digraph shall\n    be mutable or immutable. If no first argument is provided, \
then an immutable\n    digraph is returned by default.\n\n    <Example><![CDAT\
A[\ngap> gr := Digraph([[2, 3], [1], [1]]);\n<immutable digraph with 3 vertice\
s, 4 edges>\ngap> PlainTextString(gr);\n\"0 1  0 2  1 0  2 0\"\ngap> DigraphFr\
omPlainTextString(last);\n<immutable digraph with 3 vertices, 4 edges>\n]]></E\
xample>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Func Name=\"W\
ritePlainTextDigraph\" Arg=\"filename, digraph, delimiter, offset\"/>\n  <Oper\
 Name=\"ReadPlainTextDigraph\" Arg=\"filename, delimiter, offset, ignore\"/>\n\
  <Description>\n    These functions write and read a single digraph in a huma\
n-readable plain\n    text format as follows: each line contains a single edge\
, and each edge is\n    written as a pair of integers separated by the string \
<A>delimiter</A>.<P/>\n\n    <A>filename</A> should be the name of a file whic\
h will be written to or\n    read from, and <A>offset</A> should be an integer\
 which is added to each\n    vertex number as it is written or read.  For exam\
ple, if\n    <C>WritePlainTextDigraph</C> is called with <A>offset</A> <C>-1</\
C>, then\n    the vertices will be numbered in the file starting from 0 instea\
d of 1 -\n    <C>ReadPlainTextDigraph</C> would then need to be called with <A\
>offset</A>\n    <C>1</C> to convert back to the original graph.<P/>\n\n    <A\
>ignore</A> should be a list of characters which will be ignored when\n    rea\
ding the graph.\n    <Example><![CDATA[\ngap> gr := Digraph([[1, 2, 3], [1, 1]\
, [2]]);\n<immutable multidigraph with 3 vertices, 6 edges>\ngap> filename := \
Concatenation(DIGRAPHS_Dir(), \"/tst/out/plain.txt\");;\ngap> WritePlainTextDi\
graph(filename, gr, \",\", -1);\ngap> ReadPlainTextDigraph(filename, \",\", 1,\
 ['/', '%']);\n<immutable multidigraph with 3 vertices, 6 edges>\n]]></Example\
>\n  </Description>\n</ManSection>\n\n    <ManSection>\n  <Oper Name=\"WriteDI\
MACSDigraph\" Arg=\"filename, digraph\"/>\n  <Oper Name=\"ReadDIMACSDigraph\" \
Arg=\"filename\"/>\n  <Description>\n    These operations write or read the si\
ngle symmetric digraph <A>digraph</A>\n    to or from a file in DIMACS format,\
 as appropriate. The operation\n    <C>WriteDIMACSDigraph</C> records the vert\
ices and edges of <A>digraph</A>.\n    The vertex labels of <A>digraph</A> wil\
l be recorded only if they are\n    integers. See <Ref Prop=\"IsSymmetricDigra\
ph\"/> and <Ref\n      Oper=\"DigraphVertexLabels\"/>.<P/>\n\n    The first ar\
gument <A>filename</A> should be the name of the file which will\n    be writt\
en to or read from.  A file can contain one symmetric digraph in\n    DIMACS f\
ormat. If <A>filename</A> ends in one of <C>.gz</C>, <C>.bz2</C>,\n    or <C>.\
xz</C>, then the file is compressed, or decompressed, appropriately.\n    <P/>\
\n\n    The DIMACS format is described as follows.  Each line in the DIMACS fi\
le has\n    one of four types:\n    <List>\n      <Item>\n        A line begin\
ning with <C>c</C> and followed by any number of characters\n        is a comm\
ent line, and is ignored.\n      </Item>\n      <Item>\n        A line beginni\
ng with <C>p</C> defines the numbers of vertices and edges\n        the digrap\
h.  This line has the format <C>p edge &lt;nr_vertices&gt;\n          &lt;nr_e\
dges&gt;</C>, where <C>&lt;nr_vertices&gt;</C> and\n        <C>&lt;nr_edges&gt\
;</C> are replaced by the relevant integers. There\n        must be exactly on\
e such line in the file, and it must occur before any\n        of the followin\
g kinds of line.<P/>\n\n        Although it is required to be present, the val\
ue of\n        <C>&lt;nr_edges&gt;</C> will be ignored. The correct number of \
edges\n        will be deduced from the rest of the information in the file.\n\
      </Item>\n      <Item>\n        A line of the form <C>e &lt;v&gt; &lt;w&g\
t;</C>, where <C>&lt;v&gt;</C>\n        and <C>&lt;w&gt;</C> are integers in t\
he range <C>[1 ..\n          &lt;nr_vertices&gt;]</C>, specifies that there is\
 a (symmetric) edge\n        in the digraph between the vertices <C>&lt;v&gt;<\
/C> and\n        <C>&lt;w&gt;</C>. A symmetric edge only needs to be defined o\
nce; an\n        additional line <C>e &lt;v&gt; &lt;w&gt;</C>, or <C>e &lt;w&g\
t;\n          &lt;v&gt;</C>, will be interpreted as an additional, multiple, e\
dge.\n        Loops are permitted.\n      </Item>\n      <Item>\n        A lin\
e of the form <C>n &lt;v&gt; &lt;label&gt;</C>, where\n        <C>&lt;v&gt;</C\
> is an integer in the range <C>[1 ..\n          &lt;nr_vertices&gt;]</C> and \
<C>&lt;label&gt;</C> is an integer,\n        signifies that the vertex <C>&lt;\
v&gt;</C> has the label\n        <C>&lt;label&gt;</C> in the digraph. If a lab\
el is not specified for a\n        vertex, then <C>ReadDIMACSDigraph</C> will \
assign the label\n        <C>1</C>, according to the DIMACS specification.\n  \
    </Item>\n    </List>\n\n    A detailed definition of the DIMACS format can\
 be found at\n    <URL>http://mat.gsia.cmu.edu/COLOR/general/ccformat.ps</URL>\
, in Section\n    2.1. Note that optional descriptor lines, as described in Se\
ction 2.1, will\n    be ignored.\n    <P/>\n\n\n    <Example><![CDATA[\ngap> g\
r := Digraph([[2], [1, 3, 4], [2, 4], [2, 3]]);\n<immutable digraph with 4 ver\
tices, 8 edges>\ngap> filename := Concatenation(DIGRAPHS_Dir(),\n>            \
                  \"/tst/out/dimacs.dimacs\");;\ngap> WriteDIMACSDigraph(filen\
ame, gr);;\ngap> ReadDIMACSDigraph(filename);\n<immutable digraph with 4 verti\
ces, 8 edges>]]></Example>\n  </Description>\n</ManSection>\n\n  </Section>\n<\
/Chapter>\n <!-- visualising, io -->\n</Body>\n\n<Appendix>\n  <Heading>\n    \
Grape to Digraphs Command Map\n  </Heading>\n  Below is a table of &Grape; com\
mands with the &Digraphs; counterparts.\n  The sections in this chapter corres\
pond to the chapters in the &Grape;\n  manual.\n\n  <Section>\n    <Heading>\n\
      Functions to construct and modify graphs\n    </Heading>\n    <Alt Not=\
\"HTML\">\n      <E>\n        The table in this section contains more informat\
ion when viewed in\n        html format.\n      </E>\n    </Alt>\n\n    <Table\
 Align=\"|l|l|l|\">\n      <HorLine/>\n      <Row>\n        <Item>\n          \
&Grape; command\n        </Item>\n        <Item>\n          &Digraphs; command\
\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            \
Comments\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\
\n      <Row>\n        <Item>\n          <C>Graph</C>\n        </Item>\n      \
  <Item>\n          <Ref Oper=\"Digraph\"/>\n        </Item>\n        <Item>\n\
          <Alt Only=\"HTML\">\n          Used with the arguments of <C>Graph</\
C> in &Grape;, <Ref\n            Oper=\"Digraph\"/> will return an equivalent \
digraph. <P/>\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine\
/>\n\n      <Row>\n        <Item>\n          <C>EdgeOrbitsGraph</C>\n        <\
/Item>\n        <Item>\n          <Ref Oper=\"EdgeOrbitsDigraph\"/>\n        <\
/Item>\n        <Item>\n          <Alt Only=\"HTML\">\n          The operation\
 <Ref Oper=\"EdgeOrbitsDigraph\"/> behaves the same as\n          <C>EdgeOrbit\
sDigraph</C> in &Grape;.\n          </Alt>\n        </Item>\n      </Row>\n   \
   <HorLine/>\n\n      <Row>\n        <Item>\n          <C>NullGraph</C>\n    \
    </Item>\n        <Item>\n          <Ref Oper=\"NullDigraph\"/>\n          \
<Alt Only=\"HTML\">\n            or\n            <Ref Oper=\"EmptyDigraph\"/>\
\n          </Alt>\n        </Item>\n        <Item>\n          <Alt Only=\"HTM\
L\">\n            Note that, unlike in &Grape;, the arguments of  <Ref\n      \
        Oper=\"NullDigraph\"/> and <Ref Oper=\"EmptyDigraph\"/> are just\n    \
        non-negative integers. Since digraphs in &Digraphs; are immutable,\n  \
          there is no reason (although it is possible) to create a null digrap\
h\n            and then add edges, as you might be used to doing in &Grape;.\n\
          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Ro\
w>\n        <Item>\n          <C>CompleteGraph</C>\n        </Item>\n        <\
Item>\n          <Ref Oper=\"CompleteDigraph\"/>\n        </Item>\n        <It\
em>\n          <Alt Only=\"HTML\">\n            Note that, unlike in &Grape;, \
the argument to <Ref\n              Oper=\"CompleteDigraph\"/> is simply a non\
-negative integer\n            indicating the number of vertices. By default a\
 complete digraph in\n            &Digraphs; does not have any loops. If you w\
ant a complete digraph\n            with loops at every vertex, then use <Ref\
\n              Oper=\"DigraphAddAllLoops\"/>.\n          </Alt>\n        </It\
em>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          \
<C>JohnsonGraph</C>\n        </Item>\n        <Item>\n          <Ref Oper=\"Jo\
hnsonDigraph\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\
\">\n            The &Grape; function <C>JohnsonGraph</C> is equivalent to\n  \
          <Ref Oper=\"JohnsonDigraph\"/>.\n          </Alt>\n        </Item>\n\
      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>Ca\
yleyGraph</C>\n        </Item>\n        <Item>\n          <Ref Oper=\"CayleyDi\
graph\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n   \
         The operation <Ref Oper=\"CayleyDigraph\"/> behaves the same as\n    \
        <C>CayleyGraph</C> in &Grape;.\n          </Alt>\n        </Item>\n   \
   </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>AddEd\
geOrbit</C>\n        </Item>\n        <Item>\n          <Ref Oper=\"DigraphAdd\
EdgeOrbit\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\
\n            Note that, unlike in &Grape;, digraphs in &Digraphs; are immutab\
le,\n            and this operation returns a new digraph, i.e. it does not mo\
dify the\n            digraph given as an argument.\n          </Alt>\n       \
 </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n     \
     <C>RemoveEdgeOrbit</C>\n        </Item>\n        <Item>\n          <Ref O\
per=\"DigraphRemoveEdgeOrbit\"/>\n        </Item>\n        <Item>\n          <\
Alt Only=\"HTML\">\n            Note that, unlike in &Grape;, digraphs in &Dig\
raphs; are immutable,\n            and this operation returns a new digraph, i\
.e. it does not modify the\n            digraph given as an argument.\n       \
   </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n   \
     <Item>\n          <C>AssignVertexNames</C>\n        </Item>\n        <Ite\
m>\n          <Ref Oper=\"SetDigraphVertexLabels\"/>\n          <Alt Only=\"HT\
ML\">\n            and\n            <Ref Oper=\"SetDigraphVertexLabel\"/>\n   \
       </Alt>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\
\n            Use  <Ref Oper=\"SetDigraphVertexLabel\"/> to set an individual\
\n            vertex label and <Ref Oper=\"SetDigraphVertexLabels\"/> to set a\
ll of\n            the vertex labels.\n          </Alt>\n        </Item>\n    \
  </Row>\n      <HorLine/>\n    </Table>\n  </Section>\n\n  <Section>\n    <He\
ading>\n      Functions to inspect graphs, vertices and edges\n    </Heading>\
\n    <Alt Not=\"HTML\">\n      <E>\n        The table in this section contain\
s more information when viewed in\n        html format.\n      </E>\n    </Alt\
>\n\n    <Table Align=\"|l|l|l|\">\n      <HorLine/>\n\n      <Row>\n        <\
Item>\n          &Grape; command\n        </Item>\n        <Item>\n          &\
Digraphs; command\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\
\">\n            Comments\n          </Alt>\n        </Item>\n      </Row>\n  \
    <HorLine/>\n\n      <Row>\n        <Item>\n          <C>IsGraph</C>\n     \
   </Item>\n        <Item>\n          <Ref Filt=\"IsDigraph\"/>\n        </Ite\
m>\n        <Item>\n          <Alt Only=\"HTML\">\n            <Ref Filt=\"IsD\
igraph\"/> is a category and not a function like\n            <C>IsGraph</C>.\
\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <\
Row>\n        <Item>\n          <C>OrderGraph</C>\n        </Item>\n        <I\
tem>\n          <Ref Attr=\"DigraphNrVertices\"/>\n        </Item>\n        <I\
tem>\n          <Alt Only=\"HTML\">\n            The operation <Ref Attr=\"Dig\
raphNrVertices\"/> behaves the same as\n            <C>OrderGraph</C> in &Grap\
e;.\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n    \
  <Row>\n        <Item>\n          <C>IsVertex(<A>graph</A>, <A>v</A>)</C>\n  \
      </Item>\n        <Item>\n          <C><A>v</A> in DigraphVertices(<A>dig\
raph</A>)</C>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\
\n            The attribute <Ref Attr=\"DigraphVertices\"/> can be used to ret\
urn\n            the list of vertices of a digraph, or if <A>v</A> is known to\
 be\n            a positive integer, then you can simply do\n            <C><A\
>v</A> &lt;= DigraphNrVertices(<A>digraph</A>)</C>\n          </Alt>\n        \
</Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n      \
    <C>VertexName</C>\n        </Item>\n        <Item>\n          <Ref Oper=\"\
DigraphVertexLabel\"/>\n        </Item>\n        <Item>\n          <Alt Only=\
\"HTML\">\n            Unlike <C>VertexName</C> in &Grape;, the return value o\
f\n            <Ref Oper=\"DigraphVertexLabel\"/> is mutable.\n          </Alt\
>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <It\
em>\n          <C>VertexNames</C>\n        </Item>\n        <Item>\n          \
<Ref Oper=\"DigraphVertexLabels\"/>\n        </Item>\n        <Item>\n        \
  <Alt Only=\"HTML\">\n            Unlike <C>VertexNames</C> in &Grape;, the r\
eturn value of\n            <Ref Oper=\"DigraphVertexLabels\"/> is mutable.\n \
         </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row\
>\n        <Item>\n          <C>Vertices</C>\n        </Item>\n        <Item>\
\n          <Ref Attr=\"DigraphVertices\"/>\n        </Item>\n        <Item>\n\
          <Alt Only=\"HTML\">\n            The vertices of a digraph in &Digra\
phs; is always the range <C>[1\n              .. n]</C> where <C>n</C> is the \
number of vertices of the\n            digraph.  The operation <Ref Attr=\"Dig\
raphVertices\"/> behaves the\n            same as <C>Vertices</C> in &Grape;.\
\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <\
Row>\n        <Item>\n          <C>VertexDegree</C>\n        </Item>\n        \
<Item>\n          <Ref Oper=\"OutDegreeOfVertex\"/>\n          <Alt Only=\"HTM\
L\">\n            (see also: <Ref Oper=\"InDegreeOfVertex\"/>)\n          </Al\
t>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n          \
  The operation <Ref Oper=\"OutDegreeOfVertex\"/> behaves the same as\n       \
     <C>VertexDegree</C> in &Grape;.\n          </Alt>\n        </Item>\n     \
 </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>VertexD\
egrees</C>\n        </Item>\n        <Item>\n          <Ref Attr=\"OutDegreeSe\
t\"/>\n          <Alt Only=\"HTML\">\n            (see also:\n            <Ref\
 Attr=\"OutDegreeSequence\"/>,\n            <Ref Attr=\"OutDegrees\"/>,\n     \
       <Ref Attr=\"InDegrees\"/>,\n            <Ref Attr=\"InDegreeSequence\"/\
>,\n            <Ref Attr=\"InDegreeSet\"/>)\n          </Alt>\n        </Item\
>\n        <Item>\n          <Alt Only=\"HTML\">\n            The operation <R\
ef Attr=\"OutDegreeSet\"/> behaves the same as\n            <C>VertexDegrees</\
C> in &Grape;.\n          </Alt>\n        </Item>\n      </Row>\n      <HorLin\
e/>\n\n      <Row>\n        <Item>\n          <C>IsLoopy</C>\n        </Item>\
\n        <Item>\n          <Ref Prop=\"DigraphHasLoops\"/>\n        </Item>\n\
        <Item>\n          <Alt Only=\"HTML\">\n            The operation <Ref \
Prop=\"DigraphHasLoops\"/> behaves the same as\n            <C>IsLoopy</C> in \
&Grape;.\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\
\n      <Row>\n        <Item>\n          <C>IsSimpleGraph</C>\n        </Item>\
\n        <Item>\n          <Alt Only=\"HTML\">\n            <Ref Prop=\"IsSym\
metricDigraph\"/>\n            and not  <Ref Prop=\"DigraphHasLoops\"/>\n     \
     </Alt>\n          <Alt Not=\"HTML\">\n            <Ref Prop=\"IsSymmetric\
Digraph\"/>\n          </Alt>\n        </Item>\n        <Item>\n          <Alt\
 Only=\"HTML\">\n            The &Grape; function <C>IsSimpleGraph</C> is equi\
valent to\n            <Ref Prop=\"IsSymmetricDigraph\"/>\n            and not\
  <Ref Prop=\"DigraphHasLoops\"/>.\n          </Alt>\n        </Item>\n      <\
/Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>Adjacency\
</C>\n        </Item>\n        <Item>\n          <Ref Oper=\"OutNeighboursOfVe\
rtex\"/>\n          <Alt Only=\"HTML\">\n            (see also <Ref Oper=\"InN\
eighboursOfVertex\"/>)\n          </Alt>\n        </Item>\n        <Item>\n   \
       <Alt Only=\"HTML\">\n            The operation <Ref Oper=\"OutNeighbour\
sOfVertex\"/> behaves the same\n            as <C>Adjacency</C> in &Grape;.\n \
         </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row\
>\n        <Item>\n          <C>IsEdge</C>\n        </Item>\n        <Item>\n \
         <Ref Oper=\"IsDigraphEdge\" Label=\"for digraph and list\"/>\n       \
 </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            The argum\
ents of\n            <Ref Oper=\"IsDigraphEdge\" Label=\"for digraph and list\
\"/>\n            can be a digraph and an edge, or a digraph and two vertices.\
 In the\n            first form the operation\n            <Ref Oper=\"IsDigra\
phEdge\" Label=\"for digraph and list\"/>\n            behaves the same as <C>\
IsEdge</C> in &Grape;.\n          </Alt>\n        </Item>\n      </Row>\n     \
 <HorLine/>\n\n      <Row>\n        <Item>\n          <C>DirectedEdges</C>\n  \
      </Item>\n        <Item>\n          <Ref Attr=\"DigraphEdges\"/>\n       \
 </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            The attri\
bute <Ref Attr=\"DigraphEdges\"/> behaves the same\n            as <C>Directed\
Edges</C> in &Grape;.\n          </Alt>\n        </Item>\n      </Row>\n      \
<HorLine/>\n\n      <Row>\n        <Item>\n          <C>UndirectedEdges</C>\n \
       </Item>\n        <Item>\n          None\n        </Item>\n        <Item\
>\n          <Alt Only=\"HTML\">\n            There is no analogous function i\
n &Digraphs;, and no plans to\n            include one.\n          </Alt>\n   \
     </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n \
         <C>Distance</C>\n        </Item>\n        <Item>\n          <Ref Oper\
=\"DigraphShortestDistance\"\n               Label=\"for a digraph and two ver\
tices\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n   \
         The operation <Ref Oper=\"DigraphShortestDistance\"\n            Labe\
l=\"for a digraph and two vertices\"/> behaves the same as\n            <C>Dis\
tance</C> in &Grape;.\n          </Alt>\n        </Item>\n      </Row>\n      \
<HorLine/>\n\n      <Row>\n        <Item>\n          <C>Diameter</C>\n        \
</Item>\n        <Item>\n          <Ref Attr=\"DigraphDiameter\"/>\n        </\
Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            The attribut\
e <Ref Attr=\"DigraphDiameter\"/> behaves the same\n            as <C>Diameter\
</C> in &Grape;.\n          </Alt>\n        </Item>\n      </Row>\n      <HorL\
ine/>\n\n      <Row>\n        <Item>\n          <C>Girth</C>\n        </Item>\
\n        <Item>\n          <Ref Attr=\"DigraphUndirectedGirth\"/>\n        </\
Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            The attribut\
e <Ref Attr=\"DigraphUndirectedGirth\"/> behaves the same\n            as <C>G\
irth</C> in &Grape; except that in the case that the\n            argument is \
a forest, <K>infinity</K> is returned by &Digraphs;\n            whereas <C>-1\
</C> is returned by &Grape;.\n          </Alt>\n        </Item>\n      </Row>\
\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>IsConnectedGra\
ph</C>\n        </Item>\n        <Item>\n          <Ref Prop=\"IsStronglyConne\
ctedDigraph\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\"\
>\n            The attribute <Ref Prop=\"IsStronglyConnectedDigraph\"/> behave\
s the\n            same as <C>IsConnectedGraph</C> in &Grape;.\n          </Al\
t>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <I\
tem>\n          <C>IsBipartite</C>\n        </Item>\n        <Item>\n         \
 <Ref Prop=\"IsBipartiteDigraph\"/>\n          <Alt Only=\"HTML\">\n          \
  and <Ref Prop=\"IsSymmetricDigraph\"/>\n          </Alt>\n        </Item>\n \
       <Item>\n          <Alt Only=\"HTML\">\n            The &Grape; function\
 <C>IsBipartite</C> is equivalent to\n            <Ref Prop=\"IsBipartiteDigra\
ph\"/> and <Ref\n              Prop=\"IsSymmetricDigraph\"/>.\n          </Alt\
>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <It\
em>\n          <C>IsNullGraph</C>\n        </Item>\n        <Item>\n          \
<Ref Prop=\"IsNullDigraph\"/>\n          <Alt Only=\"HTML\">\n            or <\
Ref Prop=\"IsEmptyDigraph\"/>\n          </Alt>\n        </Item>\n        <Ite\
m>\n          <Alt Only=\"HTML\">\n            The &Grape; function <C>IsNullG\
raph</C> is equivalent to\n            <Ref Prop=\"IsEmptyDigraph\"/> and its \
synonym <Ref\n              Prop=\"IsNullDigraph\"/>.\n          </Alt>\n     \
   </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n   \
       <C>IsCompleteGraph</C>\n        </Item>\n        <Item>\n          <Ref\
 Prop=\"IsCompleteDigraph\"/>\n        </Item>\n        <Item>\n          <Alt\
 Only=\"HTML\">\n            The &Grape; function <C>IsCompleteGraph</C> is ro\
ughly\n            equivalent to\n            <Ref Prop=\"IsCompleteDigraph\"/\
> except that in &Digraphs;\n            a complete digraph has <E>no loops</E\
>.\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n\n  <\
/Table>\n  </Section>\n\n  <Section>\n    <Heading>\n      Functions to determ\
ine regularity properties of graphs\n    </Heading>\n    <Alt Not=\"HTML\">\n \
     <E>\n        The table in this section contains more information when vie\
wed in\n        html format.\n      </E>\n    </Alt>\n\n    <Table Align=\"|l|\
l|l|\">\n      <HorLine/>\n\n      <Row>\n        <Item>\n          &Grape; co\
mmand\n        </Item>\n        <Item>\n          &Digraphs; command\n        \
</Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            Comments\n\
          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Ro\
w>\n        <Item>\n          <C>IsRegularGraph</C>\n        </Item>\n        \
<Item>\n          <Ref Prop=\"IsOutRegularDigraph\"/>\n          <Alt Only=\"H\
TML\">\n            (see also\n            <Ref Prop=\"IsInRegularDigraph\"/>\
\n            and\n            <Ref Prop=\"IsRegularDigraph\"/>)\n          </\
Alt>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n        \
    The &Grape; function <C>IsRegularGraph</C> is\n            equivalent to <\
Ref Prop=\"IsOutRegularDigraph\"/>.\n          </Alt>\n        </Item>\n      \
</Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>LocalPar\
ameters</C>\n        </Item>\n        <Item>\n          None\n        </Item>\
\n        <Item>\n         <Alt Only=\"HTML\">\n            The &Grape; functi\
on <C>LocalParameters</C> has no equivalent\n            function in &Digraphs\
;, although this might change in the future.\n          </Alt>\n        </Item\
>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C\
>GlobalParameters</C>\n        </Item>\n        <Item>\n          None\n      \
  </Item>\n        <Item>\n         <Alt Only=\"HTML\">\n            The &Grap\
e; function <C>GlobalParameters</C> has no equivalent\n            function in\
 &Digraphs;, although this might change in the future.\n          </Alt>\n    \
    </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n  \
        <C>IsDistanceRegular</C>\n        </Item>\n        <Item>\n          <\
Ref Prop=\"IsDistanceRegularDigraph\"/>\n        </Item>\n        <Item>\n    \
      <Alt Only=\"HTML\">\n            The &Grape; function <C>IsDistanceRegul\
ar</C> is\n            equivalent to <Ref Prop=\"IsDistanceRegularDigraph\"/>.\
\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <\
Row>\n        <Item>\n          <C>CollapsedAdjacencyMat</C>\n        </Item>\
\n        <Item>\n          None\n        </Item>\n        <Item>\n         <A\
lt Only=\"HTML\">\n            The &Grape; function <C>CollapsedAdjacencyMat</\
C> has no equivalent\n            function in &Digraphs;, although this might \
change in the future.\n          </Alt>\n        </Item>\n      </Row>\n      \
<HorLine/>\n\n      <Row>\n        <Item>\n          <C>OrbitalGraphColadjMats\
</C>\n        </Item>\n        <Item>\n          None\n        </Item>\n      \
  <Item>\n         <Alt Only=\"HTML\">\n            The &Grape; function <C>Or\
bitalGraphColadjMats</C> has no equivalent\n            function in &Digraphs;\
, although this might change in the future.\n          </Alt>\n        </Item>\
\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>\
VertexTransitiveDRGs</C>\n        </Item>\n        <Item>\n          None\n   \
     </Item>\n        <Item>\n         <Alt Only=\"HTML\">\n            The &G\
rape; function <C>VertexTransitiveDRGs</C> has no equivalent\n            func\
tion in &Digraphs;, although this might change in the future.\n          </Alt\
>\n        </Item>\n      </Row>\n      <HorLine/>\n\n    </Table>\n\n  </Sect\
ion>\n\n  <Section>\n    <Heading>\n      Some special vertex subsets of a gra\
ph\n    </Heading>\n    <Alt Not=\"HTML\">\n      <E>\n        The table in th\
is section contains more information when viewed in\n        html format.\n   \
   </E>\n    </Alt>\n\n    <Table Align=\"|l|l|l|\">\n      <HorLine/>\n\n    \
  <Row>\n        <Item>\n          &Grape; command\n        </Item>\n        <\
Item>\n          &Digraphs; command\n        </Item>\n        <Item>\n        \
  <Alt Only=\"HTML\">\n            Comments\n          </Alt>\n        </Item>\
\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>\
ConnectedComponent</C>\n        </Item>\n        <Item>\n          <Ref Oper=\
\"DigraphConnectedComponent\"/>\n        </Item>\n        <Item>\n          <A\
lt Only=\"HTML\">\n            When applied to a simple di/graph and a vertex,\
\n            <C>ConnectedComponent</C> in &Grape; is equivalent to\n         \
   <Ref Oper=\"DigraphConnectedComponent\"/>.\n            <Ref Oper=\"Digraph\
ConnectedComponent\"/> can also be applied to\n            non-simple graphs (\
in the language of &Grape;).\n          </Alt>\n        </Item>\n      </Row>\
\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>ConnectedCompo\
nents</C>\n        </Item>\n        <Item>\n          <Ref Attr=\"DigraphConne\
ctedComponents\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"HTM\
L\">\n            When applied to a simple di/graph,\n            <C>Connected\
Components</C> in &Grape; is equivalent to\n            <Ref Attr=\"DigraphCon\
nectedComponents\"/>.\n            <Ref Attr=\"DigraphConnectedComponents\"/> \
can also be applied to\n            non-simple graphs (in the language of &Gra\
pe;).\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n  \
    <Row>\n        <Item>\n          <C>Bicomponents</C>\n        </Item>\n   \
     <Item>\n          <Ref Attr=\"DigraphBicomponents\"/>\n        </Item>\n \
       <Item>\n          <Alt Only=\"HTML\">\n            When applied to a si\
mple bipartite di/graph,\n            <C>Bicomponents</C> in &Grape; is equiva\
lent to\n            <Ref Attr=\"DigraphBicomponents\"/>.\n            The def\
inition of <Ref Prop=\"IsBipartiteDigraph\"/> does not require\n            it\
s argument to be simple (in the language of &Grape;), i.e. the\n            bi\
partite graphs in &Grape; are a proper subset of the bipartite\n            di\
graphs in &Digraphs;.\n          </Alt>\n        </Item>\n      </Row>\n      \
<HorLine/>\n\n      <Row>\n        <Item>\n          <C>DistanceSet</C>\n     \
   </Item>\n        <Item>\n            <Ref Oper=\"DigraphDistanceSet\"\n    \
          Label=\"for a digraph, a pos int, and an int\"/>\n        </Item>\n \
       <Item>\n          <Alt Only=\"HTML\">\n            <C>DistanceSet</C> i\
n &Grape; is equivalent to\n            <Ref Oper=\"DigraphDistanceSet\"\n    \
          Label=\"for a digraph, a pos int, and an int\"/> in &Digraphs;.\n   \
       </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\
\n        <Item>\n          <C>Layers</C>\n        </Item>\n        <Item>\n  \
        <Ref Oper=\"DigraphLayers\"/>\n        </Item>\n        <Item>\n      \
    <Alt Only=\"HTML\">\n            <C>Layers</C> in &Grape; is equivalent to\
\n            <Ref Oper=\"DigraphLayers\"/> in &Digraphs;.\n          </Alt>\n\
        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\
\n          <C>IndependentSet</C>\n        </Item>\n        <Item>\n          \
<Ref Func=\"DigraphIndependentSet\"/>\n        </Item>\n        <Item>\n      \
    <Alt Only=\"HTML\">\n            <C>IndependentSet</C> in &Grape; is equiv\
alent to\n            <Ref Func=\"DigraphIndependentSet\"/> in &Digraphs;.\n  \
        </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n    </Table\
>\n\n  </Section>\n\n  <Section>\n    <Heading>\n      Functions to construct \
new graphs from old\n    </Heading>\n    <Alt Not=\"HTML\">\n      <E>\n      \
  The table in this section contains more information when viewed in\n        \
html format.\n      </E>\n    </Alt>\n\n    <Table Align=\"|l|l|l|\">\n      <\
HorLine/>\n\n      <Row>\n        <Item>\n          &Grape; command\n        <\
/Item>\n        <Item>\n          &Digraphs; command\n        </Item>\n       \
 <Item>\n          <Alt Only=\"HTML\">\n            Comments\n          </Alt>\
\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Ite\
m>\n          <C>InducedSubgraph</C>\n        </Item>\n        <Item>\n       \
   <Ref Oper=\"InducedSubdigraph\"/>\n        </Item>\n        <Item>\n       \
   <Alt Only=\"HTML\">\n            <Ref Oper=\"InducedSubdigraph\"/> in &Digr\
aphs; does not allow a third\n            argument <C>G</C> specifying a group\
 of automorphisms on the\n            resultant graph. This may be included in\
 a future release.\n          </Alt>\n        </Item>\n      </Row>\n      <Ho\
rLine/>\n\n      <Row>\n        <Item>\n          <C>DistanceSetInduced</C>\n \
       </Item>\n        <Item>\n          None\n        </Item>\n        <Item\
>\n          <Alt Only=\"HTML\">\n            There is no analogous function i\
n &Digraphs;, and no plans to\n            include one.\n          </Alt>\n   \
     </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n \
         <C>DistanceGraph</C>\n        </Item>\n        <Item>\n          <Ref\
 Oper=\"DistanceDigraph\" Label=\"for digraph and list\"/>\n        </Item>\n \
       <Item>\n          <Alt Only=\"HTML\">\n            <C>DistanceGraph</C>\
 in &Grape; is equivalent to\n            <Ref Oper=\"DistanceDigraph\" Label=\
\"for digraph and list\"/> in\n            &Digraphs;.\n          </Alt>\n    \
    </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n  \
        <C>ComplementGraph</C>\n        </Item>\n        <Item>\n          <Re\
f Oper=\"DigraphDual\"/>\n        </Item>\n        <Item>\n          <Alt Only\
=\"HTML\">\n            <Ref Oper=\"DigraphDual\"/> in &Digraphs; is equivalen\
t to\n            <C>ComplementGraph</C> in &Grape; with the optional argument\
\n            <A>comploops</A> set to <K>true</K> (loops/nonloops are\n       \
     complemented).\n          </Alt>\n        </Item>\n      </Row>\n      <H\
orLine/>\n\n      <Row>\n        <Item>\n          <C>PointGraph</C>\n        \
</Item>\n        <Item>\n          None\n        </Item>\n        <Item>\n    \
      <Alt Only=\"HTML\">\n            There is no analogous function in &Digr\
aphs;, and no plans to\n            include one.\n          </Alt>\n        </\
Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n        \
  <C>EdgeGraph</C>\n        </Item>\n        <Item>\n          <Ref Oper=\"Edg\
eUndirectedDigraph\"/>\n        </Item>\n        <Item>\n          <Alt Only=\
\"HTML\">\n            <C>EdgeGraph</C> in &Grape; is equivalent to\n         \
   <Ref Oper=\"EdgeUndirectedDigraph\"/> in &Digraphs;.\n          </Alt>\n   \
     </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n \
         <C>SwitchedGraph</C>\n        </Item>\n        <Item>\n          None\
\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            \
There is no analogous function in &Digraphs;, and no plans to\n            inc\
lude one.\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\
\n      <Row>\n        <Item>\n          <C>UnderlyingGraph</C>\n        </Ite\
m>\n        <Item>\n          <Ref Oper=\"DigraphSymmetricClosure\"/>\n       \
 </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            <C>Underl\
yingGraph</C> in &Grape; is equivalent to\n            <Ref Oper=\"DigraphSymm\
etricClosure\"/> in &Digraphs;.\n          </Alt>\n        </Item>\n      </Ro\
w>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>QuotientGrap\
h</C>\n        </Item>\n        <Item>\n          <Ref Oper=\"QuotientDigraph\
\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n        \
    <Ref Oper=\"QuotientDigraph\"/> in &Digraphs; takes a partition\n         \
   <C>p</C> of the vertices of the digraph, rather than a set of\n            \
generating pairs.  Hence, the equivalence might not be\n            group-inva\
riant.  Also note that in &Digraphs; multiple edges may be\n            create\
d, whereas in &Grape; they are effectively combined into a\n            single\
 edge.\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\n \
     <Row>\n        <Item>\n          <C>BipartiteDouble</C>\n        </Item>\
\n        <Item>\n          <Ref Oper=\"BipartiteDoubleDigraph\"/>\n        </\
Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            <C>Bipartite\
Double</C> in &Grape; is equivalent to\n            <Ref Oper=\"BipartiteDoubl\
eDigraph\"/> in &Digraphs;.\n          </Alt>\n        </Item>\n      </Row>\n\
      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>GeodesicsGraph</\
C>\n        </Item>\n        <Item>\n          None\n        </Item>\n        \
<Item>\n          <Alt Only=\"HTML\">\n            There is no analogous funct\
ion in &Digraphs;, and no plans to\n            include one.\n          </Alt>\
\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Ite\
m>\n          <C>CollapsedIndependentOrbitsGraph</C>\n        </Item>\n       \
 <Item>\n          None\n        </Item>\n        <Item>\n          <Alt Only=\
\"HTML\">\n            There is no analogous function in &Digraphs;, although \
this feature\n            might be implemented in the future.\n          </Alt\
>\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <It\
em>\n          <C>CollapsedCompleteOrbitsGraph</C>\n        </Item>\n        <\
Item>\n          None\n        </Item>\n        <Item>\n          <Alt Only=\"\
HTML\">\n            There is no analogous function in &Digraphs;, although th\
is feature\n            might be implemented in the future.\n          </Alt>\
\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Ite\
m>\n          <C>NewGroupGraph</C>\n        </Item>\n        <Item>\n         \
 None\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n       \
     There is no analogous function in &Digraphs;.  However, the same\n       \
     results would be possible by calling <Ref Oper=\"DigraphCopy\"/> on\n    \
        the digraph to produce a copy <C>gr</C>, and then applying\n          \
  <C>SetDigraphGroup(gr, G)</C>.\n          </Alt>\n        </Item>\n      </R\
ow>\n      <HorLine/>\n\n    </Table>\n\n  </Section>\n\n  <Section>\n    <Hea\
ding>\n      Vertex-Colouring and Complete Subgraphs\n    </Heading>\n    <Alt\
 Not=\"HTML\">\n      <E>\n        The table in this section contains more inf\
ormation when viewed in\n        html format.\n      </E>\n    </Alt>\n\n    <\
Table Align=\"|l|l|l|\">\n      <HorLine/>\n\n      <Row>\n        <Item>\n   \
       &Grape; command\n        </Item>\n        <Item>\n          &Digraphs; \
command\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n     \
       Comments\n          </Alt>\n        </Item>\n      </Row>\n      <HorLi\
ne/>\n\n      <Row>\n        <Item>\n          <C>VertexColouring</C>\n       \
 </Item>\n        <Item>\n          <Ref Attr=\"DigraphGreedyColouring\" Label\
=\"for a digraph\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"H\
TML\">\n            <C>VertexColouring</C> in &Grape; is equivalent to <Ref\n \
           Attr=\"DigraphGreedyColouring\" Label=\"for a digraph\"/> in &Digra\
phs;,\n            except it returns a transformation rather than a list of ve\
rtex\n            colors.\n          </Alt>\n        </Item>\n      </Row>\n  \
    <HorLine/>\n\n      <Row>\n        <Item>\n          <C>CompleteSubgraphs<\
/C>\n        </Item>\n        <Item>\n          <Ref Func=\"DigraphCliques\"/>\
\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n            \
The functionality of <C>CompleteSubgraphs</C> in &Grape; is provided\n        \
    by <Ref Func=\"DigraphCliques\"/> and <Ref Func=\"DigraphMaximalCliques\"/\
>\n            in &Digraphs;.\n          </Alt>\n        </Item>\n      </Row>\
\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>CompleteSubgra\
phsOfGivenSize</C>\n        </Item>\n        <Item>\n          <Ref Func=\"Dig\
raphCliques\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\"\
>\n            Much of the functionality of <C>CompleteSubgraphsOfGivenSize</C\
> in\n            &Grape; is provided by <Ref Func=\"DigraphCliques\"/> and <R\
ef\n              Func=\"DigraphMaximalCliques\"/> in &Digraphs;, except that \
the\n            functionality relating to vertex weights and partial colourin\
gs is\n            not implemented.\n          </Alt>\n        </Item>\n      \
</Row>\n      <HorLine/>\n\n    </Table>\n  </Section>\n\n  <Section>\n    <He\
ading>\n      Automorphism groups and isomorphism testing for graphs\n    </He\
ading>\n    <Alt Not=\"HTML\">\n      <E>\n        The table in this section c\
ontains more information when viewed in\n        html format.\n      </E>\n   \
 </Alt>\n\n    <Table Align=\"|l|l|l|\">\n      <HorLine/>\n\n      <Row>\n   \
     <Item>\n          &Grape; command\n        </Item>\n        <Item>\n     \
     &Digraphs; command\n        </Item>\n        <Item>\n          <Alt Only=\
\"HTML\">\n            Comments\n          </Alt>\n        </Item>\n      </Ro\
w>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>AutGroupGrap\
h</C>\n        </Item>\n        <Item>\n          <Ref Attr=\"AutomorphismGrou\
p\" Label=\"for a digraph\"/>\n        </Item>\n        <Item>\n          <Alt\
 Only=\"HTML\">\n            <C>AutGroupGraph</C> in &Grape; is equivalent to\
\n            <Ref Attr=\"AutomorphismGroup\" Label=\"for a digraph\"/> in &Di\
graphs;.\n          </Alt>\n        </Item>\n      </Row>\n      <HorLine/>\n\
\n      <Row>\n        <Item>\n          <C>GraphIsomorphism</C>\n        </It\
em>\n        <Item>\n          <Ref Oper=\"IsomorphismDigraphs\" Label=\"for d\
igraphs\"/>\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n \
           <C>GraphIsomorphism</C> in &Grape; is equivalent to <Ref\n         \
   Oper=\"IsomorphismDigraphs\" Label=\"for digraphs\"/> in &Digraphs;.\n     \
       Note however that <C>GraphIsomorphism</C>'s optional argument\n        \
    <A>firstunbindcanon</A> is not applicable, since the canonical\n          \
  labellings of a digraph are not portable between sessions.\n          </Alt>\
\n        </Item>\n      </Row>\n      <HorLine/>\n\n      <Row>\n        <Ite\
m>\n          <C>IsIsomorphicGraph</C>\n        </Item>\n        <Item>\n     \
     <Ref Oper=\"IsIsomorphicDigraph\" Label=\"for digraphs\"/>\n        </Ite\
m>\n        <Item>\n          <Alt Only=\"HTML\">\n            <C>IsIsomorphic\
Graph</C> in &Grape; is equivalent to <Ref\n            Oper=\"IsIsomorphicDig\
raph\" Label=\"for digraphs\"/> in &Digraphs;.\n            Note however that \
<C>IsIsomorphicGraph</C>'s optional argument\n            <A>firstunbindcanon<\
/A> is not applicable, since the canonical\n            labellings of a digrap\
h are not portable between sessions.\n          </Alt>\n        </Item>\n     \
 </Row>\n      <HorLine/>\n\n      <Row>\n        <Item>\n          <C>GraphIs\
omorphismClassRepresentatives</C>\n        </Item>\n        <Item>\n          \
None\n        </Item>\n        <Item>\n          <Alt Only=\"HTML\">\n        \
    There is no analogous function in &Digraphs;, although this feature\n     \
       might be implemented in the future.\n          </Alt>\n        </Item>\
\n      </Row>\n      <HorLine/>\n\n    </Table>\n  </Section>\n</Appendix>\n \
 <!-- Grape to Digraphs command map -->\n\n<Bibliography Databases=\"digraphs\
\" />\n<TheIndex/>\n\n</Book>\n", 
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  labels := 
    rec( AdjacencyMatrix := [ "5.2-1", "chap5_mj.html#X7DC2CD70830BEE60" ], 
      AdjacencyMatrixMutableCopy := 
        [ "5.2-1", "chap5_mj.html#X7DC2CD70830BEE60" ], 
      AdjacencyMatrixUpperTriangleLineDecoder := 
        [ "9.2-10", "chap9_mj.html#X7DF22D1687D096D6" ], 
      ArticulationPoints := [ "5.3-14", "chap5_mj.html#X7DDE06E47E605DD7" ], 
      AsBinaryRelation := [ "3.2-1", "chap3_mj.html#X7FBC4BDB82FBEDD2" ], 
      AsDigraph := [ "3.2-2", "chap3_mj.html#X83CA27E67F685EB3" ], 
      AsGraph := [ "3.2-4", "chap3_mj.html#X7C4F13E080EC16B0" ], 
      AsMonoid := [ "5.5-1", "chap5_mj.html#X87D5C60D7B0C1309" ], 
      ("AsSemigroup (for a filter and a digraph)") := 
        [ "5.5-1", "chap5_mj.html#X87D5C60D7B0C1309" ], 
      ("AsSemigroup (for a filter, semilattice digraph, and two lists)") := 
        [ "5.5-2", "chap5_mj.html#X7C6D5EC27C51066B" ], 
      AsTransformation := [ "3.2-5", "chap3_mj.html#X7C5360B2799943F3" ], 
      ("Attributes and operations") := 
        [ "5", "chap5_mj.html#X8739F6CD78C90B14" ], 
      ("AutomorphismGroup (for a digraph and a homogeneous list)") := 
        [ "7.2-5", "chap7_mj.html#X877732B1783C391B" ], 
      ("AutomorphismGroup (for a digraph)") := 
        [ "7.2-2", "chap7_mj.html#X858C32127A190175" ], 
      ("AutomorphismGroup (for a digraph, homogeneous list, and list)") := 
        [ "7.2-6", "chap7_mj.html#X7DA2C4FE837FFE01" ], 
      BipartiteDoubleDigraph := [ "3.3-37", "chap3_mj.html#X7C6E6CB284982C7A" 
         ], ("BlissAutomorphismGroup (for a digraph and homogenous list)") := 
        [ "7.2-3", "chap7_mj.html#X7E7B0D88865A89F6" ], 
      ("BlissAutomorphismGroup (for a digraph)") := 
        [ "7.2-3", "chap7_mj.html#X7E7B0D88865A89F6" ], 
      ("BlissAutomorphismGroup (for a digraph, homogenous list, and list)") :=\
 [ "7.2-3", "chap7_mj.html#X7E7B0D88865A89F6" ], 
      BlissCanonicalDigraph := [ "7.2-9", "chap7_mj.html#X877B1D377EC197D7" ],
      ("BlissCanonicalLabelling (for a digraph and a list)") := 
        [ "7.2-8", "chap7_mj.html#X87DA265D803DB337" ], 
      ("BlissCanonicalLabelling (for a digraph)") := 
        [ "7.2-7", "chap7_mj.html#X7D676FE67A6684FF" ], 
      BooleanAdjacencyMatrix := [ "5.2-3", "chap5_mj.html#X8507DC4F794780C1" ]
        , BooleanAdjacencyMatrixMutableCopy := 
        [ "5.2-3", "chap5_mj.html#X8507DC4F794780C1" ], 
      Bridges := [ "5.3-15", "chap5_mj.html#X84D5A125848BD800" ], 
      CayleyDigraph := [ "3.1-12", "chap3_mj.html#X7FCADADC7EC28478" ], 
      ChainDigraph := [ "3.5-1", "chap3_mj.html#X870594FC866AC88E" ], 
      CharacteristicPolynomial := 
        [ "5.2-2", "chap5_mj.html#X87FA0A727CDB060B" ], 
      ChromaticNumber := [ "7.3-17", "chap7_mj.html#X807D49358529A37C" ], 
      CliqueNumber := [ "8.1-5", "chap8_mj.html#X78427A8B81FEB457" ], 
      CliquesFinder := [ "8.1-2", "chap8_mj.html#X7A3BC9FF8169ABCD" ], 
      ("Compiling the kernel module") := 
        [ "2.3", "chap2_mj.html#X849F6196875A6DF5" ], 
      CompleteBipartiteDigraph := 
        [ "3.5-3", "chap3_mj.html#X8795B0AD856014FA" ], 
      CompleteDigraph := [ "3.5-2", "chap3_mj.html#X812417E278198D9C" ], 
      CompleteMultipartiteDigraph := 
        [ "3.5-4", "chap3_mj.html#X873F29CC863241F8" ], 
      ("Creating digraphs") := [ "3", "chap3_mj.html#X7D34861E863A5D93" ], 
      CycleDigraph := [ "3.5-5", "chap3_mj.html#X80C29DDE876FFBEB" ], 
      Definitions := [ "1.1-1", "chap1_mj.html#X84541F61810C741D" ], 
      DegreeMatrix := [ "5.2-16", "chap5_mj.html#X7BEAE1C78267F54D" ], 
      DiSparse6String := [ "9.2-3", "chap9_mj.html#X782A052979EA2376" ], 
      Digraph := [ "3.1-7", "chap3_mj.html#X834843057CE86655" ], 
      ("Digraph (for a group, list, function, and function)") := 
        [ "3.1-7", "chap3_mj.html#X834843057CE86655" ], 
      ("Digraph (for a list and function)") := 
        [ "3.1-7", "chap3_mj.html#X834843057CE86655" ], 
      Digraph6String := [ "9.2-3", "chap9_mj.html#X782A052979EA2376" ], 
      DigraphAddAllLoops := [ "3.3-38", "chap3_mj.html#X8167A50A83256ED1" ], 
      DigraphAddAllLoopsAttr := [ "3.3-38", "chap3_mj.html#X8167A50A83256ED1" 
         ], ("DigraphAddEdge (for a digraph and an edge)") := 
        [ "3.3-16", "chap3_mj.html#X7E58CC4880627658" ], 
      ("DigraphAddEdge (for a digraph, source, and range)") := 
        [ "3.3-16", "chap3_mj.html#X7E58CC4880627658" ], 
      DigraphAddEdgeOrbit := [ "3.3-17", "chap3_mj.html#X7BE5C7028760B053" ], 
      DigraphAddEdges := [ "3.3-18", "chap3_mj.html#X8693A61B7F752C76" ], 
      DigraphAddVertex := [ "3.3-14", "chap3_mj.html#X83B2506D79453208" ], 
      ("DigraphAddVertices (for a digraph and a list of labels)") := 
        [ "3.3-15", "chap3_mj.html#X8134BEE7786BD3A7" ], 
      ("DigraphAddVertices (for a digraph and an integer)") := 
        [ "3.3-15", "chap3_mj.html#X8134BEE7786BD3A7" ], 
      DigraphAdjacencyFunction := 
        [ "5.2-4", "chap5_mj.html#X7AFCE34A7A04D5C1" ], 
      DigraphAllSimpleCircuits := 
        [ "5.3-24", "chap5_mj.html#X7ECD16838704FAAA" ], 
      DigraphBicomponents := [ "5.3-13", "chap5_mj.html#X7F1B5A2782F598B1" ], 
      DigraphByAdjacencyMatrix := 
        [ "3.1-8", "chap3_mj.html#X8023FE387A3AB609" ], 
      DigraphByEdges := [ "3.1-9", "chap3_mj.html#X7F37B6768349E269" ], 
      DigraphByInNeighbors := [ "3.1-11", "chap3_mj.html#X81BC49B57EAADEFB" ],
      DigraphByInNeighbours := [ "3.1-11", "chap3_mj.html#X81BC49B57EAADEFB" ]
        , 
      DigraphByOutNeighboursType := 
        [ "3.1-6", "chap3_mj.html#X86E798B779515678" ], 
      ("DigraphCartesianProduct (for a list of digraphs)") := 
        [ "3.3-30", "chap3_mj.html#X7D625CC87DBFFDED" ], 
      ("DigraphCartesianProduct (for a positive number of digraphs)") := 
        [ "3.3-30", "chap3_mj.html#X7D625CC87DBFFDED" ], 
      DigraphCartesianProductProjections := 
        [ "3.3-32", "chap3_mj.html#X8795087A78FE7D54" ], 
      DigraphClique := [ "8.1-3", "chap8_mj.html#X789854AC7B466402" ], 
      DigraphCliques := [ "8.1-4", "chap8_mj.html#X84EA2F9482B8D4AF" ], 
      DigraphCliquesReps := [ "8.1-4", "chap8_mj.html#X84EA2F9482B8D4AF" ], 
      DigraphClosure := [ "3.3-40", "chap3_mj.html#X86F9CCEA839ABC48" ], 
      ("DigraphColouring (for a digraph and a number of colours)") := 
        [ "7.3-14", "chap7_mj.html#X86D0A74B83D6B9A7" ], 
      DigraphConnectedComponent := 
        [ "5.3-10", "chap5_mj.html#X8484EC557810CD31" ], 
      DigraphConnectedComponents := 
        [ "5.3-9", "chap5_mj.html#X842FAD6A7B835977" ], 
      DigraphCopy := [ "3.3-1", "chap3_mj.html#X83D93A8A8251E6F9" ], 
      DigraphCopySameMutability := 
        [ "3.3-1", "chap3_mj.html#X83D93A8A8251E6F9" ], 
      DigraphCore := [ "7.3-18", "chap7_mj.html#X863487EF7D64EF56" ], 
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      DigraphDegeneracyOrdering := 
        [ "5.3-28", "chap5_mj.html#X827C2BD17A4547E3" ], 
      DigraphDiameter := [ "5.3-1", "chap5_mj.html#X7F16B9EB8398459C" ], 
      ("DigraphDijkstra (for a source and target)") := 
        [ "5.3-31", "chap5_mj.html#X79352A8286D1D8F6" ], 
      ("DigraphDijkstra (for a source)") := 
        [ "5.3-31", "chap5_mj.html#X79352A8286D1D8F6" ], 
      ("DigraphDirectProduct (for a list of digraphs)") := 
        [ "3.3-31", "chap3_mj.html#X84D24DC9833B54A5" ], 
      ("DigraphDirectProduct (for a positive number of digraphs)") := 
        [ "3.3-31", "chap3_mj.html#X84D24DC9833B54A5" ], 
      DigraphDirectProductProjections := 
        [ "3.3-33", "chap3_mj.html#X84FB64F185B804C2" ], 
      ("DigraphDisjointUnion (for a list of digraphs)") := 
        [ "3.3-27", "chap3_mj.html#X814F1DFC83DB273F" ], 
      ("DigraphDisjointUnion (for an arbitrary number of digraphs)") := 
        [ "3.3-27", "chap3_mj.html#X814F1DFC83DB273F" ], 
      ("DigraphDistanceSet (for a digraph, a pos int, and a list)") := 
        [ "5.3-5", "chap5_mj.html#X7CB7DDCD84621D38" ], 
      ("DigraphDistanceSet (for a digraph, a pos int, and an int)") := 
        [ "5.3-5", "chap5_mj.html#X7CB7DDCD84621D38" ], 
      DigraphDual := [ "3.3-10", "chap3_mj.html#X7F71D99D852B130F" ], 
      DigraphDualAttr := [ "3.3-10", "chap3_mj.html#X7F71D99D852B130F" ], 
      DigraphEdgeLabel := [ "5.1-11", "chap5_mj.html#X79FAEACC7F438C2F" ], 
      DigraphEdgeLabels := [ "5.1-12", "chap5_mj.html#X7C24851087D4A8FB" ], 
      ("DigraphEdgeUnion (for a list of digraphs)") := 
        [ "3.3-28", "chap3_mj.html#X7DA997697D310E44" ], 
      ("DigraphEdgeUnion (for a positive number of digraphs)") := 
        [ "3.3-28", "chap3_mj.html#X7DA997697D310E44" ], 
      DigraphEdges := [ "5.1-3", "chap5_mj.html#X7D1C6A4D7ECEC317" ], 
      DigraphEmbedding := [ "7.3-8", "chap7_mj.html#X7AD04CC186E86CCA" ], 
      DigraphEpimorphism := [ "7.3-6", "chap7_mj.html#X7CB5AD9F861684FD" ], 
      DigraphFamily := [ "3.1-6", "chap3_mj.html#X86E798B779515678" ], 
      DigraphFile := [ "9.2-4", "chap9_mj.html#X7845ACDA7D4D333D" ], 
      DigraphFloydWarshall := [ "5.3-18", "chap5_mj.html#X864A31A8809F61C2" ],
      DigraphFromDiSparse6String := 
        [ "9.2-2", "chap9_mj.html#X873D6EB8836A3C61" ], 
      DigraphFromDigraph6String := 
        [ "9.2-2", "chap9_mj.html#X873D6EB8836A3C61" ], 
      DigraphFromGraph6String := [ "9.2-2", "chap9_mj.html#X873D6EB8836A3C61" 
         ], 
      DigraphFromPlainTextString := 
        [ "9.2-12", "chap9_mj.html#X8540FC21796A793F" ], 
      DigraphFromSparse6String := 
        [ "9.2-2", "chap9_mj.html#X873D6EB8836A3C61" ], 
      DigraphGirth := [ "5.3-6", "chap5_mj.html#X79A3DA4078CF3C90" ], 
      ("DigraphGreedyColouring (for a digraph and vertex order function)") := 
        [ "7.3-15", "chap7_mj.html#X7AB7200D831013C1" ], 
      ("DigraphGreedyColouring (for a digraph and vertex order)") := 
        [ "7.3-15", "chap7_mj.html#X7AB7200D831013C1" ], 
      ("DigraphGreedyColouring (for a digraph)") := 
        [ "7.3-15", "chap7_mj.html#X7AB7200D831013C1" ], 
      DigraphGroup := [ "7.2-10", "chap7_mj.html#X803ACEDA7BBAC5B3" ], 
      DigraphHasLoops := [ "6.1-1", "chap6_mj.html#X7D92935C7D535187" ], 
      DigraphHomomorphism := [ "7.3-2", "chap7_mj.html#X85E9B019877AD7FE" ], 
      DigraphImmutableCopy := [ "3.3-1", "chap3_mj.html#X83D93A8A8251E6F9" ], 
      DigraphImmutableCopyIfImmutable := 
        [ "3.3-2", "chap3_mj.html#X8399F7427B227228" ], 
      DigraphImmutableCopyIfMutable := 
        [ "3.3-2", "chap3_mj.html#X8399F7427B227228" ], 
      DigraphInEdges := [ "5.1-13", "chap5_mj.html#X7EFAF01B7A155157" ], 
      DigraphIndependentSet := [ "8.2-2", "chap8_mj.html#X84350678782BFAB7" ],
      DigraphIndependentSets := [ "8.2-3", "chap8_mj.html#X7D2C78EB81A798A9" ]
        , 
      DigraphIndependentSetsReps := 
        [ "8.2-3", "chap8_mj.html#X7D2C78EB81A798A9" ], 
      ("DigraphJoin (for a list of digraphs)") := 
        [ "3.3-29", "chap3_mj.html#X7DDFC759860E3390" ], 
      ("DigraphJoin (for a positive number of digraphs)") := 
        [ "3.3-29", "chap3_mj.html#X7DDFC759860E3390" ], 
      DigraphLayers := [ "5.3-26", "chap5_mj.html#X870E04307C5F213F" ], 
      DigraphLongestDistanceFromVertex := 
        [ "5.3-4", "chap5_mj.html#X8223718079D98A82" ], 
      DigraphLongestSimpleCircuit := 
        [ "5.3-25", "chap5_mj.html#X7C735C4E86BDD5F6" ], 
      DigraphLoops := [ "5.2-14", "chap5_mj.html#X83271F607BD809CF" ], 
      DigraphMaximalClique := [ "8.1-3", "chap8_mj.html#X789854AC7B466402" ], 
      DigraphMaximalCliques := [ "8.1-4", "chap8_mj.html#X84EA2F9482B8D4AF" ],
      DigraphMaximalCliquesAttr := 
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      DigraphMaximalCliquesReps := 
        [ "8.1-4", "chap8_mj.html#X84EA2F9482B8D4AF" ], 
      DigraphMaximalCliquesRepsAttr := 
        [ "8.1-4", "chap8_mj.html#X84EA2F9482B8D4AF" ], 
      DigraphMaximalIndependentSet := 
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      DigraphMaximalIndependentSets := 
        [ "8.2-3", "chap8_mj.html#X7D2C78EB81A798A9" ], 
      DigraphMaximalIndependentSetsAttr := 
        [ "8.2-3", "chap8_mj.html#X7D2C78EB81A798A9" ], 
      DigraphMaximalIndependentSetsReps := 
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      DigraphMaximalIndependentSetsRepsAttr := 
        [ "8.2-3", "chap8_mj.html#X7D2C78EB81A798A9" ], 
      DigraphMaximalMatching := [ "5.1-17", "chap5_mj.html#X7B7A67277B1C9A02" 
         ], 
      DigraphMaximumMatching := [ "5.1-18", "chap5_mj.html#X78E9847A858788D1" 
         ], 
      DigraphMonomorphism := [ "7.3-4", "chap7_mj.html#X82D0FCD87D47ACA8" ], 
      DigraphMutableCopy := [ "3.3-1", "chap3_mj.html#X83D93A8A8251E6F9" ], 
      DigraphMutableCopyIfImmutable := 
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      DigraphMutableCopyIfMutable := 
        [ "3.3-2", "chap3_mj.html#X8399F7427B227228" ], 
      DigraphMycielskian := [ "3.3-41", "chap3_mj.html#X7B5AC5FE859F4D80" ], 
      DigraphMycielskianAttr := [ "3.3-41", "chap3_mj.html#X7B5AC5FE859F4D80" 
         ], DigraphNrConnectedComponents := 
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      DigraphNrEdges := [ "5.1-4", "chap5_mj.html#X85E1CFDD7E164AD0" ], 
      DigraphNrLoops := [ "5.1-5", "chap5_mj.html#X7BDABAF07917462B" ], 
      DigraphNrStronglyConnectedComponents := 
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      DigraphNrVertices := [ "5.1-2", "chap5_mj.html#X7C6F19B57CB2E882" ], 
      DigraphOddGirth := [ "5.3-7", "chap5_mj.html#X8374B7357EC189C1" ], 
      DigraphOrbitReps := [ "7.2-12", "chap7_mj.html#X8386028782F2D3FF" ], 
      DigraphOrbits := [ "7.2-11", "chap7_mj.html#X8096C5287E459279" ], 
      DigraphOutEdges := [ "5.1-14", "chap5_mj.html#X7BECFE6687ECD028" ], 
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      DigraphPeriod := [ "5.3-17", "chap5_mj.html#X853D0B0981A33433" ], 
      DigraphPlainTextLineDecoder := 
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      DigraphPlainTextLineEncoder := 
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      DigraphReflexiveTransitiveClosureAttr := 
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      DigraphReflexiveTransitiveReduction := 
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      DigraphReflexiveTransitiveReductionAttr := 
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      DigraphRemoveAllMultipleEdges := 
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      DigraphRemoveAllMultipleEdgesAttr := 
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      ("DigraphRemoveEdge (for a digraph and an edge)") := 
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      ("DigraphRemoveEdge (for a digraph, source, and range)") := 
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      DigraphRemoveEdgeOrbit := [ "3.3-22", "chap3_mj.html#X85981D9187F49018" 
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      DigraphRemoveEdges := [ "3.3-23", "chap3_mj.html#X87093FDA7F88E732" ], 
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      DigraphRemoveVertex := [ "3.3-19", "chap3_mj.html#X7B634A2B83C08B16" ], 
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      DigraphReverseAttr := [ "3.3-9", "chap3_mj.html#X78DECD26811EFD7C" ], 
      ("DigraphReverseEdge (for a digraph and an edge)") := 
        [ "3.3-26", "chap3_mj.html#X7821753D85402A8C" ], 
      ("DigraphReverseEdge (for a digraph, source, and range)") := 
        [ "3.3-26", "chap3_mj.html#X7821753D85402A8C" ], 
      ("DigraphReverseEdges (for a digraph and a list of edges)") := 
        [ "3.3-26", "chap3_mj.html#X7821753D85402A8C" ], 
      DigraphSchreierVector := [ "7.2-13", "chap7_mj.html#X8657604E87A25E5F" ]
        , ("DigraphShortestDistance (for a digraph and a list)") := 
        [ "5.3-2", "chap5_mj.html#X8104A9D37BCD8A05" ], 
      ("DigraphShortestDistance (for a digraph and two vertices)") := 
        [ "5.3-2", "chap5_mj.html#X8104A9D37BCD8A05" ], 
      ("DigraphShortestDistance (for a digraph, a list, and a list)") := 
        [ "5.3-2", "chap5_mj.html#X8104A9D37BCD8A05" ], 
      DigraphShortestDistances := 
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      DigraphShortestPath := [ "5.3-22", "chap5_mj.html#X80E9D645843973A6" ], 
      DigraphSinks := [ "5.1-6", "chap5_mj.html#X85D5E08280914EE4" ], 
      DigraphSource := [ "5.2-5", "chap5_mj.html#X7FDEBF3279759961" ], 
      DigraphSources := [ "5.1-7", "chap5_mj.html#X7F5C6268839BE98C" ], 
      DigraphStabilizer := [ "7.2-14", "chap7_mj.html#X78913684795FB256" ], 
      DigraphStronglyConnectedComponent := 
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      DigraphStronglyConnectedComponents := 
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      DigraphSymmetricClosure := 
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      DigraphSymmetricClosureAttr := 
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      DigraphTopologicalSort := [ "5.1-8", "chap5_mj.html#X785C30378064CF47" ]
        , 
      DigraphTransitiveClosure := 
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      DigraphTransitiveClosureAttr := 
        [ "3.3-12", "chap3_mj.html#X7A6C419080AD41DE" ], 
      DigraphTransitiveReduction := 
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      DigraphTransitiveReductionAttr := 
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      DigraphUndirectedGirth := [ "5.3-8", "chap5_mj.html#X84688B337BDDBB09" ]
        , DigraphVertexLabel := [ "5.1-9", "chap5_mj.html#X7CA91E4B7904F793" ]
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      DigraphVertexLabels := [ "5.1-10", "chap5_mj.html#X7E51F2FE87140B32" ], 
      DigraphVertices := [ "5.1-1", "chap5_mj.html#X7C45F7D878D896AC" ], 
      DigraphWelshPowellOrder := 
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      DigraphsMakeDoc := [ "2.4-1", "chap2_mj.html#X870631C38610AC25" ], 
      DigraphsRespectsColouring := 
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      DigraphsTestExtreme := [ "2.5-3", "chap2_mj.html#X7885EF3E785D4298" ], 
      DigraphsTestInstall := [ "2.5-1", "chap2_mj.html#X86AF4DAE80B978DA" ], 
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      ("Attributes and operations") := "<span class=\"Heading\">Attributes and\
 operations</span>", 
      ("Compiling the kernel module") := "<span class=\"Heading\">Compiling th\
e kernel module</span>", 
      ("Creating digraphs") := "<span class=\"Heading\">Creating digraphs</spa\
n>", Definitions := "<span class=\"Heading\">Definitions</span>", 
      ("Finding cliques and independent sets") := "<span class=\"Heading\">Fin\
ding cliques and independent sets</span>", 
      ("For those in a hurry") := "<span class=\"Heading\">For those in a hurr\
y</span>", Homomorphisms := "<span class=\"Heading\">Homomorphisms</span>", 
      ("Installing Digraphs") := "<span class=\"Heading\">Installing <strong c\
lass=\"pkg\">Digraphs</strong></span>", 
      ("Isomorphisms and canonical labellings") := "<span class=\"Heading\">Is\
omorphisms and canonical labellings</span>", 
      Operators := "<span class=\"Heading\">Operators</span>", 
      ("Optional package dependencies") := "<span class=\"Heading\">Optional p\
ackage dependencies</span>", 
      ("Properties of digraphs") := "<span class=\"Heading\">Properties of dig\
raphs</span>", 
      ("Rebuilding the documentation") := "<span class=\"Heading\">Rebuilding \
the documentation</span>", 
      ("Testing your installation") := "<span class=\"Heading\">Testing your i\
nstallation</span>", 
      ("The Digraphs package") := "<span class=\"Heading\">\n    The <strong c\
lass=\"pkg\">Digraphs</strong> package\n  </span>", 
      ("The Grape package") := "<span class=\"Heading\">The Grape package</spa\
n>", ("Visualising and IO") := "<span class=\"Heading\">Visualising and IO</sp\
an>" ), linelength := 76, mathmode := "MathJax", name := "WHOLEDOCUMENT", 
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    [ 
      [ "Title page", ".", [ 0, 0, 0 ], 1, 1, "title page", 
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      [ "Abstract", ".-2", [ 0, 0, 2 ], 56, 2, "abstract", 
          "X7AA6C5737B711C89" ], 
      [ "Copyright", ".-1", [ 0, 0, 1 ], 62, 2, "copyright", 
          "X81488B807F2A1CF1" ], 
      [ "Acknowledgements", ".-3", [ 0, 0, 3 ], 74, 2, "acknowledgements", 
          "X82A988D47DFAFCFA" ], 
      [ "Table of Contents", ".-4", [ 0, 0, 4 ], 81, 3, "table of contents", 
          "X8537FEB07AF2BEC8" ], 
      [ 
          "\033[1X\033[33X\033[0;-2YThe \033[5XDigraphs\033[105X\033[101X\027\\
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          "the digraphs package", "X7F202ABA780E595D" ], 
      [ "\033[1X\033[33X\033[0;-2YIntroduction\033[133X\033[101X", "1.1", 
          [ 1, 1, 0 ], 4, 5, "introduction", "X7DFB63A97E67C0A1" ], 
      [ "\033[1X\033[33X\033[0;-2YDefinitions\033[133X\033[101X", "1.1-1", 
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      [ 
          "\033[1X\033[33X\033[0;-2YInstalling \033[5XDigraphs\033[105X\033[101X\\
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      [ "\033[1X\033[33X\033[0;-2YFor those in a hurry\033[133X\033[101X", 
          "2.1", [ 2, 1, 0 ], 4, 7, "for those in a hurry", 
          "X7DA3059C79842BF3" ], 
      [ 
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1X", "2.2", [ 2, 2, 0 ], 69, 8, "optional package dependencies", 
          "X780AA9D97EBCA95D" ], 
      [ "\033[1X\033[33X\033[0;-2YThe Grape package\033[133X\033[101X", 
          "2.2-1", [ 2, 2, 1 ], 76, 8, "the grape package", 
          "X8493C7587FCF6D8B" ], 
      [ 
          "\033[1X\033[33X\033[0;-2YCompiling the kernel module\033[133X\033[101X\
", "2.3", [ 2, 3, 0 ], 91, 8, "compiling the kernel module", 
          "X849F6196875A6DF5" ], 
      [ 
          "\033[1X\033[33X\033[0;-2YRebuilding the documentation\033[133X\033[101\
X", "2.4", [ 2, 4, 0 ], 125, 9, "rebuilding the documentation", 
          "X857CBE5484CF703A" ], 
      [ "\033[1X\033[33X\033[0;-2YTesting your installation\033[133X\033[101X"
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          "X7862D3F37C5BBDEF" ], 
      [ "\033[1X\033[33X\033[0;-2YCreating digraphs\033[133X\033[101X", "3", 
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          "3.1", [ 3, 1, 0 ], 6, 11, "creating digraphs", "X7D34861E863A5D93" 
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          "X83608C407CC8836D" ], 
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      [ "\033[1X\033[33X\033[0;-2YConnectivity and cycles\033[133X\033[101X", 
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033[101X", "6.5", [ 6, 5, 0 ], 1213, 119, "homomorphisms and transformations",
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      [ "\033[1X\033[33X\033[0;-2YHomomorphisms\033[133X\033[101X", "7", 
          [ 7, 0, 0 ], 1, 121, "homomorphisms", "X84975388859F203D" ], 
      [ "\033[1X\033[33X\033[0;-2YActing on digraphs\033[133X\033[101X", 
          "7.1", [ 7, 1, 0 ], 4, 121, "acting on digraphs", 
          "X8200192B80AD2071" ], 
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      [ 
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\033[101X", "8", [ 8, 0, 0 ], 1, 150, "finding cliques and independent sets", 
          "X7A7E0B957932DF44" ], 
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          "X800DAF137BA8E25B" ], 
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          "X78A5A34783C70CD7" ], 
      [ 
          "\033[1X\033[33X\033[0;-2YSome special vertex subsets of a graph\033[13\
3X\033[101X", "A.4", [ "A", 4, 0 ], 111, 183, 
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      [ 
          "\033[1X\033[33X\033[0;-2YFunctions to construct new graphs from old\\
033[133X\033[101X", "A.5", [ "A", 5, 0 ], 133, 184, 
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133X\033[101X", "A.6", [ "A", 6, 0 ], 171, 184, 
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          "X7DFC61EC7CBDBC7E" ], 
      [ "Bibliography", "Bib", [ "Bib", 0, 0 ], 1, 185, "bibliography", 
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      [ "References", "Bib", [ "Bib", 0, 0 ], 1, 185, "references", 
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      56, 57 ], start := 0, stop := 487835, 
  toctext := "<div class=\"ContChap\"><a href=\"chap1_mj.html#X7F202ABA780E595\
D\">1 <span class=\"Heading\">\n    The <strong class=\"pkg\">Digraphs</strong\
> package\n  </span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><spa\
n class=\"nocss\">&nbsp;</span><a href=\"chap1_mj.html#X7DFB63A97E67C0A1\">1.1\
 <span class=\"Heading\">Introduction</span></a>\n</span>\n<div class=\"ContSS\
Block\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap1_mj.html#X84541F61810C741D\">1.1-1 <span class=\"Heading\">De\
finitions</span></a>\n</span>\n</div></div>\n</div>\n<div class=\"ContChap\"><\
a href=\"chap2_mj.html#X817088B27F90D596\">2 <span class=\"Heading\">Installin\
g <strong class=\"pkg\">Digraphs</strong></span></a>\n<div class=\"ContSect\">\
<span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.\
html#X7DA3059C79842BF3\">2.1 <span class=\"Heading\">For those in a hurry</spa\
n></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"tocline\"><span\
 class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X780AA9D97EBCA95D\">2.2 \
<span class=\"Heading\">Optional package dependencies</span></a>\n</span>\n<di\
v class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8493C7587FCF6D8B\">2.2-1 <span clas\
s=\"Heading\">The Grape package</span></a>\n</span>\n</div></div>\n<div class=\
\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hre\
f=\"chap2_mj.html#X849F6196875A6DF5\">2.3 <span class=\"Heading\">Compiling th\
e kernel module</span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span cla\
ss=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X857\
CBE5484CF703A\">2.4 <span class=\"Heading\">Rebuilding the documentation</span\
></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X870631C38610AC25\
\">2.4-1 DigraphsMakeDoc</a></span>\n</div></div>\n<div class=\"ContSect\"><sp\
an class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.htm\
l#X7862D3F37C5BBDEF\">2.5 <span class=\"Heading\">Testing your installation</s\
pan></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X86AF4DAE80B97\
8DA\">2.5-1 DigraphsTestInstall</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7A20088B7C406C4A\
\">2.5-2 DigraphsTestStandard</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X7885EF3E785D4298\">\
2.5-3 DigraphsTestExtreme</a></span>\n</div></div>\n</div>\n<div class=\"ContC\
hap\"><a href=\"chap3_mj.html#X7D34861E863A5D93\">3 <span class=\"Heading\">Cr\
eating digraphs</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><s\
pan class=\"nocss\">&nbsp;</span><a href=\"chap3_mj.html#X7D34861E863A5D93\">3\
.1 <span class=\"Heading\">Creating digraphs</span></a>\n</span>\n<div class=\
\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X7877ADC77F85E630\">3.1-1 IsDigraph</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap3_mj.html#X7D7EDF83820ED6F5\">3.1-2 IsMutableDigraph</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap3_mj.html#X7CAFAA89804F80BD\">3.1-3 IsImmutableDigraph</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_\
mj.html#X7E749324800B38A5\">3.1-4 IsCayleyDigraph</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#\
X80F1B6D28478D8B9\">3.1-5 IsDigraphWithAdjacencyFunction</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_m\
j.html#X86E798B779515678\">3.1-6 DigraphByOutNeighboursType</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
3_mj.html#X834843057CE86655\">3.1-7 Digraph</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8023F\
E387A3AB609\">3.1-8 DigraphByAdjacencyMatrix</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7F3\
7B6768349E269\">3.1-9 DigraphByEdges</a></span>\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7B75C1D68075\
7D6F\">3.1-10 EdgeOrbitsDigraph</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X81BC49B57EAADEFB\
\">3.1-11 DigraphByInNeighbours</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7FCADADC7EC28478\
\">3.1-12 CayleyDigraph</a></span>\n</div></div>\n<div class=\"ContSect\"><spa\
n class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap3_mj.html\
#X83608C407CC8836D\">3.2 <span class=\"Heading\">Changing representations</spa\
n></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7FBC4BDB82FBEDD\
2\">3.2-1 AsBinaryRelation</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X83CA27E67F685EB3\">3.2\
-2 AsDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap3_mj.html#X7B335342839E5146\">3.2-3 Graph</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap3_mj.html#X7C4F13E080EC16B0\">3.2-4 AsGraph</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_m\
j.html#X7C5360B2799943F3\">3.2-5 AsTransformation</a></span>\n</div></div>\n<d\
iv class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</sp\
an><a href=\"chap3_mj.html#X85126078848B420A\">3.3 <span class=\"Heading\">New\
 digraphs from old</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_m\
j.html#X83D93A8A8251E6F9\">3.3-1 DigraphImmutableCopy</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X8399F7427B227228\">3.3-2 DigraphImmutableCopyIfImmutable</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap3_mj.html#X83C51DA182CCEA2F\">3.3-3 InducedSubdigraph</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj\
.html#X7CAF093B85A93D2F\">3.3-4 ReducedDigraph</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X82\
9E3EAC7C4B3B1E\">3.3-5 MaximalSymmetricSubdigraph</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#\
X79BA6A66846D5A95\">3.3-6 MaximalAntiSymmetricSubdigraph</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_m\
j.html#X7DD9766C86D3ED20\">3.3-7 UndirectedSpanningForest</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_\
mj.html#X7D1D26D27F5B56C2\">3.3-8 QuotientDigraph</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#\
X78DECD26811EFD7C\">3.3-9 DigraphReverse</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7F71D99D\
852B130F\">3.3-10 DigraphDual</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X874883DD7DD450C4\">\
3.3-11 DigraphSymmetricClosure</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7A6C419080AD41DE\"\
>3.3-12 DigraphTransitiveClosure</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X82AD17517E273600\
\">3.3-13 DigraphTransitiveReduction</a></span>\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X83B2506D7945\
3208\">3.3-14 DigraphAddVertex</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8134BEE7786BD3A7\"\
>3.3-15 DigraphAddVertices</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7E58CC4880627658\">3.3\
-16 DigraphAddEdge</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7BE5C7028760B053\">3.3-17 Digr\
aphAddEdgeOrbit</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8693A61B7F752C76\">3.3-18 Digraph\
AddEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap3_mj.html#X7B634A2B83C08B16\">3.3-19 DigraphRemoveV\
ertex</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap3_mj.html#X7E290E847A5A299A\">3.3-20 DigraphRemoveVert\
ices</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap3_mj.html#X8433E3BC7E5EA6BF\">3.3-21 DigraphRemoveEdge<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap3_mj.html#X85981D9187F49018\">3.3-22 DigraphRemoveEdgeOrbit<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap3_mj.html#X87093FDA7F88E732\">3.3-23 DigraphRemoveEdges</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap3_mj.html#X79324AF7818C0C02\">3.3-24 DigraphRemoveLoops</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap3_mj.html#X7DCCD0247897A3DE\">3.3-25 DigraphRemoveAllMultipleEdges</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap3_mj.html#X7821753D85402A8C\">3.3-26 DigraphReverseEdges</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap3_mj.html#X814F1DFC83DB273F\">3.3-27 DigraphDisjointUnion</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap3_mj.html#X7DA997697D310E44\">3.3-28 DigraphEdgeUnion</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap3_mj.html#X7DDFC759860E3390\">3.3-29 DigraphJoin</a></span>\n<span class\
=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.\
html#X7D625CC87DBFFDED\">3.3-30 DigraphCartesianProduct</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj\
.html#X84D24DC9833B54A5\">3.3-31 DigraphDirectProduct</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X8795087A78FE7D54\">3.3-32 DigraphCartesianProductProjections</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap3_mj.html#X84FB64F185B804C2\">3.3-33 DigraphDirectProductProjections</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap3_mj.html#X8595BF937B749F22\">3.3-34 LineDigraph</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap3_mj.html#X8364C6F17A1680CB\">3.3-35 LineUndirectedDigraph</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap3_mj.html#X7FB8B48C87C0ED16\">3.3-36 DoubleDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X7C6E6CB284982C7A\">3.3-37 BipartiteDoubleDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.h\
tml#X8167A50A83256ED1\">3.3-38 DigraphAddAllLoops</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#\
X865436437DF95FEF\">3.3-39 DistanceDigraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X86F9CC\
EA839ABC48\">3.3-40 DigraphClosure</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7B5AC5FE859F4D\
80\">3.3-41 DigraphMycielskian</a></span>\n</div></div>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap3_\
mj.html#X85B5D9B97F5187B7\">3.4 <span class=\"Heading\">Random digraphs</span>\
</a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X86CF9F66788B2A24\
\">3.4-1 RandomDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X78FE275E7E77D56F\">3.4-2 R\
andomMultiDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7D36B5E57F055051\">3.4-3 Random\
Tournament</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap3_mj.html#X7A023E4787682475\">3.4-4 RandomLattice\
</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><sp\
an class=\"nocss\">&nbsp;</span><a href=\"chap3_mj.html#X7C76D1DC7DAF03D3\">3.\
5 <span class=\"Heading\">Standard examples</span></a>\n</span>\n<div class=\"\
ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap3_mj.html#X870594FC866AC88E\">3.5-1 ChainDigraph</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap3_mj.html#X812417E278198D9C\">3.5-2 CompleteDigraph</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap3_mj.html#X8795B0AD856014FA\">3.5-3 CompleteBipartiteDigraph</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap3_mj.html#X873F29CC863241F8\">3.5-4 CompleteMultipartiteDigraph</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap3_mj.html#X80C29DDE876FFBEB\">3.5-5 CycleDigraph</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_m\
j.html#X80DAE31A79FEFD40\">3.5-6 EmptyDigraph</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X80E\
D9CE785819607\">3.5-7 JohnsonDigraph</a></span>\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X823F43217A6C\
375D\">3.5-8 PetersenGraph</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7B5441F386BD105E\">3.5\
-9 GeneralisedPetersenGraph</a></span>\n</div></div>\n</div>\n<div class=\"Con\
tChap\"><a href=\"chap4_mj.html#X7AD6F77E7D95C996\">4 <span class=\"Heading\">\
Operators</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span cl\
ass=\"nocss\">&nbsp;</span><a href=\"chap4_mj.html#X84E0B5B88358C96B\">4.1 <sp\
an class=\"Heading\">Operators for digraphs</span></a>\n</span>\n<div class=\"\
ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap4_mj.html#X829B911D7EFD2D85\">4.1-1 IsSubdigraph</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap4_mj.html#X833C3299787E2309\">4.1-2 IsUndirectedSpanningTree</a></s\
pan>\n</div></div>\n</div>\n<div class=\"ContChap\"><a href=\"chap5_mj.html#X8\
739F6CD78C90B14\">5 <span class=\"Heading\">Attributes and operations</span></\
a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbs\
p;</span><a href=\"chap5_mj.html#X7E814B6478F7D015\">5.1 <span class=\"Heading\
\">Vertices and edges</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
5_mj.html#X7C45F7D878D896AC\">5.1-1 DigraphVertices</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.htm\
l#X7C6F19B57CB2E882\">5.1-2 DigraphNrVertices</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7D1\
C6A4D7ECEC317\">5.1-3 DigraphEdges</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X85E1CFDD7E164A\
D0\">5.1-4 DigraphNrEdges</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BDABAF07917462B\">5.1-\
5 DigraphNrLoops</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X85D5E08280914EE4\">5.1-6 Digrap\
hSinks</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X7F5C6268839BE98C\">5.1-7 DigraphSources</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap5_mj.html#X785C30378064CF47\">5.1-8 DigraphTopologicalSort</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap5_mj.html#X7CA91E4B7904F793\">5.1-9 DigraphVertexLabel</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap5_mj.html#X7E51F2FE87140B32\">5.1-10 DigraphVertexLabels</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X79FAEACC7F438C2F\">5.1-11 DigraphEdgeLabel</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap5_mj.html#X7C24851087D4A8FB\">5.1-12 DigraphEdgeLabels</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_m\
j.html#X7EFAF01B7A155157\">5.1-13 DigraphInEdges</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X\
7BECFE6687ECD028\">5.1-14 DigraphOutEdges</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BB8ED8\
8835F07B4\">5.1-15 IsDigraphEdge</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X848FED0B7B4ACD1F\
\">5.1-16 IsMatching</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7B7A67277B1C9A02\">5.1-17 Di\
graphMaximalMatching</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X78E9847A858788D1\">5.1-18 Di\
graphMaximumMatching</a></span>\n</div></div>\n<div class=\"ContSect\"><span c\
lass=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X7\
D7CE8328187D0DF\">5.2 <span class=\"Heading\">Neighbours and degree</span></a>\
\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7DC2CD70830BEE60\">5.\
2-1 AdjacencyMatrix</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X87FA0A727CDB060B\">5.2-2 Char\
acteristicPolynomial</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8507DC4F794780C1\">5.2-3 Boo\
leanAdjacencyMatrix</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7AFCE34A7A04D5C1\">5.2-4 Digr\
aphAdjacencyFunction</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7FDEBF3279759961\">5.2-5 Dig\
raphRange</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap5_mj.html#X7E9880767AE68E00\">5.2-6 OutNeighbours<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap5_mj.html#X85C7AA5A81DA6E11\">5.2-7 InNeighbours</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X7F5ACE807D1BC2E2\">5.2-8 OutDegrees</a></span>\n<span class\
=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.\
html#X7ADDFBFD7A365775\">5.2-9 InDegrees</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7A09EB64\
8070276D\">5.2-10 OutDegreeOfVertex</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X83315B0186850\
806\">5.2-11 OutNeighboursOfVertex</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C9CD0527CB9E6\
EF\">5.2-12 InDegreeOfVertex</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C0DA18B8291F302\">5\
.2-13 InNeighboursOfVertex</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X83271F607BD809CF\">5.2\
-14 DigraphLoops</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7DDB33B686B3A2C6\">5.2-15 Parti\
alOrderDigraphMeetOfVertices</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7BEAE1C78267F54D\">5\
.2-16 DegreeMatrix</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X865390B08331936B\">5.2-17 Lapl\
acianMatrix</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"to\
cline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X8537F40884\
00DC48\">5.3 <span class=\"Heading\">Reachability and connectivity</span></a>\
\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7F16B9EB8398459C\">5.\
3-1 DigraphDiameter</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8104A9D37BCD8A05\">5.3-2 Digr\
aphShortestDistance</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X81F99BC67E9D050F\">5.3-3 Digr\
aphShortestDistances</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8223718079D98A82\">5.3-4 Dig\
raphLongestDistanceFromVertex</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7CB7DDCD84621D38\">\
5.3-5 DigraphDistanceSet</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X79A3DA4078CF3C90\">5.3-6\
 DigraphGirth</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8374B7357EC189C1\">5.3-7 DigraphOdd\
Girth</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap5_mj.html#X84688B337BDDBB09\">5.3-8 DigraphUndirectedG\
irth</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap5_mj.html#X842FAD6A7B835977\">5.3-9 DigraphConnectedCom\
ponents</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap5_mj.html#X8484EC557810CD31\">5.3-10 DigraphConnecte\
dComponent</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap5_mj.html#X833ECD6B7A84944C\">5.3-11 DigraphStron\
glyConnectedComponents</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7EFCB5017D662254\">5.3-12 \
DigraphStronglyConnectedComponent</a></span>\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7F1B5A2782F598B\
1\">5.3-13 DigraphBicomponents</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7DDE06E47E605DD7\"\
>5.3-14 ArticulationPoints</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X84D5A125848BD800\">5.3\
-15 Bridges</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap5_mj.html#X865590147BD1C507\">5.3-16 StrongOrien\
tation</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X853D0B0981A33433\">5.3-17 DigraphPeriod</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap5_mj.html#X864A31A8809F61C2\">5.3-18 DigraphFloydWarshall</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap5_mj.html#X7FBAB09E7C0BE5CF\">5.3-19 IsReachable</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap5_mj.html#X7CAE81D97B43DDF3\">5.3-20 VerticesReachableFrom</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap5_mj.html#X8039170B82A32257\">5.3-21 DigraphPath</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html\
#X80E9D645843973A6\">5.3-22 DigraphShortestPath</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7\
C0416FE7A69CA2C\">5.3-23 IteratorOfPaths</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7ECD1683\
8704FAAA\">5.3-24 DigraphAllSimpleCircuits</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C735C\
4E86BDD5F6\">5.3-25 DigraphLongestSimpleCircuit</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8\
70E04307C5F213F\">5.3-26 DigraphLayers</a></span>\n<span class=\"ContSS\"><br \
/><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7B2E42327D\
A118E0\">5.3-27 DigraphDegeneracy</a></span>\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X827C2BD17A4547E\
3\">5.3-28 DigraphDegeneracyOrdering</a></span>\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X863FDFC4839A\
3B82\">5.3-29 HamiltonianPath</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X82F30D5681466BC6\">\
5.3-30 NrSpanningTrees</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X79352A8286D1D8F6\">5.3-31 \
DigraphDijkstra</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\
\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X82F900\
777D677F55\">5.4 <span class=\"Heading\">Cayley graphs of groups</span></a>\n<\
/span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7A000B1D7CCF7093\">5.4-1\
 GroupOfCayleyDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8528455987D7D2BF\">5.4-2 Ge\
neratorsOfCayleyDigraph</a></span>\n</div></div>\n<div class=\"ContSect\"><spa\
n class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html\
#X790FD6647ECCAE3C\">5.5 <span class=\"Heading\">Associated semigroups</span><\
/a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X87D5C60D7B0C1309\"\
>5.5-1 AsSemigroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7C6D5EC27C51066B\">5.5-2 AsSem\
igroup</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X7E2305528492DDC\
0\">5.6 <span class=\"Heading\">Planarity</span></a>\n</span>\n<div class=\"Co\
ntSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap5_mj.html#X7DC478637E8C190D\">5.6-1 KuratowskiPlanarSubdig\
raph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap5_mj.html#X78E8F09A8286501B\">5.6-2 KuratowskiOuterPlan\
arSubdigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap5_mj.html#X84E3947E7D39BA64\">5.6-3 PlanarEmbed\
ding</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap5_mj.html#X85DFB8C18088711F\">5.6-4 OuterPlanarEmbeddin\
g</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap5_mj.html#X806D2D6B85E0B269\">5.6-5 SubdigraphHomeomorphic\
ToK23</a></span>\n</div></div>\n</div>\n<div class=\"ContChap\"><a href=\"chap\
6_mj.html#X7ADDEFD478D470D5\">6 <span class=\"Heading\">Properties of digraphs\
</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"noc\
ss\">&nbsp;</span><a href=\"chap6_mj.html#X7F49388F8245F0E9\">6.1 <span class=\
\"Heading\">Edge properties</span></a>\n</span>\n<div class=\"ContSSBlock\">\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap6_mj.html#X7D92935C7D535187\">6.1-1 DigraphHasLoops</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_\
mj.html#X7DB1BC2286FC08E2\">6.1-2 IsAntiSymmetricDigraph</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_m\
j.html#X860CFB0C8665F356\">6.1-3 IsBipartiteDigraph</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.htm\
l#X790A4DBF8533516E\">6.1-4 IsCompleteBipartiteDigraph</a></span>\n<span class\
=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.\
html#X81F28D4D879FE3B2\">6.1-5 IsCompleteDigraph</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X\
7FD1A15779FEC341\">6.1-6 IsCompleteMultipartiteDigraph</a></span>\n<span class\
=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.\
html#X7E894CCF7B1C27AE\">6.1-7 IsEmptyDigraph</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X837\
62C257DED2751\">6.1-8 IsEquivalenceDigraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E8F37\
E585DAED52\">6.1-9 IsFunctionalDigraph</a></span>\n<span class=\"ContSS\"><br \
/><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7BB84CFC7E\
8B2B26\">6.1-10 IsMultiDigraph</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X8462D8E2792B23F6\"\
>6.1-11 IsReflexiveDigraph</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X81B3EA7887219860\">6.1\
-12 IsSymmetricDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7DD8D1A185EBE865\">6.1-13 \
IsTournament</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap6_mj.html#X7F0835667F29F0C0\">6.1-14 IsTransiti\
veDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap6_mj.html#X8617726C7829F796\">6.1-15 IsPreorderDig\
raph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap6_mj.html#X82BAE6D37D49A145\">6.1-16 IsPartialOrderDigr\
aph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap6_mj.html#X78D3E17B7F737516\">6.1-17 IsMeetSemilatticeDi\
graph</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chap6_mj.html#X7AAF896982EC22F\
A\">6.2 <span class=\"Heading\">Regularity</span></a>\n</span>\n<div class=\"C\
ontSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap6_mj.html#X7A3F78B37E31D9E1\">6.2-1 IsInRegularDigraph</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap6_mj.html#X7F0A806E7BCB413C\">6.2-2 IsOutRegularDigraph</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap6_mj.html#X7AF9DB1E7DB12306\">6.2-3 IsRegularDigraph</a></span>\n<\
span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap6_mj.html#X7E2082AC7CAE59CD\">6.2-4 IsDistanceRegularDigraph</a></span>\
\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"\
nocss\">&nbsp;</span><a href=\"chap6_mj.html#X780DAEB37C5E07FD\">6.3 <span cla\
ss=\"Heading\">Connectivity and cycles</span></a>\n</span>\n<div class=\"ContS\
SBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap6_mj.html#X7BD08D4478218F77\">6.3-1 IsAcyclicDigraph</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap6_mj.html#X79563B297C220FB5\">6.3-2 IsChainDigraph</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p6_mj.html#X83C08C0B7EC1A91F\">6.3-3 IsConnectedDigraph</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj\
.html#X838FAF2D825977BE\">6.3-4 IsBiconnectedDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.h\
tml#X7D2A6572820B7F24\">6.3-5 IsBridgelessDigraph</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#\
X7B37B9467C68C208\">6.3-6 IsStronglyConnectedDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.h\
tml#X80E883967EBE839E\">6.3-7 IsAperiodicDigraph</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X\
7B46EA6C7B2DF2FB\">6.3-8 IsDirectedTree</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X80FC20FA7\
AC4BC2A\">6.3-9 IsUndirectedTree</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X79DFBB198525544E\
\">6.3-10 IsEulerianDigraph</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X79EFEBC37C2D262D\">6.\
3-11 IsHamiltonianDigraph</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E91320B8028F5D8\">6.3-\
12 IsCycleDigraph</a></span>\n</div></div>\n<div class=\"ContSect\"><span clas\
s=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap6_mj.html#X7E23\
05528492DDC0\">6.4 <span class=\"Heading\">Planarity</span></a>\n</span>\n<div\
 class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap6_mj.html#X8606D415858C40AA\">6.4-1 IsPlanarDig\
raph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap6_mj.html#X8251E8B187E7F059\">6.4-2 IsOuterPlanarDigrap\
h</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><s\
pan class=\"nocss\">&nbsp;</span><a href=\"chap6_mj.html#X83DC8AD283C41326\">6\
.5 <span class=\"Heading\">Homomorphisms and transformations</span></a>\n</spa\
n>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X78C0B2637985648B\">6.5-1 IsD\
igraphCore</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap6_mj.html#X8361CA6E8401FF26\">6.5-2 IsEdgeTransit\
ive</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap6_mj.html#X7B26E4447A1611E9\">6.5-3 IsVertexTransitive</\
a></span>\n</div></div>\n</div>\n<div class=\"ContChap\"><a href=\"chap7_mj.ht\
ml#X84975388859F203D\">7 <span class=\"Heading\">Homomorphisms</span></a>\n<di\
v class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</spa\
n><a href=\"chap7_mj.html#X8200192B80AD2071\">7.1 <span class=\"Heading\">Acti\
ng on digraphs</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.h\
tml#X808972017C486F1F\">7.1-1 OnDigraphs</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7AFBA760\
8498F9CE\">7.1-2 OnMultiDigraphs</a></span>\n</div></div>\n<div class=\"ContSe\
ct\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap\
7_mj.html#X7E48B9F87A0F22D4\">7.2 <span class=\"Heading\">Isomorphisms and can\
onical labellings</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj\
.html#X83E593F3855B122E\">7.2-1 DigraphsUseNauty</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X\
858C32127A190175\">7.2-2 AutomorphismGroup</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7E7B0D\
88865A89F6\">7.2-3 BlissAutomorphismGroup</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X857758B\
18144C0CD\">7.2-4 NautyAutomorphismGroup</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X877732B1\
783C391B\">7.2-5 AutomorphismGroup</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7DA2C4FE837FFE\
01\">7.2-6 AutomorphismGroup</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7D676FE67A6684FF\">7\
.2-7 BlissCanonicalLabelling</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X87DA265D803DB337\">7\
.2-8 BlissCanonicalLabelling</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X877B1D377EC197D7\">7\
.2-9 BlissCanonicalDigraph</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X803ACEDA7BBAC5B3\">7.2\
-10 DigraphGroup</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8096C5287E459279\">7.2-11 Digra\
phOrbits</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap7_mj.html#X8386028782F2D3FF\">7.2-12 DigraphOrbitRe\
ps</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap7_mj.html#X8657604E87A25E5F\">7.2-13 DigraphSchreierVecto\
r</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap7_mj.html#X78913684795FB256\">7.2-14 DigraphStabilizer</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap7_mj.html#X7B4F24B283C9EE28\">7.2-15 IsIsomorphicDigraph</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap7_mj.html#X7D4A1FA8868DA930\">7.2-16 IsIsomorphicDigraph</a></span\
>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hr\
ef=\"chap7_mj.html#X8219FE6C839D9457\">7.2-17 IsomorphismDigraphs</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap7_mj.html#X7ED93C0F86D9D34F\">7.2-18 IsomorphismDigraphs</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap7_mj.html#X7E1C806D81DFE15E\">7.2-19 RepresentativeOutNeighbours</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap7_mj.html#X80183D4A7C51365A\">7.2-20 IsDigraphIsomorphism</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap7_mj.html#X7F16B8B3825A627A\">7.2-21 IsDigraphColouring</a></span>\n</di\
v></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chap7_mj.html#X7E1A02FE8384C03C\">7.3 <span class=\"\
Heading\">Homomorphisms of digraphs</span></a>\n</span>\n<div class=\"ContSSBl\
ock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap7_mj.html#X79ABF0E783FD67C7\">7.3-1 HomomorphismDigraphsFinder</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap7_mj.html#X85E9B019877AD7FE\">7.3-2 DigraphHomomorphism</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap7_mj.html#X8653EDA183E06D05\">7.3-3 HomomorphismsDigraphs</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap7_mj.html#X82D0FCD87D47ACA8\">7.3-4 DigraphMonomorphism</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap7_mj.html#X84B4BDB984C2A9A8\">7.3-5 MonomorphismsDigraphs</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap7_mj.html#X7CB5AD9F861684FD\">7.3-6 DigraphEpimorphism</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p7_mj.html#X7DFB1F5D873937B3\">7.3-7 EpimorphismsDigraphs</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_\
mj.html#X7AD04CC186E86CCA\">7.3-8 DigraphEmbedding</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html\
#X82EBDF137EEDC5FD\">7.3-9 EmbeddingsDigraphs</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X80F\
E9FCB79718A61\">7.3-10 IsDigraphHomomorphism</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7D6\
B5A0887903810\">7.3-11 IsDigraphEmbedding</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7F80709\
A80CBFA98\">7.3-12 DigraphsRespectsColouring</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7E9\
3B268823F6478\">7.3-13 GeneratorsOfEndomorphismMonoid</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.h\
tml#X86D0A74B83D6B9A7\">7.3-14 DigraphColouring</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7\
AB7200D831013C1\">7.3-15 DigraphGreedyColouring</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7\
F9CB3B27B9590DB\">7.3-16 DigraphWelshPowellOrder</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X\
807D49358529A37C\">7.3-17 ChromaticNumber</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X863487E\
F7D64EF56\">7.3-18 DigraphCore</a></span>\n</div></div>\n</div>\n<div class=\"\
ContChap\"><a href=\"chap8_mj.html#X7A7E0B957932DF44\">8 <span class=\"Heading\
\">Finding cliques and independent sets</span></a>\n<div class=\"ContSect\"><s\
pan class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap8_mj.ht\
ml#X788474E38446039B\">8.1 <span class=\"Heading\">Finding cliques</span></a>\
\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X80670E3E7C36183F\">8.\
1-1 IsClique</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap8_mj.html#X7A3BC9FF8169ABCD\">8.1-2 CliquesFind\
er</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap8_mj.html#X789854AC7B466402\">8.1-3 DigraphClique</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap8_mj.html#X84EA2F9482B8D4AF\">8.1-4 DigraphMaximalCliques</a></span\
>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hr\
ef=\"chap8_mj.html#X78427A8B81FEB457\">8.1-5 CliqueNumber</a></span>\n</div></\
div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&n\
bsp;</span><a href=\"chap8_mj.html#X7E31253287708348\">8.2 <span class=\"Headi\
ng\">Finding independent sets</span></a>\n</span>\n<div class=\"ContSSBlock\">\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap8_mj.html#X790733B67B0BC894\">8.2-1 IsIndependentSet</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p8_mj.html#X84350678782BFAB7\">8.2-2 DigraphIndependentSet</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8\
_mj.html#X7D2C78EB81A798A9\">8.2-3 DigraphMaximalIndependentSets</a></span>\n<\
/div></div>\n</div>\n<div class=\"ContChap\"><a href=\"chap9_mj.html#X81714DBC\
80CC4BCB\">9 <span class=\"Heading\">Visualising and IO</span></a>\n<div class\
=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hr\
ef=\"chap9_mj.html#X7CF67F8278D9469C\">9.1 <span class=\"Heading\">Visualising\
 a digraph</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X\
83B3318784E78415\">9.1-1 Splash</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7F9B99C478EE093A\
\">9.1-2 DotDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X78DA31D1869D2F94\">9.1-3 DotS\
ymmetricDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X84120D447E2CAC23\">9.1-4 DotParti\
alOrderDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7F5653C8854FAEA6\">9.1-5 DotPreord\
erDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap9_mj.html#X808D12CF81E2C19F\">9.1-6 DotHighlighted\
Digraph</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"toclin\
e\"><span class=\"nocss\">&nbsp;</span><a href=\"chap9_mj.html#X81C9B1DC791C0B\
BD\">9.2 <span class=\"Heading\">Reading and writing digraphs to a file</span>\
</a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X81FB5BE27903EC32\
\">9.2-1 String</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X873D6EB8836A3C61\">9.2-2 DigraphF\
romGraph6String</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X782A052979EA2376\">9.2-3 Graph6St\
ring</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap9_mj.html#X7845ACDA7D4D333D\">9.2-4 DigraphFile</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap9_mj.html#X7E8142007ED0CB9F\">9.2-5 ReadDigraphs</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
9_mj.html#X82A4F0767C9EFC87\">9.2-6 WriteDigraphs</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#\
X86D531B287733561\">9.2-7 IteratorFromDigraphFile</a></span>\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#\
X7AAA35867B5D8BF4\">9.2-8 DigraphPlainTextLineEncoder</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.h\
tml#X7808D99079295C22\">9.2-9 TournamentLineDecoder</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.htm\
l#X7DF22D1687D096D6\">9.2-10 AdjacencyMatrixUpperTriangleLineDecoder</a></span\
>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hr\
ef=\"chap9_mj.html#X875393338486D77D\">9.2-11 TCodeDecoder</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9\
_mj.html#X8540FC21796A793F\">9.2-12 PlainTextString</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.htm\
l#X81BD23697857B244\">9.2-13 WritePlainTextDigraph</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html\
#X804FDF6A7ED64049\">9.2-14 WriteDIMACSDigraph</a></span>\n</div></div>\n</div\
>\n<div class=\"ContChap\"><a href=\"chapA_mj.html#X800DAF137BA8E25B\">A <span\
 class=\"Heading\">\n    Grape to Digraphs Command Map\n  </span></a>\n<div cl\
ass=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a\
 href=\"chapA_mj.html#X7CC8A9DB86F9F0F4\">A.1 <span class=\"Heading\">\n      \
Functions to construct and modify graphs\n    </span></a>\n</span>\n</div>\n<d\
iv class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</sp\
an><a href=\"chapA_mj.html#X7C38A6397D2770FB\">A.2 <span class=\"Heading\">\n \
     Functions to inspect graphs, vertices and edges\n    </span></a>\n</span>\
\n</div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\
\">&nbsp;</span><a href=\"chapA_mj.html#X78A5A34783C70CD7\">A.3 <span class=\"\
Heading\">\n      Functions to determine regularity properties of graphs\n    \
</span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"tocline\">\
<span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7C74978D85F7AF5C\"\
>A.4 <span class=\"Heading\">\n      Some special vertex subsets of a graph\n \
   </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7E51B92F7E89E26\
6\">A.5 <span class=\"Heading\">\n      Functions to construct new graphs from\
 old\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"\
tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7A61E3FC\
7A2BB50E\">A.6 <span class=\"Heading\">\n      Vertex-Colouring and Complete S\
ubgraphs\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span clas\
s=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7DFC\
61EC7CBDBC7E\">A.7 <span class=\"Heading\">\n      Automorphism groups and iso\
morphism testing for graphs\n    </span></a>\n</span>\n</div>\n</div>\n<div cl\
ass=\"ContChap\"><a href=\"chapBib_mj.html\"><span class=\"Heading\">Reference\
s</span></a></div>\n<div class=\"ContChap\"><a href=\"chapInd_mj.html\"><span \
class=\"Heading\">Index</span></a></div>\n<div class=\"ContChap\"><a href=\"ch\
ap1_mj.html#X7F202ABA780E595D\">1 <span class=\"Heading\">\n    The <strong cl\
ass=\"pkg\">Digraphs</strong> package\n  </span></a>\n<div class=\"ContSect\">\
<span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap1_mj.\
html#X7DFB63A97E67C0A1\">1.1 <span class=\"Heading\">Introduction</span></a>\n\
</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap1_mj.html#X84541F61810C741D\">1.1-\
1 <span class=\"Heading\">Definitions</span></a>\n</span>\n</div></div>\n</div\
>\n<div class=\"ContChap\"><a href=\"chap2_mj.html#X817088B27F90D596\">2 <span\
 class=\"Heading\">Installing <strong class=\"pkg\">Digraphs</strong></span></\
a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbs\
p;</span><a href=\"chap2_mj.html#X7DA3059C79842BF3\">2.1 <span class=\"Heading\
\">For those in a hurry</span></a>\n</span>\n</div>\n<div class=\"ContSect\"><\
span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap2_mj.h\
tml#X780AA9D97EBCA95D\">2.2 <span class=\"Heading\">Optional package dependenc\
ies</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2_mj.html#X8493C75\
87FCF6D8B\">2.2-1 <span class=\"Heading\">The Grape package</span></a>\n</span\
>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\
\"nocss\">&nbsp;</span><a href=\"chap2_mj.html#X849F6196875A6DF5\">2.3 <span c\
lass=\"Heading\">Compiling the kernel module</span></a>\n</span>\n</div>\n<div\
 class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span\
><a href=\"chap2_mj.html#X857CBE5484CF703A\">2.4 <span class=\"Heading\">Rebui\
lding the documentation</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap2_mj.html#X870631C38610AC25\">2.4-1 DigraphsMakeDoc</a></span>\n</div></div>\
\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;\
</span><a href=\"chap2_mj.html#X7862D3F37C5BBDEF\">2.5 <span class=\"Heading\"\
>Testing your installation</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<\
span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap2_mj.html#X86AF4DAE80B978DA\">2.5-1 DigraphsTestInstall</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap2_mj.html#X7A20088B7C406C4A\">2.5-2 DigraphsTestStandard</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap2\
_mj.html#X7885EF3E785D4298\">2.5-3 DigraphsTestExtreme</a></span>\n</div></div\
>\n</div>\n<div class=\"ContChap\"><a href=\"chap3_mj.html#X7D34861E863A5D93\"\
>3 <span class=\"Heading\">Creating digraphs</span></a>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap3_\
mj.html#X7D34861E863A5D93\">3.1 <span class=\"Heading\">Creating digraphs</spa\
n></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7877ADC77F85E63\
0\">3.1-1 IsDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7D7EDF83820ED6F5\">3.1-2 IsMu\
tableDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap3_mj.html#X7CAFAA89804F80BD\">3.1-3 IsImmutable\
Digraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap3_mj.html#X7E749324800B38A5\">3.1-4 IsCayleyDigraph<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap3_mj.html#X80F1B6D28478D8B9\">3.1-5 IsDigraphWithAdjacencyFu\
nction</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap3_mj.html#X86E798B779515678\">3.1-6 DigraphByOutNeigh\
boursType</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap3_mj.html#X834843057CE86655\">3.1-7 Digraph</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap3_mj.html#X8023FE387A3AB609\">3.1-8 DigraphByAdjacencyMatrix</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap3_mj.html#X7F37B6768349E269\">3.1-9 DigraphByEdges</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap3_mj.html#X7B75C1D680757D6F\">3.1-10 EdgeOrbitsDigraph</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3\
_mj.html#X81BC49B57EAADEFB\">3.1-11 DigraphByInNeighbours</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_\
mj.html#X7FCADADC7EC28478\">3.1-12 CayleyDigraph</a></span>\n</div></div>\n<di\
v class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</spa\
n><a href=\"chap3_mj.html#X83608C407CC8836D\">3.2 <span class=\"Heading\">Chan\
ging representations</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3\
_mj.html#X7FBC4BDB82FBEDD2\">3.2-1 AsBinaryRelation</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.htm\
l#X83CA27E67F685EB3\">3.2-2 AsDigraph</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7B335342839\
E5146\">3.2-3 Graph</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7C4F13E080EC16B0\">3.2-4 AsGr\
aph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap3_mj.html#X7C5360B2799943F3\">3.2-5 AsTransformation</a>\
</span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span c\
lass=\"nocss\">&nbsp;</span><a href=\"chap3_mj.html#X85126078848B420A\">3.3 <s\
pan class=\"Heading\">New digraphs from old</span></a>\n</span>\n<div class=\"\
ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap3_mj.html#X83D93A8A8251E6F9\">3.3-1 DigraphImmutableCopy\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chap3_mj.html#X8399F7427B227228\">3.3-2 DigraphImmutableCopyIfI\
mmutable</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap3_mj.html#X83C51DA182CCEA2F\">3.3-3 InducedSubdigra\
ph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap3_mj.html#X7CAF093B85A93D2F\">3.3-4 ReducedDigraph</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap3_mj.html#X829E3EAC7C4B3B1E\">3.3-5 MaximalSymmetricSubdigraph</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap3_mj.html#X79BA6A66846D5A95\">3.3-6 MaximalAntiSymmetricSubdigr\
aph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap3_mj.html#X7DD9766C86D3ED20\">3.3-7 UndirectedSpanningFo\
rest</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap3_mj.html#X7D1D26D27F5B56C2\">3.3-8 QuotientDigraph</a>\
</span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span\
><a href=\"chap3_mj.html#X78DECD26811EFD7C\">3.3-9 DigraphReverse</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap3_mj.html#X7F71D99D852B130F\">3.3-10 DigraphDual</a></span>\n<span class\
=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.\
html#X874883DD7DD450C4\">3.3-11 DigraphSymmetricClosure</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj\
.html#X7A6C419080AD41DE\">3.3-12 DigraphTransitiveClosure</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_\
mj.html#X82AD17517E273600\">3.3-13 DigraphTransitiveReduction</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap3_mj.html#X83B2506D79453208\">3.3-14 DigraphAddVertex</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj\
.html#X8134BEE7786BD3A7\">3.3-15 DigraphAddVertices</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.htm\
l#X7E58CC4880627658\">3.3-16 DigraphAddEdge</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7BE5C\
7028760B053\">3.3-17 DigraphAddEdgeOrbit</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8693A61B\
7F752C76\">3.3-18 DigraphAddEdges</a></span>\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7B634A2B83C08B1\
6\">3.3-19 DigraphRemoveVertex</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7E290E847A5A299A\"\
>3.3-20 DigraphRemoveVertices</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8433E3BC7E5EA6BF\">\
3.3-21 DigraphRemoveEdge</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X85981D9187F49018\">3.3-2\
2 DigraphRemoveEdgeOrbit</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X87093FDA7F88E732\">3.3-2\
3 DigraphRemoveEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X79324AF7818C0C02\">3.3-24 Di\
graphRemoveLoops</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DCCD0247897A3DE\">3.3-25 Digra\
phRemoveAllMultipleEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7821753D85402A8C\">3.3-2\
6 DigraphReverseEdges</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X814F1DFC83DB273F\">3.3-27 D\
igraphDisjointUnion</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DA997697D310E44\">3.3-28 Dig\
raphEdgeUnion</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7DDFC759860E3390\">3.3-29 DigraphJo\
in</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap3_mj.html#X7D625CC87DBFFDED\">3.3-30 DigraphCartesianProd\
uct</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap3_mj.html#X84D24DC9833B54A5\">3.3-31 DigraphDirectProduc\
t</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap3_mj.html#X8795087A78FE7D54\">3.3-32 DigraphCartesianProdu\
ctProjections</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap3_mj.html#X84FB64F185B804C2\">3.3-33 DigraphDi\
rectProductProjections</a></span>\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X8595BF937B749F22\">3.3-34 \
LineDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap3_mj.html#X8364C6F17A1680CB\">3.3-35 LineUndirec\
tedDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap3_mj.html#X7FB8B48C87C0ED16\">3.3-36 DoubleDigrap\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap3_mj.html#X7C6E6CB284982C7A\">3.3-37 BipartiteDoubleDigrap\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap3_mj.html#X8167A50A83256ED1\">3.3-38 DigraphAddAllLoops</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap3_mj.html#X865436437DF95FEF\">3.3-39 DistanceDigraph</a></span\
>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hr\
ef=\"chap3_mj.html#X86F9CCEA839ABC48\">3.3-40 DigraphClosure</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p3_mj.html#X7B5AC5FE859F4D80\">3.3-41 DigraphMycielskian</a></span>\n</div></d\
iv>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nb\
sp;</span><a href=\"chap3_mj.html#X85B5D9B97F5187B7\">3.4 <span class=\"Headin\
g\">Random digraphs</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_\
mj.html#X86CF9F66788B2A24\">3.4-1 RandomDigraph</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7\
8FE275E7E77D56F\">3.4-2 RandomMultiDigraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7D36B5\
E57F055051\">3.4-3 RandomTournament</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X7A023E4787682\
475\">3.4-4 RandomLattice</a></span>\n</div></div>\n<div class=\"ContSect\"><s\
pan class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap3_mj.ht\
ml#X7C76D1DC7DAF03D3\">3.5 <span class=\"Heading\">Standard examples</span></a\
>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X870594FC866AC88E\">3\
.5-1 ChainDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X812417E278198D9C\">3.5-2 Comple\
teDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap3_mj.html#X8795B0AD856014FA\">3.5-3 CompleteBipart\
iteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap3_mj.html#X873F29CC863241F8\">3.5-4 CompleteMulti\
partiteDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">\
&nbsp;&nbsp;</span><a href=\"chap3_mj.html#X80C29DDE876FFBEB\">3.5-5 CycleDigr\
aph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap3_mj.html#X80DAE31A79FEFD40\">3.5-6 EmptyDigraph</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap3_mj.html#X80ED9CE785819607\">3.5-7 JohnsonDigraph</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap3_mj.html#X823F43217A6C375D\">3.5-8 PetersenGraph</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap3_mj.htm\
l#X7B5441F386BD105E\">3.5-9 GeneralisedPetersenGraph</a></span>\n</div></div>\
\n</div>\n<div class=\"ContChap\"><a href=\"chap4_mj.html#X7AD6F77E7D95C996\">\
4 <span class=\"Heading\">Operators</span></a>\n<div class=\"ContSect\"><span \
class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap4_mj.html#X\
84E0B5B88358C96B\">4.1 <span class=\"Heading\">Operators for digraphs</span></\
a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X829B911D7EFD2D85\">\
4.1-1 IsSubdigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap4_mj.html#X833C3299787E2309\">4.1-2 IsUnd\
irectedSpanningTree</a></span>\n</div></div>\n</div>\n<div class=\"ContChap\">\
<a href=\"chap5_mj.html#X8739F6CD78C90B14\">5 <span class=\"Heading\">Attribut\
es and operations</span></a>\n<div class=\"ContSect\"><span class=\"tocline\">\
<span class=\"nocss\">&nbsp;</span><a href=\"chap5_mj.html#X7E814B6478F7D015\"\
>5.1 <span class=\"Heading\">Vertices and edges</span></a>\n</span>\n<div clas\
s=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap5_mj.html#X7C45F7D878D896AC\">5.1-1 DigraphVertices<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap5_mj.html#X7C6F19B57CB2E882\">5.1-2 DigraphNrVertices</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap5_mj.html#X7D1C6A4D7ECEC317\">5.1-3 DigraphEdges</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p5_mj.html#X85E1CFDD7E164AD0\">5.1-4 DigraphNrEdges</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.htm\
l#X7BDABAF07917462B\">5.1-5 DigraphNrLoops</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X85D5E0\
8280914EE4\">5.1-6 DigraphSinks</a></span>\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7F5C6268839BE98C\
\">5.1-7 DigraphSources</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X785C30378064CF47\">5.1-8\
 DigraphTopologicalSort</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7CA91E4B7904F793\">5.1-9\
 DigraphVertexLabel</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7E51F2FE87140B32\">5.1-10 Dig\
raphVertexLabels</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X79FAEACC7F438C2F\">5.1-11 Digra\
phEdgeLabel</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap5_mj.html#X7C24851087D4A8FB\">5.1-12 DigraphEdge\
Labels</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap5_mj.html#X7EFAF01B7A155157\">5.1-13 DigraphInEdges</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap5_mj.html#X7BECFE6687ECD028\">5.1-14 DigraphOutEdges</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap5_mj.html#X7BB8ED88835F07B4\">5.1-15 IsDigraphEdge</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p5_mj.html#X848FED0B7B4ACD1F\">5.1-16 IsMatching</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X\
7B7A67277B1C9A02\">5.1-17 DigraphMaximalMatching</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X\
78E9847A858788D1\">5.1-18 DigraphMaximumMatching</a></span>\n</div></div>\n<di\
v class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</spa\
n><a href=\"chap5_mj.html#X7D7CE8328187D0DF\">5.2 <span class=\"Heading\">Neig\
hbours and degree</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj\
.html#X7DC2CD70830BEE60\">5.2-1 AdjacencyMatrix</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8\
7FA0A727CDB060B\">5.2-2 CharacteristicPolynomial</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X\
8507DC4F794780C1\">5.2-3 BooleanAdjacencyMatrix</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7\
AFCE34A7A04D5C1\">5.2-4 DigraphAdjacencyFunction</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X\
7FDEBF3279759961\">5.2-5 DigraphRange</a></span>\n<span class=\"ContSS\"><br /\
><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7E9880767AE\
68E00\">5.2-6 OutNeighbours</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X85C7AA5A81DA6E11\">5.\
2-7 InNeighbours</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7F5ACE807D1BC2E2\">5.2-8 OutDeg\
rees</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap5_mj.html#X7ADDFBFD7A365775\">5.2-9 InDegrees</a></span\
>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hr\
ef=\"chap5_mj.html#X7A09EB648070276D\">5.2-10 OutDegreeOfVertex</a></span>\n<s\
pan class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"\
chap5_mj.html#X83315B0186850806\">5.2-11 OutNeighboursOfVertex</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap5_mj.html#X7C9CD0527CB9E6EF\">5.2-12 InDegreeOfVertex</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_m\
j.html#X7C0DA18B8291F302\">5.2-13 InNeighboursOfVertex</a></span>\n<span class\
=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.\
html#X83271F607BD809CF\">5.2-14 DigraphLoops</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7DD\
B33B686B3A2C6\">5.2-15 PartialOrderDigraphMeetOfVertices</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_m\
j.html#X7BEAE1C78267F54D\">5.2-16 DegreeMatrix</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X86\
5390B08331936B\">5.2-17 LaplacianMatrix</a></span>\n</div></div>\n<div class=\
\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hre\
f=\"chap5_mj.html#X8537F4088400DC48\">5.3 <span class=\"Heading\">Reachability\
 and connectivity</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj\
.html#X7F16B9EB8398459C\">5.3-1 DigraphDiameter</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8\
104A9D37BCD8A05\">5.3-2 DigraphShortestDistance</a></span>\n<span class=\"Cont\
SS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8\
1F99BC67E9D050F\">5.3-3 DigraphShortestDistances</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X\
8223718079D98A82\">5.3-4 DigraphLongestDistanceFromVertex</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_\
mj.html#X7CB7DDCD84621D38\">5.3-5 DigraphDistanceSet</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.h\
tml#X79A3DA4078CF3C90\">5.3-6 DigraphGirth</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8374B7\
357EC189C1\">5.3-7 DigraphOddGirth</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X84688B337BDDBB\
09\">5.3-8 DigraphUndirectedGirth</a></span>\n<span class=\"ContSS\"><br /><sp\
an class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X842FAD6A7B83597\
7\">5.3-9 DigraphConnectedComponents</a></span>\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X8484EC557810\
CD31\">5.3-10 DigraphConnectedComponent</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X833ECD6B7\
A84944C\">5.3-11 DigraphStronglyConnectedComponents</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.htm\
l#X7EFCB5017D662254\">5.3-12 DigraphStronglyConnectedComponent</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap5_mj.html#X7F1B5A2782F598B1\">5.3-13 DigraphBicomponents</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
5_mj.html#X7DDE06E47E605DD7\">5.3-14 ArticulationPoints</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj\
.html#X84D5A125848BD800\">5.3-15 Bridges</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X86559014\
7BD1C507\">5.3-16 StrongOrientation</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X853D0B0981A33\
433\">5.3-17 DigraphPeriod</a></span>\n<span class=\"ContSS\"><br /><span clas\
s=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X864A31A8809F61C2\">5.3\
-18 DigraphFloydWarshall</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7FBAB09E7C0BE5CF\">5.3-1\
9 IsReachable</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7CAE81D97B43DDF3\">5.3-20 VerticesR\
eachableFrom</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap5_mj.html#X8039170B82A32257\">5.3-21 DigraphPat\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap5_mj.html#X80E9D645843973A6\">5.3-22 DigraphShortestPath</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap5_mj.html#X7C0416FE7A69CA2C\">5.3-23 IteratorOfPaths</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap5_mj.html#X7ECD16838704FAAA\">5.3-24 DigraphAllSimpleCircuits</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap5_mj.html#X7C735C4E86BDD5F6\">5.3-25 DigraphLongestSimpleCircuit</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap5_mj.html#X870E04307C5F213F\">5.3-26 DigraphLayers</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap5_mj.html#X7B2E42327DA118E0\">5.3-27 DigraphDegeneracy</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap5_mj.html#X827C2BD17A4547E3\">5.3-28 DigraphDegeneracyOrdering</a></span>\n\
<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\
\"chap5_mj.html#X863FDFC4839A3B82\">5.3-29 HamiltonianPath</a></span>\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5\
_mj.html#X82F30D5681466BC6\">5.3-30 NrSpanningTrees</a></span>\n<span class=\"\
ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.htm\
l#X79352A8286D1D8F6\">5.3-31 DigraphDijkstra</a></span>\n</div></div>\n<div cl\
ass=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a\
 href=\"chap5_mj.html#X82F900777D677F55\">5.4 <span class=\"Heading\">Cayley g\
raphs of groups</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.h\
tml#X7A000B1D7CCF7093\">5.4-1 GroupOfCayleyDigraph</a></span>\n<span class=\"C\
ontSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html\
#X8528455987D7D2BF\">5.4-2 GeneratorsOfCayleyDigraph</a></span>\n</div></div>\
\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;\
</span><a href=\"chap5_mj.html#X790FD6647ECCAE3C\">5.5 <span class=\"Heading\"\
>Associated semigroups</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p5_mj.html#X87D5C60D7B0C1309\">5.5-1 AsSemigroup</a></span>\n<span class=\"Con\
tSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X\
7C6D5EC27C51066B\">5.5-2 AsSemigroup</a></span>\n</div></div>\n<div class=\"Co\
ntSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"\
chap5_mj.html#X7E2305528492DDC0\">5.6 <span class=\"Heading\">Planarity</span>\
</a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span\
 class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X7DC478637E8C190D\
\">5.6-1 KuratowskiPlanarSubdigraph</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X78E8F09A82865\
01B\">5.6-2 KuratowskiOuterPlanarSubdigraph</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X84E39\
47E7D39BA64\">5.6-3 PlanarEmbedding</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X85DFB8C180887\
11F\">5.6-4 OuterPlanarEmbedding</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap5_mj.html#X806D2D6B85E0B269\
\">5.6-5 SubdigraphHomeomorphicToK23</a></span>\n</div></div>\n</div>\n<div cl\
ass=\"ContChap\"><a href=\"chap6_mj.html#X7ADDEFD478D470D5\">6 <span class=\"H\
eading\">Properties of digraphs</span></a>\n<div class=\"ContSect\"><span clas\
s=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap6_mj.html#X7F49\
388F8245F0E9\">6.1 <span class=\"Heading\">Edge properties</span></a>\n</span>\
\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7D92935C7D535187\">6.1-1 Digra\
phHasLoops</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap6_mj.html#X7DB1BC2286FC08E2\">6.1-2 IsAntiSymmetr\
icDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp\
;&nbsp;</span><a href=\"chap6_mj.html#X860CFB0C8665F356\">6.1-3 IsBipartiteDig\
raph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbs\
p;</span><a href=\"chap6_mj.html#X790A4DBF8533516E\">6.1-4 IsCompleteBipartite\
Digraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap6_mj.html#X81F28D4D879FE3B2\">6.1-5 IsCompleteDigrap\
h</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap6_mj.html#X7FD1A15779FEC341\">6.1-6 IsCompleteMultipartite\
Digraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap6_mj.html#X7E894CCF7B1C27AE\">6.1-7 IsEmptyDigraph</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap6_mj.html#X83762C257DED2751\">6.1-8 IsEquivalenceDigraph</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap6_mj.html#X7E8F37E585DAED52\">6.1-9 IsFunctionalDigraph</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap6_mj.html#X7BB84CFC7E8B2B26\">6.1-10 IsMultiDigraph</a></span>\n<spa\
n class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"ch\
ap6_mj.html#X8462D8E2792B23F6\">6.1-11 IsReflexiveDigraph</a></span>\n<span cl\
ass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_\
mj.html#X81B3EA7887219860\">6.1-12 IsSymmetricDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.h\
tml#X7DD8D1A185EBE865\">6.1-13 IsTournament</a></span>\n<span class=\"ContSS\"\
><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7F083\
5667F29F0C0\">6.1-14 IsTransitiveDigraph</a></span>\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X8617726C\
7829F796\">6.1-15 IsPreorderDigraph</a></span>\n<span class=\"ContSS\"><br /><\
span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X82BAE6D37D49A\
145\">6.1-16 IsPartialOrderDigraph</a></span>\n<span class=\"ContSS\"><br /><s\
pan class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X78D3E17B7F7375\
16\">6.1-17 IsMeetSemilatticeDigraph</a></span>\n</div></div>\n<div class=\"Co\
ntSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"\
chap6_mj.html#X7AAF896982EC22FA\">6.2 <span class=\"Heading\">Regularity</span\
></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7A3F78B37E31D9E1\
\">6.2-1 IsInRegularDigraph</a></span>\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7F0A806E7BCB413C\">6.\
2-2 IsOutRegularDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7AF9DB1E7DB12306\">6.2-3\
 IsRegularDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7E2082AC7CAE59CD\">6.2-4 IsDist\
anceRegularDigraph</a></span>\n</div></div>\n<div class=\"ContSect\"><span cla\
ss=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap6_mj.html#X780\
DAEB37C5E07FD\">6.3 <span class=\"Heading\">Connectivity and cycles</span></a>\
\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span cla\
ss=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7BD08D4478218F77\">6.\
3-1 IsAcyclicDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"no\
css\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X79563B297C220FB5\">6.3-2 IsC\
hainDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nb\
sp;&nbsp;</span><a href=\"chap6_mj.html#X83C08C0B7EC1A91F\">6.3-3 IsConnectedD\
igraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&n\
bsp;</span><a href=\"chap6_mj.html#X838FAF2D825977BE\">6.3-4 IsBiconnectedDigr\
aph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap6_mj.html#X7D2A6572820B7F24\">6.3-5 IsBridgelessDigraph<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap6_mj.html#X7B37B9467C68C208\">6.3-6 IsStronglyConnectedDigra\
ph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;\
</span><a href=\"chap6_mj.html#X80E883967EBE839E\">6.3-7 IsAperiodicDigraph</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap6_mj.html#X7B46EA6C7B2DF2FB\">6.3-8 IsDirectedTree</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap6_mj.html#X80FC20FA7AC4BC2A\">6.3-9 IsUndirectedTree</a></span>\n<span\
 class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"cha\
p6_mj.html#X79DFBB198525544E\">6.3-10 IsEulerianDigraph</a></span>\n<span clas\
s=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj\
.html#X79EFEBC37C2D262D\">6.3-11 IsHamiltonianDigraph</a></span>\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.h\
tml#X7E91320B8028F5D8\">6.3-12 IsCycleDigraph</a></span>\n</div></div>\n<div c\
lass=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><\
a href=\"chap6_mj.html#X7E2305528492DDC0\">6.4 <span class=\"Heading\">Planari\
ty</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><b\
r /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X8606D415\
858C40AA\">6.4-1 IsPlanarDigraph</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X8251E8B187E7F059\
\">6.4-2 IsOuterPlanarDigraph</a></span>\n</div></div>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap6_\
mj.html#X83DC8AD283C41326\">6.5 <span class=\"Heading\">Homomorphisms and tran\
sformations</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\"Co\
ntSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#\
X78C0B2637985648B\">6.5-1 IsDigraphCore</a></span>\n<span class=\"ContSS\"><br\
 /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X8361CA6E8\
401FF26\">6.5-2 IsEdgeTransitive</a></span>\n<span class=\"ContSS\"><br /><spa\
n class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap6_mj.html#X7B26E4447A1611E9\
\">6.5-3 IsVertexTransitive</a></span>\n</div></div>\n</div>\n<div class=\"Con\
tChap\"><a href=\"chap7_mj.html#X84975388859F203D\">7 <span class=\"Heading\">\
Homomorphisms</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><spa\
n class=\"nocss\">&nbsp;</span><a href=\"chap7_mj.html#X8200192B80AD2071\">7.1\
 <span class=\"Heading\">Acting on digraphs</span></a>\n</span>\n<div class=\"\
ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp\
;</span><a href=\"chap7_mj.html#X808972017C486F1F\">7.1-1 OnDigraphs</a></span\
>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hr\
ef=\"chap7_mj.html#X7AFBA7608498F9CE\">7.1-2 OnMultiDigraphs</a></span>\n</div\
></div>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\"\
>&nbsp;</span><a href=\"chap7_mj.html#X7E48B9F87A0F22D4\">7.2 <span class=\"He\
ading\">Isomorphisms and canonical labellings</span></a>\n</span>\n<div class=\
\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap7_mj.html#X83E593F3855B122E\">7.2-1 DigraphsUseNauty</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap7_mj.html#X858C32127A190175\">7.2-2 AutomorphismGroup</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap7_mj.html#X7E7B0D88865A89F6\">7.2-3 BlissAutomorphismGroup</a></spa\
n>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a h\
ref=\"chap7_mj.html#X857758B18144C0CD\">7.2-4 NautyAutomorphismGroup</a></span\
>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hr\
ef=\"chap7_mj.html#X877732B1783C391B\">7.2-5 AutomorphismGroup</a></span>\n<sp\
an class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"c\
hap7_mj.html#X7DA2C4FE837FFE01\">7.2-6 AutomorphismGroup</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_m\
j.html#X7D676FE67A6684FF\">7.2-7 BlissCanonicalLabelling</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_m\
j.html#X87DA265D803DB337\">7.2-8 BlissCanonicalLabelling</a></span>\n<span cla\
ss=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_m\
j.html#X877B1D377EC197D7\">7.2-9 BlissCanonicalDigraph</a></span>\n<span class\
=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.\
html#X803ACEDA7BBAC5B3\">7.2-10 DigraphGroup</a></span>\n<span class=\"ContSS\
\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X809\
6C5287E459279\">7.2-11 DigraphOrbits</a></span>\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8386028782F2\
D3FF\">7.2-12 DigraphOrbitReps</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8657604E87A25E5F\"\
>7.2-13 DigraphSchreierVector</a></span>\n<span class=\"ContSS\"><br /><span c\
lass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X78913684795FB256\">\
7.2-14 DigraphStabilizer</a></span>\n<span class=\"ContSS\"><br /><span class=\
\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7B4F24B283C9EE28\">7.2-1\
5 IsIsomorphicDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7D4A1FA8868DA930\">7.2-16 I\
sIsomorphicDigraph</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8219FE6C839D9457\">7.2-17 Isom\
orphismDigraphs</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7ED93C0F86D9D34F\">7.2-18 Isomorp\
hismDigraphs</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&n\
bsp;&nbsp;</span><a href=\"chap7_mj.html#X7E1C806D81DFE15E\">7.2-19 Representa\
tiveOutNeighbours</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X80183D4A7C51365A\">7.2-20 IsDig\
raphIsomorphism</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7F16B8B3825A627A\">7.2-21 IsDigra\
phColouring</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"to\
cline\"><span class=\"nocss\">&nbsp;</span><a href=\"chap7_mj.html#X7E1A02FE83\
84C03C\">7.3 <span class=\"Heading\">Homomorphisms of digraphs</span></a>\n</s\
pan>\n<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"\
nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X79ABF0E783FD67C7\">7.3-1 H\
omomorphismDigraphsFinder</a></span>\n<span class=\"ContSS\"><br /><span class\
=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X85E9B019877AD7FE\">7.3-\
2 DigraphHomomorphism</a></span>\n<span class=\"ContSS\"><br /><span class=\"n\
ocss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X8653EDA183E06D05\">7.3-3 Ho\
momorphismsDigraphs</a></span>\n<span class=\"ContSS\"><br /><span class=\"noc\
ss\">&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X82D0FCD87D47ACA8\">7.3-4 Digr\
aphMonomorphism</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\"\
>&nbsp;&nbsp;</span><a href=\"chap7_mj.html#X84B4BDB984C2A9A8\">7.3-5 Monomorp\
hismsDigraphs</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&\
nbsp;&nbsp;</span><a href=\"chap7_mj.html#X7CB5AD9F861684FD\">7.3-6 DigraphEpi\
morphism</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap7_mj.html#X7DFB1F5D873937B3\">7.3-7 EpimorphismsDig\
raphs</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nb\
sp;</span><a href=\"chap7_mj.html#X7AD04CC186E86CCA\">7.3-8 DigraphEmbedding</\
a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap7_mj.html#X82EBDF137EEDC5FD\">7.3-9 EmbeddingsDigraphs</a></s\
pan>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a\
 href=\"chap7_mj.html#X80FE9FCB79718A61\">7.3-10 IsDigraphHomomorphism</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap7_mj.html#X7D6B5A0887903810\">7.3-11 IsDigraphEmbedding</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap7_mj.html#X7F80709A80CBFA98\">7.3-12 DigraphsRespectsColouring</a></sp\
an>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a \
href=\"chap7_mj.html#X7E93B268823F6478\">7.3-13 GeneratorsOfEndomorphismMonoid\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chap7_mj.html#X86D0A74B83D6B9A7\">7.3-14 DigraphColouring</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap7_mj.html#X7AB7200D831013C1\">7.3-15 DigraphGreedyColouring</a></\
span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><\
a href=\"chap7_mj.html#X7F9CB3B27B9590DB\">7.3-16 DigraphWelshPowellOrder</a><\
/span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span>\
<a href=\"chap7_mj.html#X807D49358529A37C\">7.3-17 ChromaticNumber</a></span>\
\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a hre\
f=\"chap7_mj.html#X863487EF7D64EF56\">7.3-18 DigraphCore</a></span>\n</div></d\
iv>\n</div>\n<div class=\"ContChap\"><a href=\"chap8_mj.html#X7A7E0B957932DF44\
\">8 <span class=\"Heading\">Finding cliques and independent sets</span></a>\n\
<div class=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</\
span><a href=\"chap8_mj.html#X788474E38446039B\">8.1 <span class=\"Heading\">F\
inding cliques</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span class=\
\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.h\
tml#X80670E3E7C36183F\">8.1-1 IsClique</a></span>\n<span class=\"ContSS\"><br \
/><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X7A3BC9FF81\
69ABCD\">8.1-2 CliquesFinder</a></span>\n<span class=\"ContSS\"><br /><span cl\
ass=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X789854AC7B466402\">8\
.1-3 DigraphClique</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X84EA2F9482B8D4AF\">8.1-4 Digra\
phMaximalCliques</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X78427A8B81FEB457\">8.1-5 Clique\
Number</a></span>\n</div></div>\n<div class=\"ContSect\"><span class=\"tocline\
\"><span class=\"nocss\">&nbsp;</span><a href=\"chap8_mj.html#X7E3125328770834\
8\">8.2 <span class=\"Heading\">Finding independent sets</span></a>\n</span>\n\
<div class=\"ContSSBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap8_mj.html#X790733B67B0BC894\">8.2-1 IsInde\
pendentSet</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbs\
p;&nbsp;</span><a href=\"chap8_mj.html#X84350678782BFAB7\">8.2-2 DigraphIndepe\
ndentSet</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;\
&nbsp;</span><a href=\"chap8_mj.html#X7D2C78EB81A798A9\">8.2-3 DigraphMaximalI\
ndependentSets</a></span>\n</div></div>\n</div>\n<div class=\"ContChap\"><a hr\
ef=\"chap9_mj.html#X81714DBC80CC4BCB\">9 <span class=\"Heading\">Visualising a\
nd IO</span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span class=\
\"nocss\">&nbsp;</span><a href=\"chap9_mj.html#X7CF67F8278D9469C\">9.1 <span c\
lass=\"Heading\">Visualising a digraph</span></a>\n</span>\n<div class=\"ContS\
SBlock\">\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</sp\
an><a href=\"chap9_mj.html#X83B3318784E78415\">9.1-1 Splash</a></span>\n<span \
class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap\
9_mj.html#X7F9B99C478EE093A\">9.1-2 DotDigraph</a></span>\n<span class=\"ContS\
S\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X78\
DA31D1869D2F94\">9.1-3 DotSymmetricDigraph</a></span>\n<span class=\"ContSS\">\
<br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X84120D\
447E2CAC23\">9.1-4 DotPartialOrderDigraph</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7F5653C\
8854FAEA6\">9.1-5 DotPreorderDigraph</a></span>\n<span class=\"ContSS\"><br />\
<span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X808D12CF81E2\
C19F\">9.1-6 DotHighlightedDigraph</a></span>\n</div></div>\n<div class=\"Cont\
Sect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"ch\
ap9_mj.html#X81C9B1DC791C0BBD\">9.2 <span class=\"Heading\">Reading and writin\
g digraphs to a file</span></a>\n</span>\n<div class=\"ContSSBlock\">\n<span c\
lass=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9\
_mj.html#X81FB5BE27903EC32\">9.2-1 String</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X873D6EB\
8836A3C61\">9.2-2 DigraphFromGraph6String</a></span>\n<span class=\"ContSS\"><\
br /><span class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X782A052\
979EA2376\">9.2-3 Graph6String</a></span>\n<span class=\"ContSS\"><br /><span \
class=\"nocss\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7845ACDA7D4D333D\"\
>9.2-4 DigraphFile</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocs\
s\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X7E8142007ED0CB9F\">9.2-5 ReadD\
igraphs</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap9_mj.html#X82A4F0767C9EFC87\">9.2-6 WriteDigraphs</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap9_mj.html#X86D531B287733561\">9.2-7 IteratorFromDigraphFile</a\
></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</spa\
n><a href=\"chap9_mj.html#X7AAA35867B5D8BF4\">9.2-8 DigraphPlainTextLineEncode\
r</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;<\
/span><a href=\"chap9_mj.html#X7808D99079295C22\">9.2-9 TournamentLineDecoder<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap9_mj.html#X7DF22D1687D096D6\">9.2-10 AdjacencyMatrixUpperTri\
angleLineDecoder</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\
\">&nbsp;&nbsp;</span><a href=\"chap9_mj.html#X875393338486D77D\">9.2-11 TCode\
Decoder</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&\
nbsp;</span><a href=\"chap9_mj.html#X8540FC21796A793F\">9.2-12 PlainTextString\
</a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</\
span><a href=\"chap9_mj.html#X81BD23697857B244\">9.2-13 WritePlainTextDigraph<\
/a></span>\n<span class=\"ContSS\"><br /><span class=\"nocss\">&nbsp;&nbsp;</s\
pan><a href=\"chap9_mj.html#X804FDF6A7ED64049\">9.2-14 WriteDIMACSDigraph</a><\
/span>\n</div></div>\n</div>\n<div class=\"ContChap\"><a href=\"chapA_mj.html#\
X800DAF137BA8E25B\">A <span class=\"Heading\">\n    Grape to Digraphs Command \
Map\n  </span></a>\n<div class=\"ContSect\"><span class=\"tocline\"><span clas\
s=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7CC8A9DB86F9F0F4\">A.1 <span\
 class=\"Heading\">\n      Functions to construct and modify graphs\n    </spa\
n></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"tocline\"><span\
 class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X7C38A6397D2770FB\">A.2 \
<span class=\"Heading\">\n      Functions to inspect graphs, vertices and edge\
s\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\"><span class=\"toc\
line\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_mj.html#X78A5A34783C\
70CD7\">A.3 <span class=\"Heading\">\n      Functions to determine regularity \
properties of graphs\n    </span></a>\n</span>\n</div>\n<div class=\"ContSect\
\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"chapA_\
mj.html#X7C74978D85F7AF5C\">A.4 <span class=\"Heading\">\n      Some special v\
ertex subsets of a graph\n    </span></a>\n</span>\n</div>\n<div class=\"ContS\
ect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a href=\"cha\
pA_mj.html#X7E51B92F7E89E266\">A.5 <span class=\"Heading\">\n      Functions t\
o construct new graphs from old\n    </span></a>\n</span>\n</div>\n<div class=\
\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a hre\
f=\"chapA_mj.html#X7A61E3FC7A2BB50E\">A.6 <span class=\"Heading\">\n      Vert\
ex-Colouring and Complete Subgraphs\n    </span></a>\n</span>\n</div>\n<div cl\
ass=\"ContSect\"><span class=\"tocline\"><span class=\"nocss\">&nbsp;</span><a\
 href=\"chapA_mj.html#X7DFC61EC7CBDBC7E\">A.7 <span class=\"Heading\">\n      \
Automorphism groups and isomorphism testing for graphs\n    </span></a>\n</spa\
n>\n</div>\n</div>\n<div class=\"ContChap\"><a href=\"chapBib_mj.html\"><span \
class=\"Heading\">References</span></a></div>\n<div class=\"ContChap\"><a href\
=\"chapInd_mj.html\"><span class=\"Heading\">Index</span></a></div>\n" )
gap> gap> ─────────────────────────────────────────────────────────────────────────────
Loading  datastructures 0.2.5 (datastructures - GAP Data Structures)
by Markus Pfeiffer (http://www.morphism.de/~markusp),
   Max Horn (https://www.quendi.de/math),
   Christopher Jefferson (http://caj.host.cs.st-andrews.ac.uk/), and
   Steve Linton (http://sl4.host.cs.st-andrews.ac.uk/).
Homepage: https://gap-packages.github.io/datastructures
Report issues at https://github.com/gap-packages/datastructures/issues
─────────────────────────────────────────────────────────────────────────────
─────────────────────────────────────────────────────────────────────────────
Loading  NautyTracesInterface 0.2 (An interface to nauty)
by Sebastian Gutsche (https://sebasguts.github.io),
   Alice Niemeyer (http://www.maths.uwa.edu.au/~alice/), and
   Pascal Schweitzer (https://lii.rwth-aachen.de/~schweitzer).
Homepage: http://TODO/
─────────────────────────────────────────────────────────────────────────────
─────────────────────────────────────────────────────────────────────────────
Loading  orb 4.8.3 (Methods to enumerate orbits)
by Juergen Mueller (http://www.math.rwth-aachen.de/~Juergen.Mueller),
   Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef), and
   Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske).
maintained by:
   Juergen Mueller (http://www.math.rwth-aachen.de/~Juergen.Mueller),
   Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske), and
   Max Horn (https://www.quendi.de/math).
Homepage: https://gap-packages.github.io/orb
Report issues at https://github.com/gap-packages/orb/issues
─────────────────────────────────────────────────────────────────────────────
─────────────────────────────────────────────────────────────────────────────
Loading  GRAPE 4.8.3 (GRaph Algorithms using PErmutation groups)
by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~lsoicher/).
Homepage: https://gap-packages.github.io/grape
Report issues at https://github.com/gap-packages/grape/issues
─────────────────────────────────────────────────────────────────────────────
─────────────────────────────────────────────────────────────────────────────
Loading  Digraphs 1.4.0 (Digraphs - Methods for digraphs)
by Jan De Beule (http://homepages.vub.ac.be/~jdbeule/),
   Julius Jonusas (http://julius.jonusas.work),
   James Mitchell (https://jdbm.me),
   Michael Torpey (https://mtorpey.github.io),
   Maria Tsalakou (https://mariatsalakou.github.io/), and
   Wilf A. Wilson (https://wilf.me).
with contributions by:
   Stuart Burrell (sb235@st-andrews.ac.uk),
   Reinis Cirpons (rc234@st-andrews.ac.uk),
   Luke Elliott (le27@st-andrews.ac.uk),
   Max Horn (https://www.quendi.de/math),
   Christopher Jefferson (http://caj.host.cs.st-andrews.ac.uk),
   Markus Pfeiffer (https://www.morphism.de/~markusp),
   Christopher Russell (cr66@st-andrews.ac.uk),
   Finn Smith (fls3@st-andrews.ac.uk), and
   Murray Whyte (mw231@st-andrews.ac.uk).
maintained by:
   James Mitchell (https://jdbm.me) and
   Wilf A. Wilson (https://wilf.me).
Homepage: https://digraphs.github.io/Digraphs
Report issues at https://github.com/digraphs/Digraphs/issues
─────────────────────────────────────────────────────────────────────────────
#I  File: /builddir/build/BUILD/digraphs-1.4.0/../pkg/digraphs-1.4.0/doc/manual.lab written.
gap> gap> Executing(%install): /bin/sh -e /var/tmp/rpm-tmp.Jcbf90
explicitly decompress any DWARF compressed ELF sections in /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/lib/gap/pkg/digraphs-1.4.0/bin/x86_64-redhat-linux-gnu-default64-kv7/digraphs.so
extracting debug info from /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/lib/gap/pkg/digraphs-1.4.0/bin/x86_64-redhat-linux-gnu-default64-kv7/digraphs.so
+ rm -fr ../pkg
+ RPM_EC=0
++ jobs -p
+ exit 0
+ umask 022
+ cd /builddir/build/BUILD
+ '[' /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64 '!=' / ']'
+ rm -rf /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64
++ dirname /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64
+ mkdir -p /builddir/build/BUILDROOT
+ mkdir /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64
+ cd digraphs-1.4.0
+ mkdir -p /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/lib/gap/pkg/digraphs-1.4.0/doc
+ cp -a bin data gap tst VERSIONS PackageInfo.g init.g makedoc.g read.g /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/lib/gap/pkg/digraphs-1.4.0
+ cp -p doc/digraphs.bib doc/lefttoc.css doc/manual.css doc/nocolorprompt.css doc/ragged.css doc/times.css doc/toggless.css doc/chap0.html doc/chap0_mj.html doc/chap1.html doc/chap1_mj.html doc/chap2.html doc/chap2_mj.html doc/chap3.html doc/chap3_mj.html doc/chap4.html doc/chap4_mj.html doc/chap5.html doc/chap5_mj.html doc/chap6.html doc/chap6_mj.html doc/chap7.html doc/chap7_mj.html doc/chap8.html doc/chap8_mj.html doc/chap9.html doc/chap9_mj.html doc/chapA.html doc/chapA_mj.html doc/chapBib.html doc/chapBib_mj.html doc/chapInd.html doc/chapInd_mj.html doc/chooser.html doc/manual.js doc/rainbow.js doc/toggless.js doc/manual.lab doc/manual.pdf doc/manual.six doc/chap0.txt doc/chap1.txt doc/chap2.txt doc/chap3.txt doc/chap4.txt doc/chap5.txt doc/chap6.txt doc/chap7.txt doc/chap8.txt doc/chap9.txt doc/chapA.txt doc/chapBib.txt doc/chapInd.txt doc/attr.xml doc/cliques.xml doc/constructors.xml doc/digraph.xml doc/display.xml doc/examples.xml doc/grahom.xml doc/grape.xml doc/io.xml doc/isomorph.xml doc/labels.xml doc/main.xml doc/oper.xml doc/orbits.xml doc/planar.xml doc/prop.xml doc/utils.xml doc/z-appA.xml doc/z-chap0.xml doc/z-chap1.xml doc/z-chap2.xml doc/z-chap3.xml doc/z-chap4.xml doc/z-chap5.xml doc/z-chap6.xml doc/z-chap8.xml doc/z-chap9.xml doc/z-title.xml /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/lib/gap/pkg/digraphs-1.4.0/doc
+ /usr/lib/rpm/find-debuginfo.sh -j2 --strict-build-id -m -i --build-id-seed 1.4.0-1.fc34 --unique-debug-suffix -1.4.0-1.fc34.x86_64 --unique-debug-src-base gap-pkg-digraphs-1.4.0-1.fc34.x86_64 --run-dwz --dwz-low-mem-die-limit 10000000 --dwz-max-die-limit 110000000 -S debugsourcefiles.list /builddir/build/BUILD/digraphs-1.4.0
original debug info size: 2664kB, size after compression: 2516kB
/usr/lib/rpm/sepdebugcrcfix: Updated 1 CRC32s, 0 CRC32s did match.
1036 blocks
+ /usr/lib/rpm/check-buildroot
+ /usr/lib/rpm/redhat/brp-ldconfig
+ /usr/lib/rpm/brp-compress
+ /usr/lib/rpm/redhat/brp-strip-lto /usr/bin/strip
+ /usr/lib/rpm/brp-strip-static-archive /usr/bin/strip
+ /usr/lib/rpm/redhat/brp-python-bytecompile '' 1 0
+ /usr/lib/rpm/brp-python-hardlink
+ /usr/lib/rpm/redhat/brp-mangle-shebangs
*** WARNING: ./usr/src/debug/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/extern/bliss-0.73/graph.cc is executable but has no shebang, removing executable bit
Executing(%check): /bin/sh -e /var/tmp/rpm-tmp.8Usw7z
+ umask 022
+ cd /builddir/build/BUILD
+ cd digraphs-1.4.0
+ export LC_ALL=C.UTF-8
+ LC_ALL=C.UTF-8
+ cd tst
+ gap -l '/builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/lib/gap;/usr/lib/gap'
 ┌───────┐   GAP 4.11.0 of 29-Feb-2020
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: x86_64-redhat-linux-gnu-default64-kv7
 Configuration:  gmp 6.2.0, GASMAN, readline
 Loading the library and packages ...
#I  autpgrp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  alnuth package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  crisp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  ctbllib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  factint package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  fga package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  irredsol package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  laguna package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polenta package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polycyclic package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  resclasses package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  sophus package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  tomlib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
 Packages:   GAPDoc 1.6.4, IO 4.7.0, PrimGrp 3.4.1, SmallGrp 1.4.2, 
             TransGrp 3.0
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> ─────────────────────────────────────────────────────────────────────────────
Loading  datastructures 0.2.5 (datastructures - GAP Data Structures)
by Markus Pfeiffer (http://www.morphism.de/~markusp),
   Max Horn (https://www.quendi.de/math),
   Christopher Jefferson (http://caj.host.cs.st-andrews.ac.uk/), and
   Steve Linton (http://sl4.host.cs.st-andrews.ac.uk/).
Homepage: https://gap-packages.github.io/datastructures
Report issues at https://github.com/gap-packages/datastructures/issues
─────────────────────────────────────────────────────────────────────────────
─────────────────────────────────────────────────────────────────────────────
Loading  NautyTracesInterface 0.2 (An interface to nauty)
by Sebastian Gutsche (https://sebasguts.github.io),
   Alice Niemeyer (http://www.maths.uwa.edu.au/~alice/), and
   Pascal Schweitzer (https://lii.rwth-aachen.de/~schweitzer).
Homepage: http://TODO/
─────────────────────────────────────────────────────────────────────���───────
─────────────────────────────────────────────────────────────────────────────
Loading  orb 4.8.3 (Methods to enumerate orbits)
by Juergen Mueller (http://www.math.rwth-aachen.de/~Juergen.Mueller),
   Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef), and
   Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske).
maintained by:
   Juergen Mueller (http://www.math.rwth-aachen.de/~Juergen.Mueller),
   Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske), and
   Max Horn (https://www.quendi.de/math).
Homepage: https://gap-packages.github.io/orb
Report issues at https://github.com/gap-packages/orb/issues
────────────────────────────────────────────────────���────────────────────────
─────────────────────────────────────────────────────────────────────────────
Loading  GRAPE 4.8.3 (GRaph Algorithms using PErmutation groups)
by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~lsoicher/).
Homepage: https://gap-packages.github.io/grape
Report issues at https://github.com/gap-packages/grape/issues
───────────────────────────────────────────────────────────────────────────��─
─────────────────────────────────────────────────────────────────────────────
Loading  Digraphs 1.4.0 (Digraphs - Methods for digraphs)
by Jan De Beule (http://homepages.vub.ac.be/~jdbeule/),
   Julius Jonusas (http://julius.jonusas.work),
   James Mitchell (https://jdbm.me),
   Michael Torpey (https://mtorpey.github.io),
   Maria Tsalakou (https://mariatsalakou.github.io/), and
   Wilf A. Wilson (https://wilf.me).
with contributions by:
   Stuart Burrell (sb235@st-andrews.ac.uk),
   Reinis Cirpons (rc234@st-andrews.ac.uk),
   Luke Elliott (le27@st-andrews.ac.uk),
   Max Horn (https://www.quendi.de/math),
   Christopher Jefferson (http://caj.host.cs.st-andrews.ac.uk),
   Markus Pfeiffer (https://www.morphism.de/~markusp),
   Christopher Russell (cr66@st-andrews.ac.uk),
   Finn Smith (fls3@st-andrews.ac.uk), and
   Murray Whyte (mw231@st-andrews.ac.uk).
maintained by:
   James Mitchell (https://jdbm.me) and
   Wilf A. Wilson (https://wilf.me).
Homepage: https://digraphs.github.io/Digraphs
Report issues at https://github.com/digraphs/Digraphs/issues
─────────────────────────────────────────────────────────────────────────────
true
gap> Digraphs package: testinstall.tst
msecs: 293
true
gap> Digraphs package: standard/attr.tst
msecs: 2194
true
gap> Digraphs package: standard/cliques.tst
msecs: 522
true
gap> Digraphs package: standard/constructors.tst
msecs: 33
true
gap> Digraphs package: standard/display.tst
msecs: 17
true
gap> Digraphs package: standard/examples.tst
msecs: 11
true
gap> Digraphs package: standard/grahom.tst
msecs: 430
true
gap> Digraphs package: standard/grape.tst
msecs: 10
true
gap> Digraphs package: standard/io.tst
msecs: 2319
true
gap> Digraphs package: standard/isomorph.tst
msecs: 342
true
gap> Digraphs package: standard/labels.tst
msecs: 4
true
gap> Digraphs package: standard/oper.tst
msecs: 507
true
gap> Digraphs package: standard/orbits.tst
msecs: 2
true
gap> Digraphs package: standard/planar.tst
msecs: 31
true
gap> Digraphs package: standard/prop.tst
msecs: 2320
true
gap> gap> + gap -l '/builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/lib/gap;/usr/lib/gap'
 ┌───────┐   GAP 4.11.0 of 29-Feb-2020
 │  GAP  │   https://www.gap-system.org
 └───────┘   Architecture: x86_64-redhat-linux-gnu-default64-kv7
 Configuration:  gmp 6.2.0, GASMAN, readline
 Loading the library and packages ...
#I  autpgrp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  alnuth package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  crisp package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  ctbllib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  factint package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  fga package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  irredsol package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  laguna package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polenta package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  polycyclic package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  resclasses package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  sophus package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
#I  tomlib package is not available. Check that the name is correct
#I  and it is present in one of the GAP root directories (see '??RootPaths')
 Packages:   GAPDoc 1.6.4, IO 4.7.0, PrimGrp 3.4.1, SmallGrp 1.4.2, 
             TransGrp 3.0
 Try '??help' for help. See also '?copyright', '?cite' and '?authors'
gap> ─────────────────────────────────────────────────────────────────────────────
Loading  datastructures 0.2.5 (datastructures - GAP Data Structures)
by Markus Pfeiffer (http://www.morphism.de/~markusp),
   Max Horn (https://www.quendi.de/math),
   Christopher Jefferson (http://caj.host.cs.st-andrews.ac.uk/), and
   Steve Linton (http://sl4.host.cs.st-andrews.ac.uk/).
Homepage: https://gap-packages.github.io/datastructures
Report issues at https://github.com/gap-packages/datastructures/issues
─────────────────────────────────────────────────────────────────────────────
─────────────────────────────────────────────────────────────────────────────
Loading  NautyTracesInterface 0.2 (An interface to nauty)
by Sebastian Gutsche (https://sebasguts.github.io),
   Alice Niemeyer (http://www.maths.uwa.edu.au/~alice/), and
   Pascal Schweitzer (https://lii.rwth-aachen.de/~schweitzer).
Homepage: http://TODO/
───────────────────────────────────────────────────────��─────────────────────
─────────────────────────────────────────────────────────────────────────────
Loading  orb 4.8.3 (Methods to enumerate orbits)
by Juergen Mueller (http://www.math.rwth-aachen.de/~Juergen.Mueller),
   Max Neunhöffer (http://www-groups.mcs.st-and.ac.uk/~neunhoef), and
   Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske).
maintained by:
   Juergen Mueller (http://www.math.rwth-aachen.de/~Juergen.Mueller),
   Felix Noeske (http://www.math.rwth-aachen.de/~Felix.Noeske), and
   Max Horn (https://www.quendi.de/math).
Homepage: https://gap-packages.github.io/orb
Report issues at https://github.com/gap-packages/orb/issues
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Loading  GRAPE 4.8.3 (GRaph Algorithms using PErmutation groups)
by Leonard H. Soicher (http://www.maths.qmul.ac.uk/~lsoicher/).
Homepage: https://gap-packages.github.io/grape
Report issues at https://github.com/gap-packages/grape/issues
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Loading  Digraphs 1.4.0 (Digraphs - Methods for digraphs)
by Jan De Beule (http://homepages.vub.ac.be/~jdbeule/),
   Julius Jonusas (http://julius.jonusas.work),
   James Mitchell (https://jdbm.me),
   Michael Torpey (https://mtorpey.github.io),
   Maria Tsalakou (https://mariatsalakou.github.io/), and
   Wilf A. Wilson (https://wilf.me).
with contributions by:
   Stuart Burrell (sb235@st-andrews.ac.uk),
   Reinis Cirpons (rc234@st-andrews.ac.uk),
   Luke Elliott (le27@st-andrews.ac.uk),
   Max Horn (https://www.quendi.de/math),
   Christopher Jefferson (http://caj.host.cs.st-andrews.ac.uk),
   Markus Pfeiffer (https://www.morphism.de/~markusp),
   Christopher Russell (cr66@st-andrews.ac.uk),
   Finn Smith (fls3@st-andrews.ac.uk), and
   Murray Whyte (mw231@st-andrews.ac.uk).
maintained by:
   James Mitchell (https://jdbm.me) and
   Wilf A. Wilson (https://wilf.me).
Homepage: https://digraphs.github.io/Digraphs
Report issues at https://github.com/digraphs/Digraphs/issues
─────────────────────────────────────────────────────────────────────────────
true
gap> Digraphs package: standard/digraph.tst
msecs: 4359
gap> + find /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/lib/gap/pkg/digraphs-1.4.0 -size 0 -delete
+ RPM_EC=0
++ jobs -p
+ exit 0
Processing files: gap-pkg-digraphs-1.4.0-1.fc34.x86_64
Executing(%doc): /bin/sh -e /var/tmp/rpm-tmp.0gEaYY
+ umask 022
+ cd /builddir/build/BUILD
+ cd digraphs-1.4.0
+ DOCDIR=/builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/share/doc/gap-pkg-digraphs
+ export LC_ALL=C
+ LC_ALL=C
+ export DOCDIR
+ /usr/bin/mkdir -p /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/share/doc/gap-pkg-digraphs
+ cp -pr CHANGELOG.md /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/share/doc/gap-pkg-digraphs
+ cp -pr README.md /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/share/doc/gap-pkg-digraphs
+ RPM_EC=0
++ jobs -p
+ exit 0
Executing(%license): /bin/sh -e /var/tmp/rpm-tmp.h0ysFt
+ umask 022
+ cd /builddir/build/BUILD
+ cd digraphs-1.4.0
+ LICENSEDIR=/builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/share/licenses/gap-pkg-digraphs
+ export LC_ALL=C
+ LC_ALL=C
+ export LICENSEDIR
+ /usr/bin/mkdir -p /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/share/licenses/gap-pkg-digraphs
+ cp -pr GPL /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/share/licenses/gap-pkg-digraphs
+ cp -pr LICENSE /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64/usr/share/licenses/gap-pkg-digraphs
+ RPM_EC=0
++ jobs -p
+ exit 0
Provides: bundled(bliss) = 0.73 gap-pkg-digraphs = 1.4.0-1.fc34 gap-pkg-digraphs(x86-64) = 1.4.0-1.fc34
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Requires: libc.so.6()(64bit) libc.so.6(GLIBC_2.11)(64bit) libc.so.6(GLIBC_2.14)(64bit) libc.so.6(GLIBC_2.2.5)(64bit) libc.so.6(GLIBC_2.3.4)(64bit) libc.so.6(GLIBC_2.4)(64bit) libc.so.6(GLIBC_2.7)(64bit) libgcc_s.so.1()(64bit) libgcc_s.so.1(GCC_3.0)(64bit) libgcc_s.so.1(GCC_3.3.1)(64bit) libm.so.6()(64bit) libplanarity.so.0()(64bit) libpthread.so.0()(64bit) libstdc++.so.6()(64bit) libstdc++.so.6(CXXABI_1.3)(64bit) libstdc++.so.6(CXXABI_1.3.9)(64bit) libstdc++.so.6(GLIBCXX_3.4)(64bit) libstdc++.so.6(GLIBCXX_3.4.29)(64bit) rtld(GNU_HASH)
Recommends: gap-pkg-grape(x86-64) gap-pkg-nautytracesinterface(x86-64)
Processing files: gap-pkg-digraphs-doc-1.4.0-1.fc34.noarch
Provides: gap-pkg-digraphs-doc = 1.4.0-1.fc34
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Processing files: gap-pkg-digraphs-debugsource-1.4.0-1.fc34.x86_64
Provides: gap-pkg-digraphs-debugsource = 1.4.0-1.fc34 gap-pkg-digraphs-debugsource(x86-64) = 1.4.0-1.fc34
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Processing files: gap-pkg-digraphs-debuginfo-1.4.0-1.fc34.x86_64
Provides: debuginfo(build-id) = b49b939219840361f967d35c243057a9e5040aa3 gap-pkg-digraphs-debuginfo = 1.4.0-1.fc34 gap-pkg-digraphs-debuginfo(x86-64) = 1.4.0-1.fc34
Requires(rpmlib): rpmlib(CompressedFileNames) <= 3.0.4-1 rpmlib(FileDigests) <= 4.6.0-1 rpmlib(PayloadFilesHavePrefix) <= 4.0-1
Recommends: gap-pkg-digraphs-debugsource(x86-64) = 1.4.0-1.fc34
Checking for unpackaged file(s): /usr/lib/rpm/check-files /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64
Wrote: /builddir/build/RPMS/gap-pkg-digraphs-debuginfo-1.4.0-1.fc34.x86_64.rpm
Wrote: /builddir/build/RPMS/gap-pkg-digraphs-doc-1.4.0-1.fc34.noarch.rpm
Wrote: /builddir/build/RPMS/gap-pkg-digraphs-1.4.0-1.fc34.x86_64.rpm
Wrote: /builddir/build/RPMS/gap-pkg-digraphs-debugsource-1.4.0-1.fc34.x86_64.rpm
Executing(%clean): /bin/sh -e /var/tmp/rpm-tmp.bLY2b5
+ umask 022
+ cd /builddir/build/BUILD
+ cd digraphs-1.4.0
+ /usr/bin/rm -rf /builddir/build/BUILDROOT/gap-pkg-digraphs-1.4.0-1.fc34.x86_64
+ RPM_EC=0
++ jobs -p
+ exit 0
Child return code was: 0